TABLE OF CONTENTS 2539 SYMBOLS AND ABBREVIATIONS 2540 Greek Alphabet 2540 Scientific and Engineering 2542 Mathematical Signs and 2543 Letter Symbols for Mechanics MEASURING UNITS 2544 Metric Systems Of Measurement 2544 SI Unit System 2546 Prefixes for SI Units 2546 Binary Multiples 2546 SI Base Units 2548 Standard of Length 2548 U.S. Customary Unit System 2548 Fundamental Constants U.S. SYSTEM AND METRIC SYSTEM CONVERSIONS 2549 Units of Length 2549 Linear Conversion Factors 2550 Angular Conversion Factors 2550 Feet and Inches to Inches 2550 Inch to Feet and Yards 2551 Inch Fractions to Decimal Feet 2552 Feet to Inches 2552 Inch ↔ Millimeter 2553 Feet to Millimeter 2554 Fractional Inch to Millimeters 2556 Decimal Inch to Millimeters 2558 Millimeters to Inches 2560 Microinches to Micrometers 2561 Micrometers to Microinches 2562 Feet ↔ Meters 2562 Miles ↔ Kilometers 2563 Units of Area 2563 Conversion Factors 2564 Square Inch ↔ Square Centimeter 2564 Square Feet ↔ Square Meter 2565 Square Yard ↔ Square Meter 2565 Acre ↔ Hectare 2566 Units of Volume 2566 Conversion Factors 2567 Cubic Inch ↔ Cubic Centimeter 2568 Cubic Feet ↔ Cubic Meters 2568 Cubic Feet ↔ Liters 2569 U.K. Gallons ↔ Liters 2569 U.S. Gallons ↔ Liters 2570 U.S. Fluid Ounce ↔ Milliliters U.S. SYSTEM AND METRIC (Continued) SYSTEM CONVERSIONS 2570 Units of Volumetric Flow Rate 2570 Pitot Tube 2571 Units of Mass and Weight 2571 Conversion Factors 2571 Pound ↔ Kilogram 2572 Ounce ↔ Gram 2572 Density Conversion Factors 2573 Pound/Cu Inch ↔ Gram/Cu Cm 2573 Pound/Cu Inch ↔ Kg/Cu Meter 2574 Units of Pressure and Stress 2574 Conversion Factors 2574 Pound/Sq Inch ↔ Kg/Sq Cm 2575 Pound/Sq Foot ↔ Km/Sq Meter 2575 Pound/Sq Inch ↔ Kilopscal 2576 Conversion Factors Table 2576 Units of Force 2576 Conversion Factors 2577 Pound ↔ Newton 2577 Units of Moment and Torque 2577 Conversion Factors 2577 Pound-Inch ↔ Newton-Meter 2578 Poundal 2578 Units of Energy, Power, and Heat 2578 Conversion Factor Tables 2579 Btu ↔ Foot-pound 2579 Btu ↔ Kilojoule 2580 Horsepower ↔ Kilowatt 2580 Foot-pound ↔ Joule 2581 Power Conversion Factors 2581 Energy and Work Conversion 2582 Thermal Conductance Conversion 2582 Conduction 2582 Fuel Oil, Coal and Gas Equivalents 2583 Units of Temperature 2583 Thermometer Scales 2583 Conversion Formulas 2583 Absolute Temperature and Absolute Zero 2583 Thermal Energy Units 2584 Temperature Conversion Table 2586 Units of Velocity and Acceleration 2586 Velocity Conversion Factors 2586 Acceleration Conversion Factors 2586 Units of Viscosity 2587 Units of Inertia and Momentum 2587 Miscellaneous Measuring Units 2587 Ohm’s Law MEASURING UNITS Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY
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TABLE OF CONTENTS
2539
SYMBOLS AND ABBREVIATIONS
2540 Greek Alphabet2540 Scientific and Engineering2542 Mathematical Signs and2543 Letter Symbols for Mechanics
MEASURING UNITS
2544 Metric Systems Of Measurement2544 SI Unit System2546 Prefixes for SI Units2546 Binary Multiples2546 SI Base Units2548 Standard of Length2548 U.S. Customary Unit System2548 Fundamental Constants
U.S. SYSTEM AND METRIC SYSTEM CONVERSIONS
2549 Units of Length2549 Linear Conversion Factors2550 Angular Conversion Factors2550 Feet and Inches to Inches2550 Inch to Feet and Yards2551 Inch Fractions to Decimal Feet2552 Feet to Inches2552 Inch ↔ Millimeter2553 Feet to Millimeter2554 Fractional Inch to Millimeters2556 Decimal Inch to Millimeters2558 Millimeters to Inches 2560 Microinches to Micrometers2561 Micrometers to Microinches2562 Feet ↔ Meters2562 Miles ↔ Kilometers2563 Units of Area2563 Conversion Factors2564 Square Inch ↔ Square Centimeter2564 Square Feet ↔ Square Meter2565 Square Yard ↔ Square Meter2565 Acre ↔ Hectare2566 Units of Volume2566 Conversion Factors2567 Cubic Inch ↔ Cubic Centimeter2568 Cubic Feet ↔ Cubic Meters2568 Cubic Feet ↔ Liters2569 U.K. Gallons ↔ Liters2569 U.S. Gallons ↔ Liters2570 U.S. Fluid Ounce ↔ Milliliters
U.S. SYSTEM AND METRIC
(Continued)SYSTEM CONVERSIONS
2570 Units of Volumetric Flow Rate2570 Pitot Tube2571 Units of Mass and Weight2571 Conversion Factors2571 Pound ↔ Kilogram2572 Ounce ↔ Gram2572 Density Conversion Factors2573 Pound/Cu Inch ↔ Gram/Cu Cm2573 Pound/Cu Inch ↔ Kg/Cu Meter2574 Units of Pressure and Stress2574 Conversion Factors2574 Pound/Sq Inch ↔ Kg/Sq Cm2575 Pound/Sq Foot ↔ Km/Sq Meter2575 Pound/Sq Inch ↔ Kilopscal2576 Conversion Factors Table2576 Units of Force2576 Conversion Factors2577 Pound ↔ Newton2577 Units of Moment and Torque2577 Conversion Factors2577 Pound-Inch ↔ Newton-Meter2578 Poundal2578 Units of Energy, Power, and Heat2578 Conversion Factor Tables2579 Btu ↔ Foot-pound2579 Btu ↔ Kilojoule2580 Horsepower ↔ Kilowatt2580 Foot-pound ↔ Joule2581 Power Conversion Factors2581 Energy and Work Conversion2582 Thermal Conductance Conversion2582 Conduction2582 Fuel Oil, Coal and Gas
Equivalents2583 Units of Temperature2583 Thermometer Scales2583 Conversion Formulas2583 Absolute Temperature and
Absolute Zero2583 Thermal Energy Units2584 Temperature Conversion Table2586 Units of Velocity and Acceleration2586 Velocity Conversion Factors2586 Acceleration Conversion Factors2586 Units of Viscosity2587 Units of Inertia and Momentum2587 Miscellaneous Measuring Units2587 Ohm’s Law
MEASURING UNITS
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2540 MEASURING UNITS
SYMBOLS AND ABBREVIATIONS
Greek Letters and Standard Abbreviations
The Greek letters are frequently used in mathematical expressions and formulas. TheGreek alphabet is given below.
A α Alpha H η Eta N ν Nu T τ TauB β Beta Θ ϑ θ Theta Ξ ξ Xi ϒ υ UpsilonΓ γ Gamma I ι Iota O o Omicron Φ φ Phi∆ δ Delta K κ Kappa Π π Pi X χ ChiE ε Epsilon Λ λ Lambda R ρ Rho Ψ ψ PsiZ ζ Zeta M µ Mu Σ σ ς Sigma Ω ω Omega
ANSI Abbreviations for Scientific and Engineering Terms ANSI Y1.1-1972, (R 1984)
Absolute abs Decibel dBAlternating current ac Degree deg or°Ampere amp Degree Centigrade °CAmpere-hour amp hr Degree Fahrenheit °FAngstrom unit A Degree Kelvin KAntilogarithm antilog Diameter diaArithmetical average aa Direct current dcAtmosphere atm Dozen dozAtomic weight at wt Dram drAvoirdupois avdp Efficiency effBarometer baro Electric elecBoard feet (feet board measure) fbm Electromotive force emfBoiler pressure bopress Elevation elBoiling point bp Engine engBrinell hardness number Bhn Engineer engrBritish thermal unit Btu or B Engineering engrgBushel bu Equation eqCalorie cal External extCandle cd Fluid flCenter to center c to c Foot ftCentimeter cm Foot-candle fcCentimeter-gram-second (system) cgs Foot-Lambert fL or flChemical chem Foot per minute fpmChemically pure cp Foot per second fpsCircular circ Foot-pound ft lbCircular mil cmil Foot-pound-second (system) fpsCoefficient coef Free on board fobCologarithm colog Freezing point fpConcentrate conc Frequency freqConductivity cndct Fusion point fnptConstant const Gallon galCord cd Gallon per minute gpmCosecant csc Gallon per second gpsCosine cos Grain grCost, insurance, and freight cif Gram gCotangent ctn Greatest common divisor gcdCounter electromotive force cemf High pressure hpCubic cu Horsepower hpCubic centimeter cm3 or cc Horsepower-hour hp hrCubic foot ft3 or cu ft Hour h or hrCubic feet per second ft3 or cfs Hyperbolic cosine coshCubic inch in3 or cu in Hyperbolic sine sinhCubic meter m3 or cu m Hyperbolic tangent tanhCubic millimeter mm3 or cumm Inch inCubic yard yd3 or cu yd Inch per second in/s or ipsCurrent density cd Inch-pound in lbCylinder cyl
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
STANDARD ABBREVIATIONS 2541
Only the most commonly used terms have been included. These forms are recommended for thosewhose familiarity with the terms used makes possible a maximum of abbreviations. For others, lesscontracted combinations made up from this list may be used. For example, the list gives the abbrevi-ation of the term “feet per second” as “fps.” To some, however, ft per sec will be more easily under-stood.
Abbreviations should be used sparingly and only where their meaning will be clear. Ifthere is any doubt, then spell out the term or unit of measurement.
The following points are good practice when preparing engineering documentation.Terms denoting units of measurement should be abbreviated in text only when preceded bythe amounts indicated in numerals: “several inches,” “one inch,” “12 in.” A sentenceshould not begin with a numeral followed by an abbreviation. The use of conventionalsigns for abbreviations in text should be avoided: use “lb,” not “#” or “in,” not ″.
Symbols for the chemical elements are listed in the table on page 398.
Indicated horsepower-hour iph Pound-force foot lbf · ft or lb ftIntermediate pressure ip Pound-force inch lbf · in or lb inInternal intl pound-force per square foot lbf/ft2 or psfKilovolt-ampere/hour KVA-h or kVah pound-force per square inch lbf/in2 or psiKilowatt-hour meter kwhm pound per horsepower lb/hp or phpLatitude lat Power factor pfLeast common multiple lcm Quart qtLiquid liq Reactive volt-ampere meter rvaLogarithm (common) log Revolution per minute r/min or rpmLogarithm (natural) ln Revolution per second r/s or rpsLow pressure lp Root mean square rmsLumen per watt lm/W or lpw Round rndMagnetomotive force mmf Secant secMathematics (ical) math Second s or secMaximum max Sine sinMean effective pressure mep Specific gravity sp grMelting point mp Specific heat sp htMeter m Square sqMeter-kilogram-second mks Square centimeter cm2 or sq cmMicrofarad µF Square foot ft2 or sq ftMile mi Square inch in2 or sq inMile per hour mi/h or mph Square kilometer km2 or sq kmMilliampere m/A Square root of mean square rmsMinimum min Standard stdMolecular weight mol wt Tangent tanMolecule mo Temperature tempNational Electrical Code NEC Tensile strength tsOunce oz Versed sine versOunce-inch oz in Volt VPennyweight dwt Watt WPint pt Watthour WhPotential pot Week wkPotential difference pd Weight wtPound lb Yard yd
Alternative abbreviations conforming to the practice of the International Electrotechnical Commission.
Ampere A Kilovolt-ampere kVA Microfarad µF Milliampere mAAmpere-hour Ah Kilowatt kW Microwatt µW Volt VCoulomb C Milliampere mA Volt-ampere VAFarad F Kilowatthour kWh Millifarad mF Volt-coulomb VCHenry H Megawatt MW Millihenry mH Watt WJoule J Megohm Mω Millivolt mV Watthour WhKilovolt kV Microampere µA Ohm ω Volt VA
ANSI Abbreviations for Scientific and Engineering Terms (Continued) ANSI Y1.1-1972, (R 1984)
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2542 MATHEMATICAL SIGNS AND ABBREVIATIONS
Mathematical Signs and Commonly Used Abbreviations+ Plus (sign of addition) π Pi (3.1416)
+ Positive Σ Sigma (sign of summation)
− Minus (sign of subtraction) ω Omega (angles measured in radians)
− Negative g Acceleration due to gravity (32.16 ft/s2 or 9.81 m/s2)
± () Plus or minus (minus or plus) i (or j) Imaginary quantity
× Multiplied by (multiplication sign) sin Sine
· Multiplied by (multiplication sign) cos Cosine
÷ Divided by (division sign) tan Tangent
/ Divided by (division sign) cot Cotangent
: Is to (in proportion) sec Secant
= Equals csc Cosecant
≠ Is not equal to vers Versed sine
≡ Is identical to covers Coversed sine
≅ or ≈ Approximately equalssin−1 a
arcsin a or asin a
Arc the sine of which is a
> Greater than (sin a)−1 Reciprocal of sin a (1 ÷ sin a)
< Less than sinn x nth power of sin x
≥ Greater than or equal to sinh x Hyperbolic sine of x
≤ Less than or equal to cosh x Hyperbolic cosine of x
→ Approaches as a limit ∆ Delta (increment of)
Varies directly as δ Delta (variation of)
∴ Therefore d Differential (in calculus)
:: Equals (in proportion) ∂ Partial differentiation (in calculus)
Square root ∫ Integral (in calculus)
Cube root Integral between the limits a and b
4th root ! 5! = 1 × 2 × 3 × 4 × 5 (Factorial)
nth root ∠ Angle
a2 a squared (2nd power of a) Right angle
a3 a cubed (3rd power of a) ⊥ Perpendicular to
a4 4th power of a Triangle
an nth power of a Circle
a−n 1 ÷ an Parallelogram
Reciprocal value of n ° Degree (circular arc or temperature)
log Logarithm ′ Minutes or feet
loge Natural or Napierian logarithm ″ Seconds or inches
ln Natural or Napierian logarithm a ′ a prime
e Base of natural logarithms (2.71828) a″ a double prime
lim Limit value (of an expression) a1 a sub one
∞ Infinity a2 a sub two
α Alpha
commonly used to denote angles
an a sub n
β Beta ( ) Parentheses
γ Gamma [ ] Brackets
θ Theta Braces
φ Phi Absolute value of K, size of K irrespective of signµ Mu (coefficient of friction)
1–( )
3 ba∫
4
n
1n---
K
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
MATHEMATICAL SIGNS AND ABBREVIATIONS 2543
Letter Symbols for Mechanics and Time-Related Phenomena ANSI/ASME Y10.3M-1984
Acceleration, angular α (alpha) Height hAcceleration, due to gravity g Inertia, moment of I or JAcceleration, linear a Inertia, polar (area) moment ofa J
Amplitudea
a Not specified in Standard
A Inertia, product (area) moment ofa
Ixy
Angle
α (alpha)β (beta)γ (gamma)θ (theta)φ (phi)ψ (psi)
Length L or lLoad per unit distancea q or wLoad, totala P or WMass mMoment of force, including
bending moment M
Neutral axis, distance to extreme fiber froma c
Angle, solid Ω (omega) Period T
Angular frequency ω (omega) Poisson's ratio µ (mu) or ν (nu)
Angular momentum L Power P
Angular velocity ω (omega) Pressure, normal force per unit area p
Arc length s Radius rArea A Revolutions per unit of time n
Axes, through any pointaX-X, Y-Y, or Z-Z
Second moment of area (second axial moment of area)
Ia
Bulk modulus K Second polar moment of area IP or JBreadth (width) b Section modulus ZCoefficient of expansion, lineara α (alpha) Shear force in beam sectiona V
Coefficient of friction µ (mu) Spring constant (load per unit deflection)a k
Concentrated load (same as force) F Statical moment of any area
about a given axisa Q
Deflection of beam, maxa δ (delta) Strain, normal ε (epsilon)Density ρ (rho) Strain, shear γ (gamma)
Depth d, δ (delta), or t Stress, concentration factora K
Diameter D or d Stress, normal σ (sigma)Displacementa u, v, w Stress, shear τ (tau)Distance, lineara s Temperature, absoluteb
b Specified in ANSI Y10.4-1982 (R1988)
T, or θ (theta)Eccentricity of application of
loada e Temperatureb t, or θ (theta)
Efficiencya η (eta) Thickness d, δ (delta), or tElasticity, modulus of E Time tElasticity, modulus of, in shear G Torque TElongation, totala δ (delta) Velocity, linear vEnergy, kinetic Ek, K, T Volume V
Energy, potential EP, V, or Φ (phi)
Wavelength λ (lambda)
Factor of safetya N, or n Weight WForce or load, concentrated F Weight per unit volume γ (gamma)Frequency f Work WGyration, radius ofa k
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2544 METRIC SYSTEMS
MEASURING UNITS
Metric Systems Of Measurement
A metric system of measurement was first established in France in the years followingthe French Revolution, and various systems of metric units have been developed since thattime. All metric unit systems are based, at least in part, on the International Metric Stan-dards, which are the meter and kilogram, or decimal multiples or submultiples of thesestandards.
In 1795, a metric system called the centimeter-gram-second (cgs) system was proposed,and was adopted in France in 1799. In 1873, the British Association for the Advancementof Science recommended the use of the cgs system, and since then it has been widely usedin all branches of science throughout the world. From the base units in the cgs system arederived the following:
Unit of velocity = 1 centimeter per secondAcceleration due to gravity (at Paris) = 981 centimeters per second per second
Unit of force = 1 dyne = 1⁄981 gram
Unit of work = 1 erg = 1 dyne-centimeterUnit of power = 1 watt = 10,000,000 ergs per second
Another metric system called the MKS (meter-kilogram-second) system of units wasproposed by Professor G. Giorgi in 1902. In 1935, the International Electro-technicalCommission (IEC) accepted his recommendation that this system of units of mechanicsshould be linked with the electromagnetic units by the adoption of a fourth base unit. In1950, the IEC adopted the ampere, the unit of electric current, as the fourth unit, and theMKSA system thus came into being.
A gravitational system of metric units, known as the technical system, is based on themeter, the kilogram as a force, and the second. It has been widely used in engineering.Because the standard of force is defined as the weight of the mass of the standard kilogram,the fundamental unit of force varies due to the difference in gravitational pull at differentlocations around the earth. By international agreement, a standard value for accelerationdue to gravity was chosen (9.81 meters per second squared) that for all practical measure-ments is approximately the same as the local value at the point of measurement.
The International System of Units (SI).—The Conference Generale des Poids etMesures (CGPM), which is the body responsible for all international matters concerningthe metric system, adopted in 1954, a rationalized and coherent system of units, based onthe four MKSA units (see above), and including the kelvin as the unit of temperature andthe candela as the unit of luminous intensity. In 1960, the CGPM formally named this sys-tem the Système International d'Unites, for which the abbreviation is SI in all languages. In1971, the 14th CGPM adopted a seventh base unit, the mole, which is the unit of quantity(“amount of substance”).
In the period since the first metric system was established in France toward the end of the18th century, most of the countries of the world have adopted a metric system. At thepresent time, most of the industrially advanced metric-using countries are changing fromtheir traditional metric system to SI. Those countries that are currently changing or consid-ering change from the English system of measurement to metric have the advantage thatthey can convert directly to the modernized system. The United Kingdom, which can besaid to have led the now worldwide move to change from the English system, went straightto SI.
The use of SI units instead of the traditional metric units has little effect on everyday lifeor trade. The units of linear measurement, mass, volume, and time remain the same, viz.meter, kilogram, liter, and second.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SI METRIC UNITS 2545
The SI, like the traditional metric system, is based on decimal arithmetic. For each phys-ical quantity, units of different sizes are formed by multiplying or dividing a single basevalue by powers of 10. Thus, changes can be made very simply by adding zeros or shiftingdecimal points. For example, the meter is the basic unit of length; the kilometer is a multi-ple (1000 meters); and the millimeter is a sub-multiple (one-thousandth of a meter).
In the older metric systems, the simplicity of a series of units linked by powers of ten is anadvantage for plain quantities such as length, but this simplicity is lost as soon as morecomplex units are encountered. For example, in different branches of science and engi-neering, energy may appear as the erg, the calorie, the kilogram-meter, the liter-atmo-sphere, or the horsepower-hour. In contrast, the SI provides only one basic unit for eachphysical quantity, and universality is thus achieved.
As mentioned before, there are seven base units, which are for the basic quantities oflength, mass, time, electric current, thermodynamic temperature, amount of substance,and luminous intensity, expressed as the meter (m), the kilogram (kg), the second (s), theampere (A), the kelvin (K), the mole (mol), and the candela (cd). The units are defined inthe accompanying Table 1.
The SI is a coherent system. A system is said to be coherent if the product or quotient ofany two unit quantities in the system is the unit of the resultant quantity. For example, in acoherent system in which the foot is the unit of length, the square foot is the unit of area,whereas the acre is not.
Other physical quantities are derived from the base units. For example, the unit of veloc-ity is the meter per second (m/s), which is a combination of the base units of length andtime. The unit of acceleration is the meter per second squared (m/s2). By applying New-ton's second law of motion—force is proportional to mass multiplied by acceleration—theunit of force is obtained that is the kilogram-meter per second squared (kg-m/s2). This unitis known as the newton, or N. Work, or force times distance is the kilogram-meter squaredper second squared (kg-m2/s2), which is the joule (1 joule = 1 newton-meter), and energy isalso expressed in these terms. The abbreviation for joule is J. Power or work per unit timeis the kilogram-meter squared per second cubed (kg-m2/s3), which is the watt (1 watt = 1joule per second = 1 newton-meter per second). The abbreviation for watt is W. The termhorsepower is not used in the SI and is replaced by the watt, which together with multiplesand submultiples—kilowatt and milliwatt, for example—is the same unit as that used inelectrical work.
The use of the newton as the unit of force is of particular interest to engineers. In practicalwork using the English or traditional metric systems of measurements, it is a commonpractice to apply weight units as force units. Thus, the unit of force in those systems is thatforce that when applied to unit mass produces an acceleration g rather than unit accelera-tion. The value of gravitational acceleration g varies around the earth, and thus the weightof a given mass also varies. In an effort to account for this minor error, the kilogram-forceand pound-force were introduced, which are defined as the forces due to “standard grav-ity” acting on bodies of one kilogram or one pound mass, respectively. The standard grav-itational acceleration is taken as 9.80665 meters per second squared or 32.174 feet persecond squared. The newton is defined as “that force, which when applied to a body havinga mass of one kilogram, gives it an acceleration of one meter per second squared.” It isindependent of g. As a result, the factor g disappears from a wide range of formulas indynamics. However, in some formulas in statics, where the weight of a body is importantrather than its mass, g does appear where it was formerly absent (the weight of a mass of Wkilograms is equal to a force of Wg newtons, where g = approximately 9.81 meters per sec-ond squared). Details concerning the use of SI units in mechanics calculations are given onpage 142 and throughout the Mechanics section in this Handbook. The use of SI units instrength of materials calculations is covered in the section on that subject.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2546 SI METRIC UNITS
Decimal multiples and sub-multiples of the SI units are formed by means of the prefixesgiven in the following table, which represent the numerical factors shown.
Factors and Prefixes for Forming Decimal Multiples of SI Units
For more information on SI practice, the reader is referred to the following publications:Metric Practice Guide, published by the American Society for Testing and Materials,
1916 Race St., Philadelphia, PA 19103.ISO International Standard 1000. This publication covers the rules for use of SI units,
their multiples and sub-multiples. It can be obtained from the American National Stan-dards Institute 11 West 42nd Street, New York, NY 10036.
The International System of Units, Special Publication 330 of the National Bureau ofStandards—available from the Superintendent of Documents, U.S. Government Print-ing Office, Washington, DC 20402.
Binary Multiples.—The International Electrotechnical Commission has assigned the fol-lowing prefixes to represent exponential binary multiples. This avoids confusion withstandard SI decimal prefixes when representing powers of 2, as in bits and bytes.
Example 1:2 Ki = 2 × 210 = 2 × 1,024 = 2,048. This does not equal 2 K = 2 × 103 = 2,000.
Example 2:1 mebibyte = 1 × 220 = 1,048,576 bytes. Again this does not equal 1 megabyte= 1 × 106 = 1,000,000 bytes, a value that is often confused with 1,048,576 bytes.
Factor by which theunit is multiplied Prefix Symbol
Factor by which theunit is multiplied Prefix Symbol
1012 tera T 10−2 centi c109 giga G 10−3 milli m106 mega M 10−6 micro µ
103 kilo k 10−9 nano n102 hecto h 10−12 pico p10 deka da 10−15 femto f10−1 deci d 10−18 atto a
Symbol Name Binary Power Symbol Name Binary Power Symbol Name Binary Power
Ki kibi 210 Gi gibi 230 Pi pebi 250
Mi mebi 220 Ti tebi 240 Ei exbi 260
Table 1. International System (SI) UnitsPhysicalQuantity
Name ofUnit
UnitSymbol Definition
Basic SI Units
Length meter m Distance traveled by light in vacuo during 1/299,792,458 of a second.
Mass kilogram kgMass of the international prototype which is in the custody of the
Bureau International des Poids et Mesures (BIPM) at Sèvres, near Paris.
Time second sThe duration of 9,192,631,770 periods of the radiation corresponding to
the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
ElectricCurrent ampere A
The constant current which, if maintained in two parallel rectilinear conductors of infinite length, of negligible circular cross section, and placed at a distance of one meter apart in a vacuum, would produce between these conductors a force equal to 2 × 10−7 N/m length.
ThermodynamicTemperature
degreekelvin K The fraction 1 ⁄273.16 of the thermodynamic temperature of the triple
point of water.Amount ofSubstance mole mol The amount of substance of a system which contains as many elemen-
tary entities as there are atoms in 0.012 kilogram of carbon 12.
LuminousIntensity candela cd
Luminous intensity, in the perpendicular direction, of a surface of 1 ⁄600,000 square meter of a black body at the temperature of freezing platinum under a pressure of 101,325 newtons per square meter.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
SI METRIC UNITS 2547
Table 2. International System (SI) Units with Complex Names
SI Units Having Special Names
Force newtonN =
kg·m/s2That force which, when applied to a body having a mass of one kilo-
gram, gives it an acceleration of one meter per second squared.
Work,Energy,Quantityof Heat
joule J = N·m The work done when the point of application of a force of one newton is displaced through a distance of one meter in the direction of the force.
ElectricCharge coulomb C = A·s The quantity of electricity transported in one second by a current of one
ampere.
ElectricPotential volt V = W/A
The difference of potential between two points of a conducting wire carrying a constant current of one ampere, when the power dissipated between these points is equal to one watt.
ElectricCapacitance farad F = C/V
The capacitance of a capacitor between the plates of which there appears a difference of potential of one volt when it is charged by a quantity of electricity equal to one coulomb.
ElectricResistance ohm Ω = V/A
The resistance between two points of a conductor when a constant dif-ference of potential of one volt, applied between these two points, pro-duces in this conductor a current of one ampere, this conductor not being the source of any electromotive force.
MagneticFlux weber Wb = V·s
The flux which, linking a circuit of one turn produces in it an electro-motive force of one volt as it is reduced to zero at a uniform rate in one second.
Inductance henry H = V·s/AThe inductance of a closed circuit in which an electromotive force of
one volt is produced when the electric current in the circuit varies uni-formly at the rate of one ampere per second.
LuminousFlux lumen 1m = cd·sr The flux emitted within a unit solid angle of one steradian by a point
source having a uniform intensity of one candela.
Illumination lux lx = lm/m2 An illumination of one lumen per square meter.
Physical Quantity SI Unit Unit Symbol
SI Units Having Complex Names
Area square meter m2
Volume cubic meter m3
Frequency hertza
a Hz = cycle/second
HzDensity (Mass Density) kilogram per cubic meter kg/m3
Velocity meter per second m/sAngular Velocity radian per second rad/sAcceleration meter per second squared m/s2
Angular Acceleration radian per second squared rad/s2
Pressure pascalb
b Pa = newton/meter2
PaSurface Tension newton per meter N/mDynamic Viscosity newton second per meter squared N s/m2
Kinematic Viscosity meter squared per second m2/s
Diffusion CoefficientThermal Conductivity watt per meter degree Kelvin W/(m °K)Electric Field Strength volt per meter V/mMagnetic Flux Density teslac
c T = weber/meter2
TMagnetic Field Strength ampere per meter A/mLuminance candela per square meter cd/m2
Table 1. (Continued) International System (SI) UnitsPhysicalQuantity
Name ofUnit
UnitSymbol Definition
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2548 U.S. CUSTOMARY UNIT SYSTEM
Standard of Length.—In 1866 the United States, by act of Congress, passed a law mak-ing legal the meter, the only measure of length that has been legalized by the United StatesGovernment. The United States yard is defined by the relation: 1 yard = 3600⁄3937 meter. Thelegal equivalent of the meter for commercial purposes was fixed as 39.37 inches, by law, inJuly, 1866, and experience having shown that this value was exact within the error ofobservation, the United States Office of Standard Weights and Measures was, in 1893,authorized to derive the yard from the meter by the use of this relation. The United Statesprototype meters Nos. 27 and 21 were received from the International Bureau of Weightsand Measures in 1889. Meter No. 27, sealed in its metal case, is preserved in a fireproofvault at the Bureau of Standards.
Comparisons made prior to 1893 indicated that the relation of the yard to the meter, fixedby the Act of 1866, was by chance the exact relation between the international meter andthe British imperial yard, within the error of observation. A subsequent comparison madebetween the standards just mentioned indicates that the legal relation adopted by Congressis in error 0.0001 inch; but, in view of the fact that certain comparisons made by the EnglishStandards Office between the imperial yard and its authentic copies show variations asgreat if not greater than this, it cannot be said with certainty that there is a differencebetween the imperial yard of Great Britain and the United States yard derived from themeter. The bronze yard No. 11, which was an exact copy of the British imperial yard bothin form and material, had shown changes when compared with the imperial yard in 1876and 1888, which could not reasonably be said to be entirely due to changes in Bronze No.11. On the other hand, the new meters represented the most advanced ideas of standards,and it therefore seemed that greater stability as well as higher accuracy would be securedby accepting the international meter as a fundamental standard of length.
U.S. Customary Unit System
The USCS is originated from the foot-pound-second unit system or English unit system.The USCS system and English unit system are same for the measures of length and mass,but it varies for the measure of capacity. The U.S. gallon is defined as 231 cubic inches andbushel as 2,150.42 cubic inches where as the corresponding English units are 277.42 cubicinches and 2,219.36 cubic inches.
Fundamental Constants
Name Symbol USCS units SI units
Avogadro’s number NA 6.022 × 1023 mol−1
Boltzman constant k 5.65 × 10−24 ft·lbf/°R 1.38065 × 10−23 J/°KFaraday Constant F 96487 C/mol
Gravitational constant g 32.174 lbm-ft/lbf-sec2 9.80667 m/sec2
1 fathom = 2 yards = 6 feet1 knot = nautical unit of speed =
1 nautical mile per hour1.1508 statute miles per hour1.8516 kilometers per hour
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2550 LINEAR MEASURE AND CONVERSION FACTORS
Table 3. Feet and Inches to Inches Conversion
Example: A tape measure reads 17 feet 8 inches. How many inches is this? Solution: Read downthe first column of Table 3 to find 10 ft 0 inch = 120 inches. Next, find the intersection of the 7 ft rowand the 8 inch column to get 92 inches. Add both results to get 120 inches + 92 inches = 212 inches.
Table 4. Inches to Feet and Yards Conversion
One degree at the equator =60 nautical miles69.047 statute miles111.098 kilometers
One minute at the equator =1 nautical mile1.1508 statute miles1.8516 kilometers
360 degrees at the equator =circumference at equator21,600 nautical miles 24,856.8 statute miles39,995.4 kilometers
Table 2. Circular and Angular Measure Conversion Factors
circumference of circle =360 degrees = 2π radian = 6.283185 radian
Example: Convert 783⁄4 inches to feet. Solution: From Table 4, find 70 inches = 5.8333 feet and add to that 83⁄4 inches = 0.7292 feet found in Table 8a at the intersection of the 3⁄4 inch row and the 8 inch column. Thus, 783⁄4 inches = 5.8333 + 0.7292 = 6.5625 feet.
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2552 LINEAR MEASURE AND CONVERSION FACTORS
Table 6. Feet to Inches Conversionfeet inch feet inch feet inch feet inch feet inch feet inch feet inch
Copyright 2004, Industrial Press, Inc., New York, NY
MILLIMETER TO INCH CONVERSION 2553
Table 8a. Inch to Millimeters Conversion
All values in this table are exact. For inches to centimeters, shift decimal point in mm column oneplace to left and read centimeters, thus, for example, 40 in. = 1016 mm = 101.6 cm.
Table 8b. Millimeters to Inch Conversion
Based on 1 inch = 25.4 millimeters, exactly. For centimeters to inches, shift decimal point of cen-timeter value one place to right and enter mm column, thus, for example, 70 cm = 700 mm =27.55906 inches.
Copyright 2004, Industrial Press, Inc., New York, NY
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Based on 1 inch = 25.4 millimeters, exactly. All values in this table are exact. Example: Convert 2123⁄64 inches to millimeters. Solution: From the first page of thistable, find 20 inches = 508.0 millimeters and add to that 123⁄64 inches = 34.528125 millimeters found at the intersection of the 1- inch column and the row containing23⁄64 inch . Thus, 2123⁄64 inches = 508.0 + 34.528125 = 542.528125 mm, exactly.
Copyright 2004, Industrial Press, Inc., New York, NY
DECIMAL INCH TO MILLIMETER CONVERSION 2557
Based on 1 inch = 25.4 millimeters, exactly. All values in this table are exact. Use Table 8a toobtain whole inch and other decimal equivalents to add to decimal equivalents above. Example:Convert 10.9983 in. to mm. Solution: 10.9983 in. = 254.0 + 25.3492 + 0.00762 = 279.35682 mm.
Table 12. (Continued) Millimeters to Inches Conversion →
Millimeters↓
0 1 2 3 4 5 6 7 8 9
Inches
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2560 MICROINCH TO MICRON CONVERSION
Table 13a. Microinches to Micrometers (microns) Conversion
Both tables based on 1 microinch = 0.0254 micrometers, exactly. All values in both parts of thistable are exact; figures to the right of the last place figures are all zeros.
Use the small table below to convert microinches to micrometers for ranges higher than given in the main table above. Appropri-ate quantities chosen from both tables are simply added to obtain the higher converted value:
The table given below can be used with the preceding main table to obtain higher converted values, simply by adding appropri-ate quantities chosen from each table:
Copyright 2004, Industrial Press, Inc., New York, NY
2566 CUBIC MEASURE AND CONVERSION FACTORS
Units of Volume
Table 21. Cubic Measure and Conversion Factors
Metric System U.S. System
1 cubic meter (m3) =1000 cubic decimeters (liters)1,000,000 cubic centimeters1.30795 cubic yards35.314667 cubic feet61,023.74 cubic inches264.17205 U.S. gallons219.96925 British Imperial gallons
1 liter (l) or 1 cubic decimeter (dm3) =1 liter = volume of 1 kg water at 39.2°F0.001 cubic meter1000 cubic centimeters10 deciliters0.03531466 cubic foot61.023744 cubic inches0.2642 U.S. gallon0.21997 British Imperial gallon1.0566882 U.S. quarts33.814 U.S. fluid ounces
1 cubic centimeter (cm3) =0.001 liter1000 cubic millimeters0.061024 cubic inch
1 cubic yard (yd3) =27 cubic feet201.97403 U.S. gallons46,656 cubic inch0.7646 cubic meter
1 cubic foot (ft3) =1728 cubic inches7.4805 U.S. gallons6.23 British Imperial gallons 0.02831685 cubic meter28.31685 liters
1 cubic inch (in3) =0.55411256 U.S. fluid ounces16.387064 cubic centimeters
Shipping MeasureFor measuring internal capacity of a vessel:
1 register ton = 100 cubic feetFor measurement of cargo:
1 shipping ton =Approximately 40 cubic feet of merchan-dise is considered a shipping ton, unless that bulk would weigh more than 2000 pounds, in which case the freight charge may be based upon weight
40 cubic feet =32.143 U.S. bushels31.16 Imperial bushels
British (Imperial) Liquid and Dry Measure U.S. Liquid Measure
1 British Imperial gallon =0.1605 cubic foot277.42 cubic inches1.2009 U.S. gallon160 Imperial fluid ounces4 Imperial quarts8 Imperial pints4.54609 liters
Copyright 2004, Industrial Press, Inc., New York, NY
2570 FLOW CONVERSION FACTORS
1 U.S. fluid ounce = 29.57353 milliliters
1 milliliter = 0.003814 U.S. fluid ounce
Units of Volumetric Flow Rate
Table 28a. Volume Flow per Second Conversion
Pitot Tube.— A pitot tube is a small, transparent, open tube bent at right angle. It is a hol-low tube that is placed longitudinally in the direction of fluid flow, allowing the flow toenter one end at the fluids velocity of approach. When the fluids enter the pitot tube, itcomes to a stop, all of the velocity head is converted to pressure head. The differencebetween the total and static energies is the kinetic energy of the fluid. The velocity of thefluid can be calculated by using the Bernoulli equation.
Table 27a. U.S. Fluid Ounces to Milliliters Conversionoz mL oz mL oz mL oz mL oz mL
Copyright 2004, Industrial Press, Inc., New York, NY
2574 PRESSURE AND STRESS CONVERSION FACTORS
Units of Pressure and Stress
1 lb/in2 = 0.07030697 kg/cm2
1 kg/cm2 = 14.22334 lb/in2
Table 35. Pressure and Stress Conversion Factors
1 kilogram per sq. millimeter (kgf ⁄mm2) =1422.32 pounds per square inch
1 kilogram per sq. centimeter (kgf ⁄cm2) =14.223 pounds per square inch
1 bar =1,000,000 dynes per square centimeter1000 millibars100 kilopascals750.06168 torr1.0197162 kilogram force per sq. centime-ter14.50377 pounds per square inch29.529983 inches of mercury at 0°C10,197.162 mm water at 4°C33.455256 feet of water at 4°C
1 millibar =100,000 dynes per square centimeter100 pascal
1 pound per square inch =144 pounds per square foot0.068 atmosphere2.042 inches of mercury at 62°F27.7 inches of water at 62°F2.31 feet of water at 62°F0.0703 kilogram per square centimeter6.894757 kilopascals6894.757 pascal
1 atmosphere =30 inches of mercury at 62°F14.7 pounds per square inch2116.3 pounds per square foot33.95 feet of water at 62°F
1 foot of water at 62°F =62.355 pounds per square foot0.433 pound per square inch
1 inch of mercury at 62°F =1.132 foot of water13.58 inches of water0.491 pound per square inch
1 inch of water =0.0735559 inch mercury at 0°C1.8683205 torr0.5780367 ounce force per square inch0.0024583 atmosphere
Table 36a. Pounds per Square Inch to Kilograms per Square Centimeter Conversion lb/in2 kg/cm2 lb/in2 kg/cm2 lb/in2 kg/cm2 lb/in2 kg/cm2 lb/in2 kg/cm2
Copyright 2004, Industrial Press, Inc., New York, NY
2578 ENERGY, POWER, AND HEAT CONVERSION FACTORS
1 newton meter = 8.850748 pound-inches
Poundal.—The expression “poundal” is sometimes used in connection with calculationsin mechanics. Many mechanical handbooks, however, do not define it, because of its lim-ited use. A poundal is a unit of force, and is defined as that force which, acting on a mass ofone pound for one second, produces a velocity of one foot per second. A foot-poundal is aunit of energy equal to the energy resulting when a force of one poundal acts through a dis-tance of one foot. In order to reduce foot-poundals to foot-pounds, multiply the number offoot-poundals by 0.03108. Dividing the number of foot-poundals by 32.16 (accelerationdue to gravity) will also give foot-pounds.
1 horsepower-hour =0.746 kilowatt-hour1,980,000 foot-pounds2545 Btu (British thermal units)2.64 pounds of water evaporated at 212°F17 pounds of water raised from 62° to 212°F
1 kilowatt-hour =100 watt-hours1.34 horsepower-hour2,655,200 foot-pounds3,600,000 joules3415 Btu3.54 pounds of water evaporated at 212°F22.8 pounds of water raised from 62° to 212°F
Table 43c. Power Conversion Factors
1 horsepower =746 watts0.746 kilowatt33,000 foot-pounds/minute550 foot-pounds/second2545 Btu/hour42.4 Btu/minute0.71 Btu/second2.64 pounds of water evapo-
rated per hour at 212°F
1 kilowatt =1000 watts1.34 horsepower2,654,200 foot-pounds/hour44,200 foot-pounds/minute737 foot-pounds/second3415 Btu/hour57 Btu/minute0.95 Btu/second3.54 pounds of water evapo-
rated per hour at 212°F
1 watt =1 joule/second0.00134 horsepower0.001 kilowatt3.42 Btu/hour44.22 foot-pounds/minute0.74 foot-pounds/second0.0035 pound of water evapo-
rated per hour at 212°F
Table 43d. Heat Conversion Factors
1 Btu (British thermal unit) =1052 watt-seconds778 foot-pounds0.252 kilogram-calorie0.000292 kilowatt-hour0.000393, horsepower-hour0.00104 pound of water evap-
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Table 50. Thermal Conductance Conversion Factors
Figures in bold face indicate the conversion is exact
Conduction.—Whenever the molecules of a working substance,whether liquid, solid, or vapor, are restrained so that no appreciable rela-tive translatory motion occurs among them, the kinetic energies of thevarious molecules will be largely due to vibration. If a temperature dif-ference exists in the working substance, some adjacent molecules willnecessarily be at different temperatures hence will possess differentdegrees of vibratory motion. In this case the molecule which is vibratingmost rapidly will transfer some of its motion to the slower-moving mole-cule next to it, the one then undergoing a decrease in temperature and theother an increase. In this way, thermal energy will be transferred by themechanism of conduction from the region of higher to the region of lowertemperature. The process will continue spontaneously until the entiresystem has reached a uniform equilibrium temperature.
In contrast to radiation, conduction only occurs when a working sub-stance is present and when the molecules of that working substance retain
practically fixed positions with respect to one another. Thus, conductiveheat flow would always occur through solids, but would take place in liq-uids and vapors only if special conditions prevented or greatly reducedthe normal translatory motion of the molecules within these materials.Fuel Oil, Coal and Gas Equivalents.—One gallon of fuel oil equals13.1 pounds of coal, equals 160 cubic feet of natural gas. One barrel offuel oil equals 0.278 ton of coal, equals 680.6 cubic feet of natural gas.One pound of fuel oil equals 1.75 pounds of coal, equals 21.3 cubic feetof natural gas. One pound of coal equals 0.763 gallon of oil, equals 12.2cubic feet of natural gas. One ton of coal equals 3.6 barrels of oil, equals24,500 cubic feet of natural gas. The heating value of the average mid-continent fuel oil having a Baume gravity of 26.9 is 19,376 British ther-mal units per pound of oil, and 143,950 British thermal units per gallon ofoil. The specific gravity and the heat value may be expressed approxi-mately by means of a simple formula, as follows: BTU per pound =18,650 + 40 × (Degrees Baume − 10).
Copyright 2004, Industrial Press, Inc., New York, NY
TEMPERATURE 2583
Units of Temperature
Thermometer Scales.—There are two thermometer scales in general use: the Fahrenheit(F), which is used in the United States and in other countries still using the English systemof units, and the Celsius (C) or Centigrade used throughout the rest of the world.
In the Fahrenheit thermometer, the freezing point of water is marked at 32 degrees on thescale and the boiling point, at atmospheric pressure, at 212 degrees. The distance betweenthese two points is divided into 180 degrees. On the Celsius scale, the freezing point ofwater is at 0 degrees and the boiling point at 100 degrees. The following formulas may beused for converting temperatures given on any one of the scales to the other scale:
Tables on the pages that follow can be used to convert degrees Celsius into degrees Fahr-enheit or vice versa. In the event that the conversions are not covered in the tables, usethose applicable portions of the formulas given above for converting.
Table 51. Temperature Conversion Fomulas
Absolute Temperature and Absolute Zero.—A point has been determined on the ther-mometer scale, by theoretical considerations, that is called the absolute zero and beyondwhich a further decrease in temperature is inconceivable. This point is located at −273.15degrees Celsius or −459.67 degrees F. A temperature reckoned from this point, instead offrom the zero on the ordinary thermometers, is called absolute temperature. Absolute tem-perature in degrees C is known as “degrees Kelvin” or the “Kelvin scale” (K) and absolutetemperature in degrees F is known as “degrees Rankine” or the “Rankine scale” (R).
Measures of the Quantity of Thermal Energy.—The unit of quantity of thermal energyused in the United States is the British thermal unit, which is the quantity of heat or thermalenergy required to raise the temperature of one pound of pure water one degree F. (Ameri-can National Standard abbreviation, Btu; conventional British symbol, B.Th.U.) TheFrench thermal unit, or kilogram calorie, is the quantity of heat or thermal energy requiredto raise the temperature of one kilogram of pure water one degree C. One kilogram calorie= 3.968 British thermal units = 1000 gram calories. The number of foot-pounds of mechan-ical energy equivalent to one British thermal unit is called the mechanical equivalent ofheat, and equals 778 foot-pounds.
In the modern metric or SI system of units, the unit for thermal energy is the joule (J); acommonly used multiple being the kilojoule (kJ), or 1000 joules. See page 2544 for anexplanation of the SI System. One kilojoule = 0.9478 Btu. Also in the SI System, the watt(W), equal to joule per second (J/s), is used for power, where one watt = 3.412 Btu per hour.
To Convert To Use Formula To Convert To Use Formula
Table converts °C → °F and °R, or °F → °C and °K. Find “convert from” temperature in bold column and read result from °F and °R or °C and °K columns. Example 1: 183 °C = 361.4 °F and 821.1 °R. Example 2: 183 °F = 83.9 °C and 357.0 °K.
Table 52. (Continued) °C → °F and °R Temperature Conversion °F → °C and °K °K °C °F °R °K °C °F °R °K °C °F °R
Machinery's Handbook 27th Edition
Copyright 2004, Industrial Press, Inc., New York, NY
2586 VELOCITY AND ACCELERATION CONVERSION FACTORS
Units of Velocity and Acceleration
Table 53. Velocity Conversion Factors
Figures in bold face indicate the conversion is exact
Table 54. Acceleration Conversion Factors
Figures in bold face indicate the conversion is exact.
Units of Viscosity
Table 55a. Oil Viscosity Conversion Factors
ρ = Specific gravity of the oil.Figures in bold face indicate the conversion is exact
Copyright 2004, Industrial Press, Inc., New York, NY
MOMENT OF INERTIA CONVERSION FACTORS 2587
Units of Moment of Inertia and Momentum
Miscellaneous Measuring Units
Ohm’s Law.—The following figure represents basic electrical relationships. This charthas been formatted in such a way that each variable has been related to the other three vari-ables. This figure is simply for reference.
Table 56. Moment of Inertia Conversion FactorsMultiply By To Obtain
Moment of Inertia and Section Modulus
moment of inertia [kg · m2] 23.73036 pound-foot2
moment of inertia [kg · m2] 3417.171 pound-inch2
moment of inertia [lb · ft2] 0.04214011 kilogram-meter2 (kg · m2)moment of inertia [lb · inch2] 0.0002926397 kilogram-meter2 (kg · m2)moment of section [foot4] 0.008630975 meter4 (m4)moment of section [inch4] 41.62314 centimeter4