When a car turns, the inner and outer front wheels follow circles of different radius and so must be steered to different angles. Adjust the wheelbase, track width and steering angle to see the inner and outer steer angles and the turn radius update in real time, and build an intuition for Ackermann geometry.
Parameters
Wheelbase L
mm
Distance between the front and rear axles
Track width t
mm
Distance between the left and right front kingpins
Mean (reference) steer angle δ
°
Reference steer angle taken at the rear-axle centre
Results
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Turn radius (rear-axle centre) (mm)
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Inner steer angle δ_inner (deg)
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Outer steer angle δ_outer (deg)
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Ackermann difference (deg)
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Outer front-wheel radius (mm)
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Geometry verdict
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Top-down vehicle turning — Ackermann geometry
All four wheels turn about a common centre on the extended rear-axle line. The inner wheel (red) is clearly steered more sharply than the outer wheel (blue).
Reference turn radius R (to the rear-axle centre), inner steer angle δ_inner and outer steer angle δ_outer. L is the wheelbase, t the track width and δ the mean steer angle. The inner wheel is closer to the turn centre and so always needs the larger steering angle.
Ackermann steer-angle difference Δδ and the turning radius swept by the outer front wheel, R_outer. A larger Δδ means a more pronounced inner-outer angle gap, typical of low-speed, large-steer manoeuvres.
What is the Ackermann Steering Geometry Simulator?
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I always assumed the two front tyres turned to exactly the same angle when you steer. Is that wrong?
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Look closely and they are not the same. When a car goes around a curve, all four wheels actually circle one common "turn centre". That centre sits on the line you get by extending the rear axle straight out sideways. So the inner front wheel, being closer to the centre, follows a smaller circle, while the outer front wheel follows a larger one. To roll cleanly around circles of different radius, the inner and outer wheels have to be steered to different angles.
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I see. So what happens if you just steer both to exactly the same angle, kept parallel?
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Then the circle each wheel "wants" to trace has a different centre. Both wheels point the same way but need different circles, so one or both must skid sideways. That is tyre scrub. Every turn drags rubber across the road, wearing the tyres faster and eating energy. The slower you go and the more you turn the wheel, the bigger the gap. Push the steering-angle slider on the left up toward 40 degrees and watch the difference open up.
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So how is that "steer the inner wheel more" actually achieved? The driver does not steer the two wheels separately.
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That is the clever part of the Ackermann linkage. You angle the left and right steering arms inward, into a slight V. Then, even with a single tie rod connecting both wheels, the inner wheel automatically takes a larger angle than the outer one as you steer. The driver does nothing special. It is named after the 19th-century patent agent Rudolph Ackermann, although he actually popularised an invention by the German Georg Lankensperger.
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Is this turn radius the same as the minimum turning radius you see in brochures?
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They are related. The "outer front-wheel radius" this tool gives is the radius of the circle the outer tyre traces. The brochure "minimum turning radius" adds the front body overhang and tyre width on top, so it is the radius drawn by the outermost point of the body — usually about 0.3 to 0.5 m larger. It is the number you use to judge whether a road is wide enough for a U-turn, or whether you can fit into a parking space. Move the wheelbase slider and you will see how a longer wheelbase enlarges the turn radius.
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Do racing cars use the same Ackermann geometry?
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Not necessarily. Full Ackermann is ideal when speeds are low and the tyres barely slip, but when you take a corner at high lateral acceleration the tyre slip angles take over. The heavily loaded outer tyre changes the picture, and the required steer-angle relationship can reverse compared to low speed. That is why formula cars sometimes deliberately run anti-Ackermann, steering the outer wheel more sharply. Most road cars use partial Ackermann — around 50 to 80 percent of the ideal — as a compromise with cost and ride.
Frequently Asked Questions
When a car turns, all four wheels rotate about one common centre that lies on the extended line of the rear axle. The inner front wheel is closer to that centre than the outer one, so it traces a circle of smaller radius. To roll cleanly around a smaller circle it must be steered to a sharper angle, so the inner wheel always takes a larger steer angle than the outer. If the two wheels were held parallel, one or both would have to slide sideways, scrubbing the tyres and wasting energy. The Ackermann linkage angles the steering arms inward so this difference is generated automatically.
The difference equals inner steer angle minus outer steer angle, and it depends on the steering input and the wheelbase-to-track ratio. At small steering angles (highway driving) it is close to zero; at large angles (parking) it can reach several degrees up to about ten. This tool classifies a difference below 2 degrees as almost parallel (small steer), 2 to 8 degrees as standard Ackermann, and 8 degrees or more as a large steer angle with a pronounced difference. Passenger cars typically show a 5 to 10 degree difference at full lock.
Full Ackermann delivers the geometrically ideal inner and outer steer angles, assuming low speed and tyres that barely slip. Most production cars use partial Ackermann (roughly 50 to 80 percent of ideal) as a compromise between cost, linkage packaging and ride. Racing cars sometimes deliberately use anti-Ackermann, where the outer wheel is steered more sharply. At high lateral acceleration the tyre slip angles dominate and the heavily loaded outer tyre changes the ideal geometry, so the low-speed ideal can reverse.
The outer front-wheel turning radius is the radius of the outermost arc swept by a wheel, and it is a base figure for estimating the minimum turning circle and the road or parking width a vehicle needs. This tool computes it as outerRadius = sqrt((R + t/2)^2 + L^2) from the rear-axle turn radius R, track width t and wheelbase L. The published minimum turning radius adds the body overhang and tyre width on top, and is used to judge whether a U-turn or a parking manoeuvre is feasible.
Real-World Applications
Passenger-car steering design: The steering linkage of every conventional automobile is laid out using Ackermann geometry. By choosing the knuckle (steering) arm angle and the tie-rod position, engineers build in the inner-outer steer-angle difference. Most mass-produced cars use partial Ackermann — around 50 to 80 percent of ideal — as a compromise with cost and ride, and this tool helps you understand the baseline ideal (full Ackermann) those designs are measured against.
Turning paths of large vehicles and trailers: Buses, heavy trucks and articulated trailers have long wheelbases and very large turn radii. When designing intersections, ramps and car-park layouts, planners must reserve enough swept space for these vehicles, including the off-tracking between the front and rear wheel paths. You can see directly how a longer wheelbase enlarges the turn radius by moving the wheelbase slider in this tool.
Motorsport setup: Racing teams choose between full, partial and anti-Ackermann depending on the tyre slip angles and load transfer during cornering. The optimum differs between circuits dominated by slow corners and high-speed tracks, and the Ackermann percentage is tuned by relocating the steering-arm attachment points. The geometric ideal computed here is the starting reference for that work.
Autonomous driving and path planning: Self-driving and robotics path planners frequently approximate vehicle motion with a "bicycle model", whose foundation is the Ackermann relation R = L/tanδ. Tight-space three-point turns, automated parallel parking and the steering control of forklifts and AGVs (automated guided vehicles) all rest on this wheeled-vehicle kinematics.
Common Misconceptions and Pitfalls
A common misconception is that "as long as the Ackermann geometry is correct, the tyres will never scrub". The formulas here are a "kinematic" ideal that assumes low-speed driving where the tyres barely slip sideways. In real driving, cornering tyres always develop slip angles, and load transfer changes the contact load on the inner and outer wheels. At high lateral acceleration the geometry that was ideal at low speed can become a disadvantage — which is exactly why racing cars use anti-Ackermann. Treat Ackermann geometry strictly as a low-speed reference.
Next, the assumption that "the steer angle is a single number". With an Ackermann linkage the inner and outer wheels always have different angles by design. The "mean (reference) steer angle" in this tool is a representative value taken at the rear-axle centre, and it is distinct from the actual handwheel angle or the steering gear ratio of a real car. In design work you must distinguish the inner steer angle, the outer steer angle and the reference angle, and always be clear about which one you are discussing.
Finally, the misconception that "wheelbase and track width affect cornering in the same way". The turn radius R = L/tanδ is directly proportional to the wheelbase L, so lengthening L enlarges the turn radius directly. Track width t, on the other hand, strongly affects the inner-outer steer-angle difference Δδ but does not appear in the reference turn radius R about the rear-axle centre at all. A long wheelbase favours straight-line stability but hurts the turning circle — explore this trade-off by moving the parameters in this tool.
How to Use
Enter wheelbase (mm): typical passenger car 2700–2900 mm, SUV 3000–3200 mm
Set track width (mm): standard front axle 1500–1600 mm for compact vehicles, 1700–1800 mm for trucks
Input desired steer angle (deg): 0–45° for normal turning maneuvers, up to 50° for extreme parking
Simulator calculates inner/outer wheel angles using Ackermann geometry equations and reports turn radius at rear-axle centre
Worked Example
Mid-size sedan with wheelbase 2800 mm, track width 1550 mm, commanded steer angle 25°. Ackermann geometry yields inner front wheel δ_inner = 28.6°, outer δ_outer = 22.1°, difference 6.5°. Turn radius (rear-axle centre) = 5840 mm. Outer front-wheel path radius = 6380 mm. Without Ackermann compensation, both wheels at 25° produces understeer and tire scrub at highway speeds; geometry correction reduces slip angle and wear.
Practical Notes
Ackermann difference increases with steer angle and wheelbase; compact cars (WB 2500 mm) show ~4° difference at 30°, while long-wheelbase trucks (WB 4000 mm) exceed 7°
Track width primarily affects absolute radius magnitudes; narrow tracks (1400 mm) produce tighter turns than wide SUV setups (1800 mm) at identical steer input
Verify geometry verdict: "Correct Ackermann" confirms proper mechanical linkage; deviations indicate worn tie-rods or bent steering arms requiring alignment check
Use for kinematic analysis only; add tire slip model for real cornering forces above 0.5g lateral acceleration