Turning Radius Calculator (Wheelbase & Steering Angle)

How it works

turning radius (outer front wheel) R = wheelbase ÷ sin(δ) · turning circle = 2 × R · outer rear radius = wheelbase ÷ tan(δ) · inner rear radius = outer rear radius − track · Ackermann inner angle = arctan(wheelbase ÷ inner rear radius) · δ = outer front wheel steering angle

At low speed a car turns about a point on the line of its rear axle. With Ackermann steering geometry each front wheel points along a circle around that point, so the inner wheel steers more than the outer one. The outer front wheel traces the largest circle, and twice its radius is the curb-to-curb turning circle quoted in specifications. The wall-to-wall figure is larger because the bumper overhangs the wheels, and tyre slip makes real values a little bigger than this geometric estimate.

Worked example

A car with a 2.7 m wheelbase whose outer front wheel steers 35°: R = 2.7 ÷ sin 35° = 2.7 ÷ 0.574 = 4.71 m, so the turning circle is 9.41 m curb to curb. The outer rear wheel follows a 3.86 m radius, the inner rear 2.31 m, and the inner front wheel must steer 49.5°.

Sources: Ackermann steering geometry · Turning radius

Frequently asked questions