Unit Conversion Cheat Sheet for Engineering Students (SI ↔ Imperial, Pressure, Energy, Power)
The conversions every mechanical, civil, electrical and chemical engineering student actually uses — with the dimensional-analysis method that stops you from losing a $327 million spacecraft.
In 1999 NASA's Mars Climate Orbiter burned up in the Martian atmosphere because one team delivered thruster data in pound-force·seconds while the navigation software expected newton·seconds. A factor of 4.45 — the lbf→N conversion — cost roughly $327 million. Unit conversion is not a "freshman skill". It is the skill.
This cheat sheet collects the conversions that show up in every engineering curriculum, plus the one method that makes errors visible before they become expensive.
1. The method: dimensional analysis (multiply by 1)
Every conversion factor is a fraction equal to 1. Chain them so unwanted units cancel diagonally:
65 mi/h × (1609.344 m / 1 mi) × (1 h / 3600 s) = 29.06 m/sIf a unit doesn't cancel, you flipped a fraction. Write the units out every time — in exams and in code review. It takes ten seconds and catches 90% of mistakes.
2. Length, area, volume
| From | To | Multiply by | Notes |
|---|---|---|---|
| 1 inch | mm | 25.4 | Exact by definition (1959) |
| 1 foot | m | 0.3048 | Exact |
| 1 mile | km | 1.609344 | Exact |
| 1 nautical mile | m | 1852 | Exact; ships, aviation |
| 1 in² | mm² | 645.16 | = 25.4² |
| 1 ft² | m² | 0.09290304 | = 0.3048² |
| 1 acre | m² | 4046.856 | ≈ 0.4047 ha |
| 1 US gallon | L | 3.785412 | UK gallon = 4.546 L — different! |
| 1 ft³ | L | 28.3168 |
3. Mass, force, weight
| From | To | Multiply by |
|---|---|---|
| 1 lbm (pound-mass) | kg | 0.45359237 |
| 1 lbf (pound-force) | N | 4.448222 |
| 1 kgf | N | 9.80665 |
| 1 slug | kg | 14.5939 |
| 1 short ton (US) | kg | 907.185 |
| 1 tonne (metric) | kg | 1000 |
In the US customary system, lbm and lbf are different quantities linked by gc = 32.174 lbm·ft/(lbf·s²). In SI that constant is 1, which is the entire reason SI exists. If you see lb without a subscript in a mechanics problem, ask which one before doing anything.
4. Pressure and stress
| Unit | Pa | Equivalents |
|---|---|---|
| 1 bar | 100 000 | ≈ 0.987 atm ≈ 14.50 psi |
| 1 atm | 101 325 | = 760 mmHg = 14.696 psi |
| 1 psi | 6 894.76 | 1 ksi = 6.895 MPa |
| 1 MPa | 10⁶ | = 1 N/mm² — the structural engineer's favourite identity |
| 1 mmHg (torr) | 133.322 | medical, vacuum |
| 1 inH₂O | 249.09 | HVAC duct pressure |
Remember 1 MPa = 1 N/mm². Steel yield strength of 250 MPa means 250 N on every square millimetre. Working in N and mm avoids 10⁶ factors entirely in stress calculations.
5. Energy, power, and the units that pretend to be each other
| Unit | Joules | Context |
|---|---|---|
| 1 kWh | 3 600 000 | Electricity bills |
| 1 BTU | 1 055.06 | HVAC, US heating |
| 1 kcal (food Calorie) | 4 184 | Nutrition |
| 1 eV | 1.602 × 10⁻¹⁹ | Semiconductors, physics |
| 1 ft·lbf | 1.3558 | Torque-looking, but energy |
| Power | Watts |
|---|---|
| 1 hp (mechanical) | 745.7 |
| 1 hp (metric, PS) | 735.5 |
| 1 BTU/h | 0.29307 |
| 1 ton of refrigeration | 3 516.85 (= 12 000 BTU/h) |
6. Temperature — the only non-multiplicative conversion
°F = °C × 9/5 + 32 K = °C + 273.15
°C = (°F − 32) × 5/9 °R = °F + 459.67For differences (ΔT), drop the offset: a 10 °C rise is an 18 °F rise, and a 10 K rise. Thermal conductivity in W/(m·K) and W/(m·°C) are therefore identical.
7. Quick sanity anchors
- 1 m/s ≈ 3.6 km/h ≈ 2.24 mph
- 1 kg on Earth weighs ≈ 9.81 N ≈ 2.2 lbf
- Room temperature ≈ 20 °C ≈ 68 °F ≈ 293 K
- Atmospheric pressure ≈ 1 bar ≈ 14.7 psi ≈ 10 m of water
- 1 kWh ≈ 3 412 BTU; 1 hp ≈ ¾ kW
Memorize these five lines. When a homework answer says a car travels at 2 900 m/s, the anchor tells you instantly that something is wrong.
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