Turning Radius Calculator (Ackermann Steering)
Turning circle of a car, van or trailer from its wheelbase, track width and maximum steering angle, with how tight the inner rear wheel cuts in.
Results
What this tool does
With Ackermann steering all four wheels roll around a common centre in line with the rear axle, so the inner rear wheel follows the tightest circle and the outer front wheel the widest — that is the turning circle quoted in brochures, measured kerb to kerb at the tyre. The difference between the two is the ring the wheels sweep, which is why long vehicles cut corners. Bodywork overhanging the wheels sweeps a larger 'wall-to-wall' circle than this. Real steering geometry is close to, but not exactly, ideal Ackermann.
Formula
inner rear radius = L ÷ tan δᵢ · outer front radius = √(L² + (L ÷ tan δᵢ + T)²) · δₒ = atan(L ÷ (L ÷ tan δᵢ + T))
Variables
| Symbol | Meaning | Unit |
|---|---|---|
wb | Wheelbase | m |
sa | Maximum steering angle of the inner front wheel | ° |
tw | Track width (between wheel centres) | m |
TC | Turning circle (outer front wheel) | m |
RR | Radius of the inner rear wheel | m |
OA | Steering angle the outer wheel needs (Ackermann) | ° |
SW | Width of the ring the wheels sweep | m |
Worked example
- Wheelbase2.7 m
- Maximum steering angle of the inner front wheel38 °
- Track width (between wheel centres)1.55 m
- Turning circle (outer front wheel)11.38 m
- Radius of the inner rear wheel3.46 m
- Steering angle the outer wheel needs (Ackermann)28.3 °
- Width of the ring the wheels sweep2.23 m
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.