Calculator
Fields marked * are required. Choose an input mode, then enter vehicle geometry. Results appear above after you submit.
Formula used
This tool uses common low-speed kinematic steering relationships.
Ackermann (ideal) wheel angles
δin = arctan( L / (R − T/2) )
δout = arctan( L / (R + T/2) )
δavg = arctan( L / R )
Where L is wheelbase, T is track width, and R is the turn radius to the rear axle midpoint.
Curvature mode
k = 1 / R
δavg = arctan( L · k )
Useful when curvature comes from mapping, sensors, or path planning.
Steering wheel + ratio
δavg ≈ (SWA / SR)
R ≈ L / tan(δavg)
SWA is steering wheel angle, SR is steering ratio (deg/deg).
Optional dynamics (illustrative)
yaw rate r = v / R
lateral acceleration ay = v² / R
These assume steady-state circular motion without tire slip modeling.
How to use this calculator
- Select an input mode that matches your known data.
- Enter wheelbase and track width using your chosen units.
- Provide radius, curvature, or steering wheel inputs as required.
- Optionally enter speed to estimate yaw rate and lateral acceleration.
- Press Calculate to show results above the form.
- Download CSV or PDF to archive or share outputs.
Example data table
These examples assume ideal Ackermann geometry and radius mode.
| Wheelbase L (m) | Track T (m) | Radius R (m) | Inner δ (deg) | Outer δ (deg) | Average δ (deg) | Lat accel (g) |
|---|---|---|---|---|---|---|
| 2.70 | 1.60 | 10.00 | 16.36 | 14.04 | 15.11 | 0.708 |
| 2.85 | 1.55 | 12.00 | 14.25 | 12.58 | 13.36 | 1.049 |
| 2.50 | 1.45 | 8.00 | 18.96 | 15.99 | 17.35 | 0.393 |
Tip: tighter radius increases inner angle and lateral acceleration.
FAQs
1) What does Ackermann steering mean?
Ackermann geometry steers the inner wheel more than the outer wheel. It aligns wheel paths toward a common instantaneous center of rotation, reducing tire scrub in low-speed turns.
2) Which radius should I enter?
Use the turn radius to the rear axle midpoint, measured in plan view. If you only know a curb-to-curb circle, convert it carefully or use curvature mode with k = 1/R.
3) Why must radius exceed half the track width?
For ideal Ackermann, the inner wheel uses R − T/2. If R is too small, that term becomes zero or negative, making the angle undefined and physically unrealistic for the assumed geometry.
4) What is Parallel steer used for?
Parallel steer sets inner and outer wheel angles equal. It is useful for simplified models, some linkages at small angles, or quick comparisons when exact Ackermann behavior is not required.
5) How accurate is the steering wheel angle method?
It estimates average road wheel angle using steering ratio, then derives radius from geometry. Real systems vary with compliance, tire slip, and variable-ratio racks, so treat it as a first-order approximation.
6) Can this calculator predict tire slip angles?
Not directly. The tool is kinematic and assumes ideal rolling without slip. You can still use the lateral acceleration output to feed a tire model, if you have cornering stiffness data.
7) Why is the outer front path radius larger?
During a turn, the outer front wheel travels a wider arc around the instantaneous center. That is why its path radius and turning circle diameter are larger than the inner wheel’s path radius.
8) What units should I prefer for engineering work?
Meters are easiest for consistency, especially with curvature and dynamics. If you use inches or feet, the calculator converts internally, but be consistent across wheelbase, track width, and radius.