If you've ever blanked on how many pascals are in a bar during an exam, or spent ten minutes converting feet to meters on a problem set that was supposed to take fifteen — this post is for you. Unit conversions are the unglamorous backbone of every engineering discipline. They don't get a dedicated lecture. Nobody writes a textbook chapter about them. And yet they show up everywhere: thermodynamics, fluid mechanics, structural analysis, electrical circuits, heat transfer.
This is the cheat sheet I wish someone had handed me in my first year. Bookmark it, print it, tape it to your monitor — whatever works.
Why Unit Conversions Still Trip Up Engineers
Most conversion mistakes don't come from ignorance. They come from context switching — you're deep in a calculation, your brain is juggling three variables, and you grab a conversion factor from memory that's slightly wrong. The result? An answer that's off by a factor of 1,000, and a grade that reflects it.
The fix isn't to memorize more. It's to memorize the *right* ones with enough repetition that they become automatic. Everything below is worth that investment.
Length Conversions
These come up in civil, mechanical, and aerospace constantly. Get them locked in.
| From | To | Factor |
|---|---|---|
| 1 inch | centimeters | 2.54 cm |
| 1 foot | meters | 0.3048 m |
| 1 yard | meters | 0.9144 m |
| 1 mile | kilometers | 1.60934 km |
| 1 meter | feet | 3.28084 ft |
| 1 kilometer | miles | 0.62137 mi |
| 1 millimeter | inches | 0.03937 in |
The one to burn in: 1 inch = 2.54 cm exactly. Everything else in imperial-to-metric length derives from this.
Mass and Weight Conversions
Note the distinction engineers often blur under exam pressure: mass is measured in kilograms or slugs; weight is a force (Newtons or pounds-force). The conversions below are mass-to-mass unless noted.
| From | To | Factor |
|---|---|---|
| 1 kilogram | pounds (mass) | 2.20462 lb |
| 1 pound (mass) | kilograms | 0.45359 kg |
| 1 slug | kilograms | 14.5939 kg |
| 1 metric ton | kilograms | 1,000 kg |
| 1 short ton (US) | kilograms | 907.185 kg |
| 1 ounce | grams | 28.3495 g |
Watch out for: slug vs. kilogram in dynamics problems. In SI, F = ma gives Newtons when mass is in kg and acceleration is in m/s². In US customary, F = ma gives pound-force only when mass is in slugs, not pounds-mass.
Force Conversions
| From | To | Factor |
|---|---|---|
| 1 Newton | pound-force | 0.22481 lbf |
| 1 pound-force | Newtons | 4.44822 N |
| 1 kilonewton | pound-force | 224.809 lbf |
| 1 kip | Newtons | 4,448.22 N |
| 1 dyne | Newtons | 1 × 10⁻⁵ N |
The one to burn in: 1 lbf ≈ 4.448 N. You'll use this in statics, mechanics of materials, and fluid mechanics.
Pressure and Stress Conversions
Pressure conversions are where students most commonly lose points. The number of units in use simultaneously — Pa, kPa, MPa, bar, atm, psi, psf — is genuinely excessive.
| From | To | Factor |
|---|---|---|
| 1 Pascal (Pa) | N/m² | 1 (by definition) |
| 1 kilopascal (kPa) | psi | 0.14504 psi |
| 1 megapascal (MPa) | psi | 145.038 psi |
| 1 bar | Pascals | 100,000 Pa |
| 1 atmosphere (atm) | kPa | 101.325 kPa |
| 1 atmosphere (atm) | psi | 14.696 psi |
| 1 psi | kPa | 6.89476 kPa |
| 1 mm Hg (Torr) | Pa | 133.322 Pa |
The Pressure Hierarchy Worth Knowing
1 atm ≈ 101.325 kPa ≈ 1.01325 bar ≈ 14.696 psi ≈ 760 mmHg
If you know this chain, you can navigate between any pressure unit without a table.
Energy and Work Conversions
Thermodynamics, heat transfer, and power systems all mix SI and imperial energy units freely. This table covers the critical ones.
| From | To | Factor |
|---|---|---|
| 1 Joule (J) | N·m | 1 (by definition) |
| 1 Joule | calories (thermochemical) | 0.23885 cal |
| 1 kilocalorie (kcal) | Joules | 4,184 J |
| 1 British Thermal Unit (BTU) | Joules | 1,055.06 J |
| 1 BTU | kilocalories | 0.25200 kcal |
| 1 kilowatt-hour (kWh) | Joules | 3,600,000 J |
| 1 kilowatt-hour | BTU | 3,412.14 BTU |
| 1 electronvolt (eV) | Joules | 1.602 × 10⁻¹⁹ J |
| 1 foot-pound (ft·lbf) | Joules | 1.35582 J |
The one to burn in: 1 BTU ≈ 1,055 J. Every heat transfer problem that mixes US and SI systems runs through this.
Power Conversions
| From | To | Factor |
|---|---|---|
| 1 Watt (W) | J/s | 1 (by definition) |
| 1 kilowatt (kW) | horsepower (mechanical) | 1.34102 hp |
| 1 horsepower (mechanical) | Watts | 745.7 W |
| 1 horsepower (metric) | Watts | 735.499 W |
| 1 BTU/hour | Watts | 0.29307 W |
| 1 ton of refrigeration | Watts | 3,516.85 W |
| 1 ton of refrigeration | BTU/hour | 12,000 BTU/hr |
Note: mechanical horsepower and metric horsepower are not the same. Most engineering problems in the US use mechanical hp (745.7 W).
Temperature Conversions
Temperature is unique because it uses offset conversions, not just multiplication factors. Get the formulas, not just the numbers.
| Conversion | Formula |
|---|---|
| Celsius → Fahrenheit | °F = (°C × 9/5) + 32 |
| Fahrenheit → Celsius | °C = (°F − 32) × 5/9 |
| Celsius → Kelvin | K = °C + 273.15 |
| Fahrenheit → Rankine | °R = °F + 459.67 |
| Kelvin → Rankine | °R = K × 9/5 |
Critical Temperature Reference Points
| Point | °C | °F | K |
|---|---|---|---|
| Absolute zero | −273.15 | −459.67 | 0 |
| Water freezes | 0 | 32 | 273.15 |
| Water boils | 100 | 212 | 373.15 |
| Body temperature | 37 | 98.6 | 310.15 |
For temperature differences (ΔT), you don't use the offset — just the scale factor. A change of 1°C = a change of 1 K = a change of 1.8°F.
Volume and Flow Conversions
Fluid mechanics students, this section is for you specifically.
| From | To | Factor |
|---|---|---|
| 1 liter | cubic meters | 0.001 m³ |
| 1 gallon (US) | liters | 3.78541 L |
| 1 gallon (US) | cubic feet | 0.133681 ft³ |
| 1 cubic foot | liters | 28.3168 L |
| 1 cubic meter | gallons (US) | 264.172 gal |
| 1 barrel (oil, US) | gallons | 42 gal |
| 1 barrel (oil, US) | liters | 158.987 L |
For flow rates, just divide your volume conversion factor by seconds. 1 gallon per minute (GPM) = 6.309 × 10⁻⁵ m³/s.
Angle Conversions
Short and essential for dynamics, control systems, and robotics.
| From | To | Factor |
|---|---|---|
| 1 radian | degrees | 57.2958° |
| 1 degree | radians | 0.017453 rad |
| 1 revolution | degrees | 360° |
| 1 revolution | radians | 2π rad |
| 1 RPM | rad/s | π/30 ≈ 0.10472 rad/s |
The Conversion Habits That Actually Prevent Mistakes
Beyond memorizing numbers, three process habits will save you more points than any table.
Always carry units through your algebra. Don't strip units to "clean up" your work. Units that cancel correctly are a real-time error check. If your answer to a velocity problem comes out in kg·m instead of m/s, you'll catch it immediately.
Write out your conversion as a fraction equal to 1. Instead of multiplying 55 mph by 1.609 and hoping for the best, write: 55 mi/hr × (1.609 km / 1 mi) = 88.5 km/hr. The unit cancellation is explicit and auditable.
Check your answer against physical intuition. A car speed of 88,500 km/hr should immediately trigger a flag. A pressure of 0.00689 MPa when you expected something close to atmospheric should too. Build the habit of sanity-checking magnitude, not just the calculation.
Check your unit conversions instantly
A Note on SI Prefixes (The Multipliers Underneath Everything)
Every conversion table above is useless if you're fuzzy on SI prefixes. These aren't optional.
| Prefix | Symbol | Multiplier |
|---|---|---|
| Giga | G | 10⁹ |
| Mega | M | 10⁶ |
| Kilo | k | 10³ |
| Hecto | h | 10² |
| Deci | d | 10⁻¹ |
| Centi | c | 10⁻² |
| Milli | m | 10⁻³ |
| Micro | μ | 10⁻⁶ |
| Nano | n | 10⁻⁹ |
| Pico | p | 10⁻¹² |
The conversions on this page won't make you a better engineer by themselves. But getting them wrong — or having to look them up mid-problem under exam pressure — will cost you. Repetition is the only real answer. Use them, run through the tables when you have a spare ten minutes, and let the ones you use most often become reflexive.
The ones you use every week will memorize themselves. The ones you use once a semester need the table. That's why you bookmark it.
