Paritian

Automotive

Wheel Torque Calculator (Gearing, Tractive Force and Road Speed)

Torque at the wheels, the pushing force at the road and the road speed at a given engine speed, from the engine torque, the gear and final-drive ratios and the tyre radius.

Results

Torque at the driven wheels 3071 N·m
Tractive force at the road (before slip) 9719 N
Road speed at that engine speed 26.2 km/h
Engine power at that torque and speed 78.5 kW
Wheel speed 220 rpm
How it changes
Torque at the driven wheelsGearbox ratio in the chosen gear 0.5 – 6.0. Torque at the driven wheels: 438.75 → 5265Torque at the driven wheels02000400060001.02.03.04.05.06.0Gearbox ratio in the chosen gear

The dashed line marks the value you entered.

What this tool does

Gearing multiplies torque: wheel torque is the engine torque times the gearbox ratio times the final-drive ratio, less the losses in the drivetrain — 85–90 % is a commonly assumed efficiency for a manual gearbox. Dividing by the tyre's rolling radius turns it into the force pushing the car along, which is why first gear pulls hardest while a tall gear trades force for speed. Power is the same in every gear; gearing only decides how it is split between force and speed. The real limit on launch is grip: the tyres cannot transmit more than the friction coefficient times the load on the driven wheels, so this tractive force is a ceiling before slip.

Formula

wheel torque = engine torque × gearbox ratio × final drive × η · F = wheel torque ÷ tyre radius · v = 2π n r ÷ (60 × gearbox × final drive)

Variables

SymbolMeaningUnit
tqEngine torqueN·m
grGearbox ratio in the chosen gear—
fdFinal drive (differential) ratio—
efDrivetrain efficiency (gearbox, differential, shafts)%
rrRolling radius of the tyremm
rpRotational speedrpm
WTTorque at the driven wheelsN·m
FTTractive force at the road (before slip)N
RSRoad speed at that engine speedkm/h
EPEngine power at that torque and speedkW
WRWheel speedrpm

Worked example

  • Engine torque250 N·m
  • Gearbox ratio in the chosen gear3.5
  • Final drive (differential) ratio3.9
  • Drivetrain efficiency (gearbox, differential, shafts)90 %
  • Rolling radius of the tyre316 mm
  • Rotational speed3000 rpm
  • Torque at the driven wheels3071 N·m
  • Tractive force at the road (before slip)9719 N
  • Road speed at that engine speed26.2 km/h
  • Engine power at that torque and speed78.5 kW
  • Wheel speed220 rpm

Limitations

  • The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
  • Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.