Power and Weight
Power to Weight: The Ratio That Decides More Than Power
Power per tonne predicts acceleration above the traction limit and says nothing below it. Which weight you divide by can move the answer by 15 per cent on its own.
Power to weight is the most useful single number on a specification sheet and the easiest one to calculate dishonestly. It predicts acceleration well above the traction limit, where the engine is the constraint, and predicts nothing below it, where the tyres are. And because there are four different weights in circulation, the same car can honestly be quoted at 344 or 299 PS per tonne depending on which one is used.
Calculating it so it means something
Divide power by mass. The only decisions are which units and which mass, and both matter more than the arithmetic.
- Use kilowatts per tonne. PS per tonne and hp per tonne are both in circulation and differ by 1.4 per cent from each other, which is enough to reorder a close comparison.
- Use mass in running order. It is the only weight defined in law, including at least 90 per cent fuel and a 75 kg driver, and it is the only one guaranteed to mean the same thing across two manufacturers.
- Use crankshaft power consistently, or wheel power consistently, and never mix them.
| Weight used | Mass | PS per tonne | kW per tonne | Against running order |
|---|---|---|---|---|
| Dry weight | 1,455 kg | 344 | 253 | +15.1 % |
| Kerb weight, unladen | 1,525 kg | 328 | 241 | +9.8 % |
| DIN kerb weight | 1,600 kg | 313 | 230 | +4.7 % |
| Mass in running order | 1,675 kg | 299 | 220 | reference |
What the ratio predicts, and what it does not
Above the traction limit the ratio is close to decisive, because the work needed to change speed is proportional to mass and the rate at which that work can be done is the power. A 100 to 200 km/h run on a 1,600 kg car requires 1.85 MJ, and the time it takes is that energy divided by the power available, plus roughly 8 to 12 per cent for drag and rolling resistance.
Below the traction limit it predicts almost nothing. A launch is limited by the friction coefficient multiplied by the load on driven wheels, and for an all wheel drive car maximum acceleration is μg, in which mass cancels out entirely. A 1,400 kg car and a 2,200 kg car with the same tyres and the same drive layout have the same launch ceiling, whatever their power to weight ratios say.
| Regime | Limit | Does power to weight predict it? |
|---|---|---|
| Standing start to about 100 km/h | Tyre friction and drive layout | No |
| 100 to 200 km/h | Power against mass and drag | Yes, strongly |
| Top speed | Power against drag alone | No, mass barely matters |
| Braking | Tyre friction, mass cancels | No |
| Cornering | Tyre friction and downforce | No |
Read down that table and the ratio's real domain is narrow: one row out of five. It is the right number for a rolling acceleration comparison and the wrong number for almost everything else, which is a stronger claim than the way it is usually used.
Why top speed ignores it
At maximum speed the car is holding a constant velocity, so no work is being done against inertia and mass appears only through rolling resistance. What matters is power against CdA. A heavy, slippery car will out-run a light, draggy one with the same power every time, which is why estate cars sometimes surprise people and why a light car with a large wing does not.
Questions readers ask
How do you calculate power to weight ratio?
Divide power by mass, ideally in kilowatts per tonne, using mass in running order as defined by EU type approval. The unit and the weight definition both matter: PS per tonne and hp per tonne differ by 1.4 per cent, and the weight choice can move the answer by 15 per cent.
Does power to weight predict 0 to 100 km/h?
Poorly. Below about 100 km/h most cars are limited by tyre friction and drive layout rather than power, and for an all wheel drive car the launch ceiling is μg, in which mass cancels out entirely. The ratio predicts rolling acceleration well and standing acceleration badly.
What is a good power to weight ratio?
It depends entirely on which weight was used, which is why the question is hard to answer honestly. On mass in running order, 220 kW per tonne describes a fast car and 300 kW per tonne a very fast one. The same cars quoted against dry weight would read 15 per cent higher.
Why does top speed not follow power to weight?
Because at constant speed no work is being done against inertia. Top speed is set by power against CdA, the drag coefficient multiplied by frontal area, so a heavy slippery car beats a light draggy one with the same power.
Should I use crank or wheel power?
Either, consistently. Brochure figures are crankshaft power measured to SAE J1349, DIN 70020 or UNECE Regulation 85. Dynamometer readings are wheel power and are lower by the drivetrain loss. Mixing the two produces a ratio that means nothing.
Sources
- Commission Regulation (EU) No 1230/2012, on mass in running order, the 90 per cent fuel load and the 75 kg driver.
- UNECE Regulation No. 85, on the net power figure that forms the numerator.
- Autosport technical forum, tyre coefficient of friction, on the friction values that set the traction limit where the ratio stops applying.
Example figures use a 500 PS car at the four weights given. Energy for the 100 to 200 km/h comparison is ½m(v₂² − v₁²) at 1,600 kg.