Theoretical Tractive Force Calculator
Calculate theoretical tractive force from wheel torque and tire radius. Estimate the resulting acceleration and grade capability.
Combine wheel torque and tire radius.
Theoretical Tractive Force Calculator: Tire Size Inputs
Compare two tire sizes here. Use the formulas and reference tables below for this tool's specific calculation.
How Theoretical Tractive Force Calculator Works?
The Theoretical Tractive Force Calculator works by dividing wheel torque by tire radius and comparing the result with vehicle weight. The tool uses 4 steps.
Enter wheel torque
Type the axle torque, or the engine torque with gear, axle and efficiency values.
Enter tire radius
Type the loaded radius or the tire size for the tool to calculate radius.
Enter vehicle mass
Type the gross mass, for example 2,000 kg (4,409 lb).
Read force and capability
The calculator returns force in N and lbf, acceleration in m/s² and g, and the steepest grade the force can hold before rolling resistance and traction limits.
Theoretical Tractive Force Calculator Formula
The Theoretical Tractive Force Calculator formula is F_t = T_wheel ÷ r_loaded.
F_t = T_wheel ÷ ra = F_t ÷ mθ = arcsin(F_t ÷ (m × 9.81))F_max = μ × N_drive- T_wheel
- Total torque at the driven wheels (N·m)
- r
- Loaded tire radius (m)
- m
- Vehicle mass (kg)
- μ
- Tire-road friction coefficient (0.7–1.0 on dry asphalt)
Worked example
5,961 N·m of wheel torque on a 0.445 m (17.5 in) radius gives 13,411 N (3,015 lbf). On a 2,000 kg (4,409 lb) truck, that equals 6.71 m/s² (0.68 g) before drag and rolling resistance.
Theoretical Tractive Force Calculator Conversion Table
The Theoretical Tractive Force Calculator conversion table converts one tractive force into acceleration and grade angle for 6 vehicle masses.
| Vehicle mass | Tractive force | Acceleration | Acceleration (g) | Max grade angle |
|---|---|---|---|---|
| 1,200 kg (2,646 lb) | 13,411 N | 11.18 m/s² | 1.14 g | Force exceeds weight |
| 1,600 kg (3,527 lb) | 13,411 N | 8.38 m/s² | 0.85 g | 58.7° |
| 2,000 kg (4,409 lb) | 13,411 N | 6.71 m/s² | 0.68 g | 43.1° |
| 2,500 kg (5,512 lb) | 13,411 N | 5.36 m/s² | 0.55 g | 33.1° |
| 3,000 kg (6,614 lb) | 13,411 N | 4.47 m/s² | 0.46 g | 27.1° |
| 3,500 kg (7,716 lb) | 13,411 N | 3.83 m/s² | 0.39 g | 23.0° |
Grade angle uses θ = arcsin(F ÷ m·g) and ignores rolling resistance. Traction limits cap real values on low-grip surfaces.
What is Theoretical Tractive Force Calculator?
A Theoretical Tractive Force Calculator is a tool that converts wheel torque into the pushing force a tire applies to the road. Tractive force is the force that accelerates the vehicle, climbs grades and pulls trailers.
The result is theoretical. Real force is capped by tire grip. A tire can transmit no more force than the friction coefficient times the load on the driven wheels.
Tire radius sits in the denominator. A larger tire lowers tractive force in direct proportion.
What are the uses of Theoretical Tractive Force Calculator?
There are 4 main uses of the Theoretical Tractive Force Calculator, including grade climbing and towing comparisons.
Grade climbing
Estimate the steepest grade a setup climbs in first gear.
Towing comparisons
Compare pulling force with and without a tire upgrade.
Traction limits
Compare engine force with the grip limit of the tires.
Engineering coursework
Teach the link between torque, radius and force.