SI Imperial unit conversion mechanical
Converting between the International System of Units and the Imperial system is a daily task in mechanical engineering, where drawings, specifications, and equipment from different origins coexist. This reference provides verified conversion factors for the most commonly used mechanical quantities: from length, mass, and force to pressure, energy, power, torque, density, velocity, and moment of inertia. Each factor is presented with its direct and reverse formula, and notes are included on the appropriate number of significant figures for workshop and design calculations. The precision of the factors follows international definitions established by the BIPM and ASTM E380 / IEEE/ASTM SI 10 standards.
Base and derived SI units
Section titled “Base and derived SI units”| Quantity | SI unit (symbol) | Common Imperial unit (symbol) | Exact equivalence |
|---|---|---|---|
| Length | metre (m) | foot (ft) | 1 m / 3,28084 ft |
| Length | metre (m) | inch (in) | 1 m / 39,3701 in |
| Mass | kilogram (kg) | pound mass (lb) | 1 kg / 2,20462 lb |
| Force | newton (N) | pound force (lbf) | 1 N / 0,224809 lbf |
| Pressure, stress | pascal (Pa) | psi (lbf/in²) | 1 Pa / 0,000145038 psi |
| Pressure, stress | megapascal (MPa) | psi (lbf/in²) | 1 MPa / 145,038 psi |
| Pressure, stress | megapascal (MPa) | ksi (klbf/in²) | 1 MPa / 0,145038 ksi |
| Energy, work | joule (J) | foot·pound force (ft·lbf) | 1 J / 0,737562 ft·lbf |
| Energy, work | joule (J) | British thermal unit (BTU) | 1 J / 0,000947817 BTU |
| Power | watt (W) | horsepower (hp) | 1 W / 0,00134102 hp |
| Power | kilowatt (kW) | horsepower (hp) | 1 kW / 1,34102 hp |
| Torque, moment | newton metre (N·m) | pound force foot (lbf·ft) | 1 N·m / 0,737562 lbf·ft |
| Torque, moment | newton metre (N·m) | pound force inch (lbf·in) | 1 N·m / 8,85075 lbf·in |
| Velocity | metre per second (m/s) | foot per second (ft/s) | 1 m/s / 3,28084 ft/s |
| Velocity | metre per second (m/s) | mile per hour (mph) | 1 m/s / 2,23694 mph |
| Angular velocity | radian per second (rad/s) | revolution per minute (rpm) | 1 rad/s / 9,54930 rpm |
| Density | kilogram per cubic metre (kg/m³) | pound mass per cubic foot (lb/ft³) | 1 kg/m³ / 0,062428 lb/ft³ |
| Moment of inertia | kilogram metre squared (kg·m²) | pound square foot (lb·ft²) | 1 kg·m² / 23,7304 lb·ft² |
| Dynamic viscosity | pascal second (Pa·s) | pound force second per square inch (lbf·s/in²) | 1 Pa·s / 0,000145038 lbf·s/in² |
| Kinematic viscosity | square metre per second (m²/s) | square foot per second (ft²/s) | 1 m²/s / 10,7639 ft²/s |
| Volumetric flow rate | cubic metre per second (m³/s) | gallon per minute (gpm) | 1 m³/s / 15850,3 gpm |
SI to Imperial conversion table for mechanics
Section titled “SI to Imperial conversion table for mechanics”| Quantity | SI unit | Imperial unit | Multiplication factor: SI → Imperial | Multiplication factor: Imperial → SI |
|---|---|---|---|---|
| Length | millimetre (mm) | inch (in) | 0,0393701 | 25,4 |
| Length | metre (m) | foot (ft) | 3,28084 | 0,3048 |
| Area | square millimetre (mm²) | square inch (in²) | 0,00155000 | 645,16 |
| Area | square metre (m²) | square foot (ft²) | 10,7639 | 0,0929030 |
| Volume | cubic millimetre (mm³) | cubic inch (in³) | 0,0000610237 | 16 387,064 |
| Volume | cubic metre (m³) | cubic foot (ft³) | 35,3147 | 0,0283168 |
| Mass | kilogram (kg) | pound mass (lb) | 2,20462 | 0,453592 |
| Mass per length | kilogram per metre (kg/m) | pound mass per foot (lb/ft) | 0,671969 | 1,48816 |
| Force | newton (N) | pound force (lbf) | 0,224809 | 4,44822 |
| Force | kilonewton (kN) | pound force (lbf) | 224,809 | 0,00444822 |
| Force per length | newton per metre (N/m) | pound force per inch (lbf/in) | 0,00571015 | 175,127 |
| Pressure, stress | pascal (Pa) | psi (lbf/in²) | 0,000145038 | 6 894,76 |
| Pressure, stress | kilopascal (kPa) | psi (lbf/in²) | 0,145038 | 6,89476 |
| Pressure, stress | megapascal (MPa) | psi (lbf/in²) | 145,038 | 0,00689476 |
| Pressure, stress | megapascal (MPa) | ksi (klbf/in²) | 0,145038 | 6,89476 |
| Pressure, stress | gigapascal (GPa) | Msi (Mlbf/in²) | 0,145038 | 6,89476 |
| Energy, work, heat | joule (J) | foot·pound force (ft·lbf) | 0,737562 | 1,35582 |
| Energy, work, heat | kilojoule (kJ) | BTU (British thermal unit) | 0,947817 | 1,05506 |
| Power | watt (W) | horsepower (hp) | 0,00134102 | 745,70 |
| Power | kilowatt (kW) | horsepower (hp) | 1,34102 | 0,74570 |
| Torque, moment | newton metre (N·m) | pound force foot (lbf·ft) | 0,737562 | 1,35582 |
| Torque, moment | newton metre (N·m) | pound force inch (lbf·in) | 8,85075 | 0,112985 |
| Velocity | metre per second (m/s) | foot per minute (ft/min) | 196,850 | 0,00508 |
| Velocity | kilometre per hour (km/h) | mile per hour (mph) | 0,621371 | 1,60934 |
| Acceleration | metre per second squared (m/s²) | foot per second squared (ft/s²) | 3,28084 | 0,3048 |
| Density | kilogram per cubic metre (kg/m³) | pound mass per cubic inch (lb/in³) | 0,0000361273 | 27 679,9 |
| Density | kilogram per litre (kg/L) | pound mass per gallon (lb/gal) | 8,34540 | 0,119826 |
| Area moment of inertia | millimetre to the fourth (mm⁴) | inch to the fourth (in⁴) | 0,00000240211 | 416 231,4 |
| Heat transfer coefficient | watt per square metre kelvin (W/(m²·K)) | BTU per hour square foot fahrenheit (BTU/(h·ft²·°F)) | 0,176110 | 5,67826 |
Direct and inverse conversion formulas
Section titled “Direct and inverse conversion formulas”| Quantity | Direct conversion (SI → Imperial) | Inverse conversion (Imperial → SI) |
|---|---|---|
| Length (mm ↔ in) | in = mm ÷ 25,4 | mm = in × 25,4 |
| Length (m ↔ ft) | ft = m × 3,28084 | m = ft × 0,3048 |
| Area (mm² ↔ in²) | in² = mm² ÷ 645,16 | mm² = in² × 645,16 |
| Mass (kg ↔ lb) | lb = kg × 2,20462 | kg = lb × 0,453592 |
| Force (N ↔ lbf) | lbf = N × 0,224809 | N = lbf × 4,44822 |
| Pressure (MPa ↔ psi) | psi = MPa × 145,038 | MPa = psi × 0,00689476 |
| Energy (J ↔ ft·lbf) | ft·lbf = J × 0,737562 | J = ft·lbf × 1,35582 |
| Power (kW ↔ hp) | hp = kW × 1,34102 | kW = hp × 0,74570 |
| Torque (N·m ↔ lbf·ft) | lbf·ft = N·m × 0,737562 | N·m = lbf·ft × 1,35582 |
| Velocity (m/s ↔ ft/min) | ft/min = m/s × 196,850 | m/s = ft/min × 0,00508 |
| Velocity (km/h ↔ mph) | mph = km/h × 0,621371 | km/h = mph × 1,60934 |
| Density (kg/m³ ↔ lb/ft³) | lb/ft³ = kg/m³ × 0,062428 | kg/m³ = lb/ft³ × 16,0185 |
| Temperature (°C ↔ °F) | °F = (°C × 9/5) + 32 | °C = (°F − 32) × 5/9 |
Temperature conversion factors
Section titled “Temperature conversion factors”Temperature conversion is not a simple multiplicative factor, since the Celsius and Fahrenheit scales have different zero points and different degree sizes. For temperature differences (ΔT) used in heat transfer, thermal expansion, or temperature coefficient calculations, the factor is linear.
| Conversion type | Formula | Numerical example |
|---|---|---|
| Point temperature: Celsius to Fahrenheit | °F = (°C × 9/5) + 32 | 100 °C / 212 °F |
| Point temperature: Fahrenheit to Celsius | °C = (°F − 32) × 5/9 | 212 °F / 100 °C |
| Temperature difference: Δ°C to Δ°F | Δ°F = Δ°C × 1,8 | Δ of 10 °C / Δ of 18 °F |
| Temperature difference: Δ°F to Δ°C | Δ°C = Δ°F ÷ 1,8 | Δ of 18 °F / Δ of 10 °C |
| Absolute temperature: Kelvin to Rankine | °R = K × 1,8 | 300 K / 540 °R |
| Absolute temperature: Rankine to Kelvin | K = °R ÷ 1,8 | 540 °R / 300 K |
Notes on precision and special cases
Section titled “Notes on precision and special cases”The number of significant figures used in the conversion factors should be selected based on the design tolerance and measurement uncertainty of the original measurement. For general mechanical workshop work, four significant figures are usually sufficient; for metrology and calibration, it is recommended to use the exact factors defined by international agreements.
The inch is defined internationally as exactly 25,4 millimetres since 1959. This exact value should be used as the basis for all length, area, and volume conversions in mechanical engineering. The avoirdupois pound mass is defined as exactly 0,45359237 kilograms. The pound force is derived from the pound mass and the standard acceleration of gravity at sea level, defined as 9,80665 m/s² (32,1740 ft/s²). For this reason, the conversion factor between newton and pound force uses the relation 1 lbf = 4,4482216152605 N.
In stress and pressure calculations, ksi (kilopound per square inch) is exactly equal to 1000 psi, and is used extensively in structural and materials mechanics in the Imperial system. A typical ASTM A36 structural steel has a yield strength of 250 MPa (36 ksi). Conversion from MPa to ksi is performed by dividing by 6,89476 or multiplying by 0,145038.
For torque, it is critical not to confuse pound force foot with pound force inch. Many design errors in bolted joints originate from confusion between these two units. Remember: 1 lbf·ft = 12 lbf·in. When converting N·m to lbf·ft, multiply by 0,737562; when converting N·m to lbf·in, multiply by 8,85075.
The density of water at 4 °C and 1 atm pressure is 1000 kg/m³ or 62,4280 lb/ft³. This value is used as reference in specific gravity calculations. In the Imperial system, density is also frequently expressed in pounds per gallon: 1 lb/gal = 0,119826 kg/L. A British Imperial gallon (4,54609 L) differs from the US gallon (3,78541 L); all conversions in this reference use the US gallon as it is the standard in American engineering technical documentation.
Frequently Asked Questions (FAQ)
Section titled “Frequently Asked Questions (FAQ)”What is the exact factor to convert millimetres to inches?
Section titled “What is the exact factor to convert millimetres to inches?”The international inch is defined as exactly 25,4 mm, therefore 1 mm is exactly equal to 0,0393700787401575 in. For general mechanical engineering work, use 1 mm = 0,03937 in with four decimals, or 1 in = 25,4 mm exactly.
How do I convert MPa to ksi to read steel specifications?
Section titled “How do I convert MPa to ksi to read steel specifications?”Divide the value in MPa by 6,89476 to obtain ksi. For example, a steel with a yield strength of 345 MPa has a yield strength of 50 ksi (345 ÷ 6,89476 ≈ 50,04). The typical value of 250 MPa equals 36,3 ksi, which corresponds to ASTM A36 structural steel.
Why are there two conversion factors for mass and force in the Imperial system?
Section titled “Why are there two conversion factors for mass and force in the Imperial system?”The Imperial system distinguishes between pound mass and pound force, unlike the SI where kilogram is mass and newton is force. One pound force is the force exerted by standard gravity on one pound mass. Therefore 1 kg of mass equals 2,20462 lb of mass, but 1 N of force equals 0,224809 lbf. In mechanical engineering calculations, you must identify whether the specification refers to mass or force in order to choose the correct factor.
How do I correctly convert a dimensional tolerance from micrometres to inches?
Section titled “How do I correctly convert a dimensional tolerance from micrometres to inches?”Divide the value in micrometres (µm) by 25,4 to obtain thousandths of an inch, also called “mil” (0,001 in). A tolerance of 5 µm equals 0,000197 in or 0,197 mil. For surface roughness, 3,2 µm Ra equals 126 µin (microinches). Remember that 1 µm = 39,37 µin.
What is the difference between Imperial gallon and US gallon when converting flow rates?
Section titled “What is the difference between Imperial gallon and US gallon when converting flow rates?”The US gallon equals 3,78541 litres, while the British Imperial gallon equals 4,54609 litres. When converting 1 m³/s to gallons per minute, you will obtain 15 850,3 gpm if using US gallons, but only 13 198,2 gpm if using Imperial gallons. In American engineering documentation, the US gallon is the standard.
What precision should I use when converting temperatures for thermal expansion calculations?
Section titled “What precision should I use when converting temperatures for thermal expansion calculations?”For temperature differences, use the exact factor Δ°F = Δ°C × 1,8. If the point temperature is 20 °C, the difference from the ambient reference temperature is not converted using the full formula, but by multiplying by 1,8. A 50 °C increase is exactly equal to a 90 °F increase.
References
Section titled “References”- engineeringtoolbox.com: https://www.engineeringtoolbox.com/si-unit-system-d_30.html
- unitconverters.net: https://www.unitconverters.net/engineering-converters.html
- convertworld.com: https://www.convertworld.com/en/pressure/kilopound-per-square-inch.html