Educational explanation, not professional design advice. Last reviewed 11 November 2026. Disclaimer
In plain English
Every measurement has a number and a unit. The same length can be written 1 m, 100 cm, 1000 mm or 39.37 in; the quantity is the same, only the unit changes. Engineering mixes units from different countries and trades, so converting correctly is a basic skill — and a common source of costly mistakes.
The International System of Units (SI) is the modern metric system used worldwide in science and engineering. It is built from a few base units, with prefixes such as kilo and milli for larger and smaller sizes.
Technical definition
The SI has seven base units: the metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). All other units are derived from them, for example the newton (N = kg·m/s²) for force, the pascal (Pa = N/m²) for pressure, the joule (J = N·m) for energy and the watt (W = J/s) for power. Prefixes multiply a unit by powers of ten: k (kilo) = 10³, M (mega) = 10⁶, m (milli) = 10⁻³, µ (micro) = 10⁻⁶.
How it works and where it is used
A reliable way to convert is to multiply by a conversion factor equal to one, written as a fraction so that the unwanted unit cancels. For example, 150 psi × (6894.76 Pa ÷ 1 psi) = 1 034 214 Pa = 10.34 bar. Writing the units in every step shows immediately when a factor is upside down.
| Quantity | Conversion | Trap to avoid |
|---|---|---|
| Force | 1 kgf = 9.80665 N | kg is mass, not force |
| Pressure | 1 bar = 100 kPa = 14.504 psi | gauge pressure vs absolute pressure |
| Torque | 1 lbf·ft = 1.3558 N·m | lbf·in is twelve times smaller |
| Power | 1 hp (mechanical) = 745.7 W; 1 metric hp = 735.5 W | several different horsepowers |
| Volume | 1 US gallon = 3.785 L; 1 UK gallon = 4.546 L | US and UK gallons differ by 20% |
| Mass | 1 tonne = 1000 kg; short ton = 907.2 kg; long ton = 1016 kg | “ton” alone is ambiguous |
| Cooling | 1 TR = 12 000 Btu/h = 3.517 kW | tons of refrigeration are not tons of mass |
Formula
value in new unit = value × (size of old unit ÷ size of new unit)
Area factor = (length factor)² Volume factor = (length factor)³
°F = °C × 9/5 + 32 K = °C + 273.15 a temperature difference of 1 K = 1 °C = 1.8 °F
Because 1 m = 1000 mm, 1 m² = 1 000 000 mm² and 1 m³ = 10⁹ mm³ = 1000 L.
Worked example
- Pressure: a compressor set to 150 psi: 150 × 6894.76 = 1 034 214 Pa = 10.34 bar.
- Torque: a bolt specified at 50 lbf·ft: 50 × 1.3558 = 67.8 N·m.
- Area: a plate of 2.5 m² is 2.5 × 1 000 000 = 2 500 000 mm² — not 2500 mm².
- Volume: a tank of 1.7 m³ holds 1.7 × 1000 = 1700 L, or 1700 ÷ 3.785 = 449 US gallons.
- Temperature difference: a 10 K rise is a rise of 18 °F, not 50 °F (50 °F is the temperature that equals 10 °C).
In the workshop and in practice
Use SI units for calculations and convert only at the start (inputs) and the end (results). Keep all values in base units — metres, kilograms, seconds, pascals — inside a formula, then convert the answer to the unit you need. Check that the result has the expected unit (dimensional check): if a force formula gives kg·m/s², it is in newtons; if it gives anything else, there is a mistake.
Common mistakes and misconceptions
- Squaring or cubing the factor wrongly. mm to m divides lengths by 1000, areas by 10⁶ and volumes by 10⁹.
- Treating kilograms as force. A mass of 100 kg weighs about 981 N.
- Mixing gauge and absolute pressure. Absolute = gauge + atmospheric pressure (about 1.013 bar at sea level).
- Converting temperature differences with the +32. The offset applies to temperatures, not to differences.
- Capital and small letters. mW (milliwatt) and MW (megawatt) differ by a factor of a billion; Mb (megabit) and MB (megabyte) by eight.
Related calculators
- Unit Converter — Convert length, area, volume, mass, pressure, force, torque, energy, power, temperature and more.
- Inch Fraction ↔ Decimal ↔ mm Converter — Convert fractional inches (like 3/8") to mm, or mm to the nearest inch fraction.
- Area Calculator — Area and perimeter of rectangles, triangles, trapezoids and ellipses.
Related topics
- Area and Volume of Common Shapes — The formulas for everyday areas and volumes, and how to handle shapes that are made of several simple parts.
References
- BIPM: The International System of Units (SI Brochure, 9th edition)
- ISO 80000-1: Quantities and units — General
- NIST Special Publication 811: Guide for the Use of the International System of Units