How to use the ackermann steering and turning radius calculator
- Choose meters or inches, then enter the wheelbase and the distance between the two steering pivots.
- Enter the angle of the inner wheel, the one on the inside of the turn.
- Optionally open the advanced options and enter a measured outer angle to find the percent Ackermann.
- Read the ideal outer wheel angle and the turn radii.
Formula
cot(outer) = cot(inner) + pivot distance / wheelbase
Rear axle radius at the inner wheel = wheelbase / tan(inner)
Rear axle radius at the outer wheel = inner radius + pivot distance
Front wheel path radius = wheelbase / sin(wheel angle)
Percent Ackermann = (inner - measured outer) / (inner - ideal outer) x 100
In pure Ackermann steering the lines through all four wheel axles meet at one point on the extension of the rear axle, so no wheel scrubs sideways in a slow turn.
A small car
The wheelbase is 2.7 m, the pivots are 1.5 m apart and the inner wheel is steered 30 degrees. The ideal outer angle is 23.612 degrees.
The rear axle radius is 4.677 m at the inner wheel, 5.427 m at the middle and 6.177 m at the outer wheel. The outer front wheel follows a path of radius 6.741 m and the inner front wheel 5.400 m. If the outer wheel measures 25.5 degrees, the steering is 70.4% Ackermann.
Why the inner wheel turns more
When a car turns, the wheels on the inside follow a smaller circle than the wheels on the outside. If both front wheels pointed the same way, one of them would have to drag sideways. The Ackermann layout turns the inner wheel more than the outer one so that all four wheels roll about a common center.
The geometry gives the exact outer angle for a chosen inner angle. The wider the pivots are compared with the wheelbase, the larger the difference between the two angles becomes.
Real steering is not always pure
At speed, tires work at a small slip angle, and the best angles differ from pure Ackermann. Race cars often use less Ackermann, or even the reverse, so that the outer tire, which carries more load, turns as much as it needs. Off-road and farm vehicles often sit close to the pure form for tight low-speed turns.
The percent Ackermann compares the measured outer angle with the ideal, where 100% is the pure form and 0% is parallel steering. Use measured angles from a turntable or an alignment rack for a real vehicle.
Assumptions and limits
- Low-speed rolling with no tire slip, on a flat surface.
- The distance between the pivots is entered by you. The track width is close but not the same.
- Radii are to the wheel center line, not to the body or the tire edge.
- The figures are examples. Nothing is uploaded.
Frequently asked questions
What is the turning circle?
The page gives the path radius of the outer front wheel. The full curb-to-curb circle also depends on the body overhang and tire width, which are not included.
What does 100% Ackermann mean?
The outer wheel turns exactly the ideal angle, so all four wheels share one turn center.
Can the percentage be above 100%?
Yes, if the outer wheel turns less than the ideal. That is more than pure Ackermann, which some designs use deliberately.
Does it work for a trailer or a four-wheel steering car?
No. It models a vehicle with a fixed rear axle and two steered front wheels.