Two famous incidents show what's at stake. In 1999 NASA lost the Mars Climate Orbiter because one team's software reported thruster impulse in pound-force seconds while another team's software expected newton-seconds, a factor of 4.45. And in 1983 an Air Canada Boeing 767 ran out of fuel in mid-air, later nicknamed the Gimli Glider, because the fuel load had been worked out with a pounds-per-litre factor where a kilograms-per-litre one was needed, leaving it with less than half the fuel the crew thought they had. The pilots glided it to a safe landing on a disused runway; nobody was killed.
Most unit mistakes are less dramatic but just as easy to make. Here they are.
1. Squared and cubed units
1 m = 100 cm, but 1 m² is not 100 cm². Square the factor as well:
1 m² = (100 cm)² = 10,000 cm²
1 m³ = (100 cm)³ = 1,000,000 cm³ = 1,000 litres
1 ft² = (12 in)² = 144 in²
A wall 2.4 m by 4 m has an area of 9.6 m². In square centimetres that's 9.6 × 10,000 = 96,000 cm², not 960. If a spec sheet quotes something per cm², an error here is a factor of 100.
The unit converter has separate area and volume sections so you don't have to remember the squared factors.
2. Gauge pressure vs absolute pressure
Most pressure gauges read gauge pressure: how far above atmospheric pressure you are. A flat tyre reads 0, even though the air inside is at about 1 bar. Absolute pressure is gauge pressure plus atmospheric (1.01325 bar at sea level). Gas laws need absolute pressure, and they also need absolute temperature in kelvin.
A tyre is set to 2.2 bar (gauge) at 15 °C. After a long drive the air inside reaches 45 °C. What does the gauge read now, assuming the volume doesn't change?
Wrong: 2.2 × 45/15 = 6.6 bar. That uses gauge pressure and Celsius, and triples the pressure.
Right: convert to absolute units first.
P₁ = 2.2 + 1.013 = 3.213 bar (abs) T₁ = 15 + 273.15 = 288.15 K
T₂ = 45 + 273.15 = 318.15 K
P₂ = P₁ × T₂ / T₁ = 3.213 × 318.15 / 288.15 = 3.548 bar (abs)
Gauge reading = 3.548 − 1.013 = 2.53 bar
A rise of about 0.33 bar, not a tripling. It's also why tyre pressures should be checked when the tyres are cold.
On datasheets, look for "psig" or "barg" (gauge) and "psia" or "bara" (absolute). If neither is stated, ask.
3. Temperatures vs temperature differences
Converting a temperature uses °F = °C × 9/5 + 32. Converting a temperature change uses only the 9/5:
20 °C (a temperature) = 68 °F
a rise of 20 °C = a rise of 36 °F (not 68)
A change of 1 °C is exactly the same size as a change of 1 K, so in formulas like Q = mcΔT you can use either for ΔT. But for anything involving a ratio of temperatures (gas laws, radiation, efficiency of heat engines) you must use kelvin.
Energy to heat 2 kg of water from 15 °C to 60 °C, with c = 4,186 J/(kg·K):
Q = m c ΔT = 2 × 4186 × (60 − 15) = 376,740 J ≈ 0.105 kWh
ΔT is 45 whether you think of it in °C or K.
4. Power vs energy: kW and kWh
A kilowatt (kW) is a rate: how fast energy is used. A kilowatt-hour (kWh) is an amount: 1 kW for 1 hour, which is 3.6 MJ.
- A 3 kW kettle boiling for 2 minutes uses 3 × (2/60) = 0.1 kWh.
- A battery "rated at 10 kWh" stores energy; one "rated at 5 kW" can deliver energy at that rate. A home battery needs both figures.
- "kW per hour" is almost always a mistake for kWh, and "kWh per hour" is just kW.
5. Mass vs force: kilograms vs newtons
In everyday speech we "weigh" things in kilograms, but kilograms measure mass. Weight is a force, measured in newtons: weight = mass × g. On Earth, a 50 kg load weighs 50 × 9.80665 = 490 N.
The confusion is made worse by the old unit kilogram-force (kgf), defined as 9.80665 N, which still appears on some load ratings, spring scales and older drawings. Pound (lb) and pound-force (lbf) have the same problem in imperial units, and that's exactly the confusion that cost NASA the Mars Climate Orbiter.
6. Three different tons
| Name | Used in | Mass |
|---|---|---|
| Tonne (metric ton) | Everywhere using SI | 1,000 kg |
| Long ton | Traditional UK | 2,240 lb = 1,016.05 kg |
| Short ton | USA | 2,000 lb = 907.18 kg |
They're within 12% of each other, which is close enough to go unnoticed and far enough to overload a lifting point.
7. UK gallons, US gallons and fuel economy
An imperial gallon is exactly 4.54609 litres; a US gallon is 3.785411784 litres. So the same car does about 20% more miles per UK gallon than per US gallon. To convert to litres per 100 km:
L/100 km = 282.48 / mpg (UK)
L/100 km = 235.21 / mpg (US)
50 mpg (UK) = 5.65 L/100 km
50 mpg (US) = 4.70 L/100 km
Note that L/100 km is upside down compared with mpg: lower is better. You can't convert between them with a simple multiplying factor, which is why the unit converter doesn't list mpg alongside length or volume.
8. Angles: rpm, degrees and radians
Formulas such as power = torque × angular speed need angular speed in radians per second. 3,000 rpm is 3000 × 2π / 60 = 314.16 rad/s. Plug in 3,000, or 50 (revolutions per second), and the answer is wrong by a large factor. More in degrees vs radians.
The habit that catches all of these
Write the units next to every number, all the way through the calculation, and cancel them like algebra. If the units on the answer come out as anything other than what you expected, you've made a mistake, and usually the leftover units tell you where.
Power = torque × angular speed
= 40 N·m × 314.16 rad/s
= 12,566 N·m/s
= 12,566 W (since 1 N·m/s = 1 J/s = 1 W)
Radians are dimensionless, so they drop out. If you'd used rpm, you'd be left with N·m/min, a clear sign something needs converting.
A second habit: before you trust a result, ask whether it's the right size. A domestic kettle using 100 kWh, a tyre at 6.6 bar after a drive, or a 50 kg box weighing 50 N should all set off alarms.