Calculate vehicle turning radius, steering angle or wheelbase with a chosen path reference. Circle mode also estimates a simplified radial swept band, not the road width required for a U-turn.
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Turning Radius Formula
The turning radius is calculated from the bicycle model of vehicle steering. The calculator uses the front axle reference formula:
TR = WB / sin(a)
An equivalent formulation referenced by many engineering texts uses the rear axle center as the reference point:
TR₁ = WB / tan(a)
Formula source: Liniger A. & Van Gool L. (2020). “Safe Motion Planning for Autonomous Driving using an Adversarial Road Model,” Robotics: Science & Systems XVI.
- TR = turning radius (front axle center path)
- TR₁ = turning radius (rear axle center path)
- WB = wheelbase (center-to-center distance, front axle to rear axle)
- a = steering angle of the front wheels (not the steering wheel angle)
The outer front-wheel-center radius is TR₂ = sqrt(WB² + (TR₁ + TW/2)²), where TW is front wheel-center spacing. This point model excludes tire-edge and body geometry and is not a manufacturer curb-to-curb measurement. For steering angles between 0° and 90°, tan(a) exceeds sin(a), so the front axle center follows a larger-radius path than the rear axle center. See the MathWorks Ackermann geometry equations.
Ackermann Steering Geometry
In ideal low-speed rolling, the inner and outer front wheels follow different arcs. The equations below use R = rear-axle-center path radius and TW = front track width. They apply when R is greater than TW/2:
Inner wheel angle: θ₁ = arctan(WB / (R − TW/2))
Outer wheel angle: θ₂ = arctan(WB / (R + TW/2))
For WB = 2.7 m, TW = 1.5 m and a rear-axle-center radius R = 6 m, the ideal inner angle is about 27.22° and the outer angle about 21.80°, a difference of 5.41°. The bicycle-model angle is an equivalent angle; an individual inner or outer wheel angle should not be substituted for it. Actual steering systems may differ from this ideal geometry.
Example Problem
How to calculate a turning radius?
- Determine the wheelbase.
Measure center-to-center from the front axle to the rear axle. For this example, the wheelbase is 2.7 m (approximately 8.86 ft).
- Determine the steering angle.
Use the equivalent front steering angle from straight ahead, not steering-wheel rotation or an individual wheel angle. For this example, use 35 degrees.
- Calculate the turning radius.
Front axle path: TR = WB / sin(a) = 2.7 / sin(35°) = 2.7 / 0.5736 = 4.71 m. Rear axle path: TR = WB / tan(a) = 2.7 / tan(35°) = 2.7 / 0.7002 = 3.86 m.
Vehicle Turning Radius Reference
The table contains illustrative bicycle-model examples, not manufacturer specifications. Its circle diameters refer to the front axle center, with 2 × WB / sin(a). Tire-edge curb-to-curb and body-envelope wall-to-wall values require additional geometry; use the manufacturer’s stated measurement for a particular vehicle. Articulated vehicles require another model.
| Illustrative vehicle class | Example wheelbase | Equivalent steer angle | Front-center circle diameter |
|---|---|---|---|
| City car example | 1.9 m / 6.23 ft | 38° | 6.17 m / 20.25 ft |
| Compact car example | 2.6 m / 8.53 ft | 35° | 9.07 m / 29.74 ft |
| Mid-size sedan example | 2.8 m / 9.19 ft | 35° | 9.76 m / 32.03 ft |
| Compact SUV example | 2.7 m / 8.86 ft | 34° | 9.66 m / 31.68 ft |
| Large SUV / truck example | 3.5 m / 11.48 ft | 32° | 13.21 m / 43.34 ft |
| Two-axle bus example | 6.0 m / 19.69 ft | 28° | 25.56 m / 83.86 ft |
| Articulated transit bus | Multiple wheelbases | Model dependent | Not modeled by this calculator |
Road and Parking Design Standards
The following approximate simple-curve corner radii reflect selected TxDOT intersection guidance. They are not vehicle minimum turning radii or universal construction requirements. Choose geometry for actual turning movements, vehicle encroachment, lanes and pedestrian crossings; the guidance also discusses compound curves and swept-path analysis.
| Application | Approximate simple-curve corner radius | Traffic consideration |
|---|---|---|
| Minor cross street; passenger vehicles | 4.6–7.6 m (15–25 ft) | Passenger vehicles; site conditions apply |
| Minor cross street; new construction where space permits | 7.6 m (25 ft) or more | Selected traffic and turning movement |
| Major cross street, where feasible | 9.1 m (30 ft) or more | Occasional truck; encroachment matters |
| Frequent large trucks or buses | 12.2 m (40 ft) or more | Compound curves may better fit the path |
| Arterial-arterial with frequent large vehicles | 22.9 m (75 ft) or more | WB-62 or larger; consider compound curves |
FAQ
What is a turning radius?
The turning radius is the radius of the circular arc a vehicle follows when the steering wheel is at a given angle. It is measured from the Instantaneous Center of Rotation (ICR) to a specific reference point on the vehicle, typically the front axle center or the outer front tire contact patch. A smaller value means the vehicle can turn in a tighter space.
What is a good turning radius for a car?
A smaller measured turning circle generally helps in confined maneuvers. Whether a car fits a parking aisle or a U-turn depends on its width, overhang, steering range, approach and exit path, not a single universal radius threshold. Compare like-for-like manufacturer measurements and check the actual maneuver.
Is a smaller or larger turning radius better?
A smaller minimum turning radius generally helps with low-speed parking and tight turns. This value alone does not determine high-speed stability or steering sensitivity; those depend on other vehicle characteristics and operating conditions.
Do bigger tires affect turning radius?
A different tire size may affect available steering lock and body clearance, depending on the vehicle. Track width means wheel-center spacing; tire width is a separate dimension. Wider tires change the tire-edge envelope and do not automatically change track width or radius by a fixed amount. Reassess measured clearances and the manufacturer’s specifications after a modification.
What is the difference between turning radius and turning circle?
Turning circle is a circular path’s diameter, twice its radius. Curb-to-curb measurements concern the outer tire path, while wall-to-wall measurements consider the vehicle body envelope and are typically larger. Specify the measurement reference: this calculator’s axle-center and outer-wheel-center paths exclude tire-edge and body overhang geometry.
How does wheelbase affect turning radius?
At the same equivalent steering angle, a 10% increase in wheelbase increases the front- and rear-axle-center path radii by 10%, because those radii are proportional to wheelbase. Outer-wheel, tire-edge and body-envelope measurements also depend on track width and other dimensions. A larger steering angle reduces the center-path radius in the ideal low-speed model.
How is turning radius measured on a real vehicle?
Real-vehicle measurements must identify the reference and test conditions. At low speed on a suitable flat surface, a full-lock circular path can be measured to the outer tire boundary; its diameter divided by two gives that path’s radius. Body-envelope measurements also account for overhang. Use the manufacturer’s stated procedure and specifications rather than equating this ideal point model with a certified measurement.
