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Most mistakes in engineering calculations are unit mistakes: a diameter in millimetres put into a formula that expects metres, or a pressure in psi read as bar. Working consistently in SI units, and checking the dimensions of every equation, removes most of them. Keep this page next to your calculations.
SI base units
Seven base units define everything else. Mechanical engineering uses the first five most.
| Quantity | Unit | Symbol | Dimension |
|---|---|---|---|
| Mass | kilogram | kg | M |
| Length | metre | m | L |
| Time | second | s | T |
| Temperature | kelvin | K | Θ |
| Electric current | ampere | A | I |
| Amount of substance | mole | mol | N |
| Luminous intensity | candela | cd | J |
Derived units
| Quantity | Unit | Symbol | In base units | Dimensions |
|---|---|---|---|---|
| Force | newton | N | kg·m/s² | MLT⁻² |
| Pressure, stress | pascal | Pa | N/m² | ML⁻¹T⁻² |
| Energy, work, heat | joule | J | N·m | ML²T⁻² |
| Power | watt | W | J/s | ML²T⁻³ |
| Torque, moment | newton metre | N·m | kg·m²/s² | ML²T⁻² |
| Frequency | hertz | Hz | 1/s | T⁻¹ |
| Density | — | kg/m³ | kg/m³ | ML⁻³ |
| Dynamic viscosity | pascal second | Pa·s | kg/(m·s) | ML⁻¹T⁻¹ |
| Kinematic viscosity | — | m²/s | m²/s | L²T⁻¹ |
| Angular velocity | — | rad/s | 1/s | T⁻¹ |
Torque and energy share the same base units, but they are different quantities. Write torque as N·m and energy as J to keep them apart.
Prefixes
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| giga | G | 10⁹ | Young’s modulus of steel, 200 GPa |
| mega | M | 10⁶ | Yield strength, 250 MPa |
| kilo | k | 10³ | Load, 30 kN |
| milli | m | 10⁻³ | Dimension, 25 mm |
| micro | µ | 10⁻⁶ | Tolerance or surface finish, 0.8 µm |
A useful identity for stress: 1 MPa = 1 N/mm². If forces are in newtons and lengths in millimetres, stresses come out directly in MPa, and Young’s modulus must be in N/mm² too (steel: 200 000 N/mm²).
Conversion table
| From | To SI | Notes |
|---|---|---|
| 1 inch (in) | 25.4 mm | Exact |
| 1 foot (ft) | 0.3048 m | Exact |
| 1 pound mass (lb) | 0.4536 kg | |
| 1 pound force (lbf) | 4.448 N | |
| 1 kilogram force (kgf) | 9.807 N | Still found on older drawings and gauges |
| 1 psi (lbf/in²) | 6.895 kPa | 1 ksi = 6.895 MPa |
| 1 bar | 100 kPa | 1 bar ≈ 14.5 psi |
| 1 standard atmosphere | 101.325 kPa | |
| 1 horsepower (hp) | 745.7 W | Metric horsepower (PS) = 735.5 W |
| 1 lbf·ft | 1.356 N·m | Torque |
| 1 kWh | 3.6 MJ | |
| 1 BTU | 1055 J | |
| 1 calorie | 4.184 J | |
| 1 rev/min | 2π/60 = 0.1047 rad/s | |
| 1 litre | 0.001 m³ | |
| 1 US gallon | 3.785 L | |
| 1 km/h | 0.2778 m/s | Divide by 3.6 |
| 1 centipoise (cP) | 1 mPa·s | Water at 20 °C is about 1 cP |
| °F to °C | T(°C) = (T(°F) − 32) / 1.8 | |
| °C to K | T(K) = T(°C) + 273.15 | Temperature differences are equal in K and °C |
Worked examples
Worked example 1: hydraulic pressure
A hydraulic pump is rated at 3000 psi. What is that in MPa and bar?
Worked example 2: power from torque and speed
A gearbox output shaft carries 200 N·m at 1500 rev/min. Find the power.
Worked example 3: mixed units
A drawing gives a 1.5 in diameter steel pin. Find its area in mm² and the shear stress under a 2000 lbf single-shear load.
Dimensional analysis
Every term in a correct equation has the same dimensions. Checking this takes a minute and catches missing factors, wrong powers and unit slips.
Worked example 4: is Bernoulli's equation consistent?
Check the three terms of .
- Pressure : ML⁻¹T⁻²
- : (ML⁻³)(L²T⁻²) = ML⁻¹T⁻²
- : (ML⁻³)(LT⁻²)(L) = ML⁻¹T⁻²
Dimensional analysis also builds dimensionless groups such as the Reynolds number, . Its dimensions are (ML⁻³)(LT⁻¹)(L) / (ML⁻¹T⁻¹), which cancel completely. Groups like this let a test on a small model predict the behaviour of a full-size part.
Good habits
- Convert everything to base SI units (or to a consistent N–mm–MPa set) before you start.
- Carry units through every line of a calculation, not only the answer.
- Write the answer with sensible precision: three significant figures is usually enough.
- On drawings, state the unit system once in the title block (for example “All dimensions in mm”) and stay with it.
Key points
- Seven base units define all others; mechanical work uses kg, m, s and K most.
- 1 MPa = 1 N/mm², so the N–mm system gives stresses in MPa directly.
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Check that every term in an equation has the same dimensions.