Enter the wheelbase length and the steering angle of the front wheels into the calculator to determine the turning radius. The calculator solves for any missing variable given the other two.
- All Automotive Calculators
- Wheel Speed Calculator
- Piston Speed Calculator (mean)
- HP to Torque Calculator
- CC to HP Calculator
- GVWR (Gross Vehicle Weight Rating) Calculator
- Trailer Tongue Length Calculator
- Aircraft Turn Radius Calculator
- MPH to G Force Calculator
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 curb-to-curb turning radius reported by manufacturers adds approximately half the front track width (TW) to the front axle formula: TR₂ = WB / sin(a) + TW/2. Because sin(a) > tan(a) for angles under 90°, the front axle path is always tighter than the rear axle path for a given steering angle. The difference is small at low angles but becomes significant near maximum lock.
Ackermann Steering Geometry
During any turn, the inner and outer front wheels must trace arcs of different radii to avoid tire scrub. Ackermann geometry defines the required angle for each wheel given the overall turning radius (R) and front track width (TW):
Inner wheel angle: θ₁ = arctan(WB / (R − TW/2))
Outer wheel angle: θ₂ = arctan(WB / (R + TW/2))
The inner wheel always steers at a sharper angle than the outer. For a typical passenger car (WB = 2.7 m, TW = 1.5 m) taking a 6 m radius turn, the inner wheel requires about 24.2° and the outer about 19.8° – a spread of 4.4°. Road cars typically achieve 70–100% Ackermann compliance. Race cars sometimes use anti-Ackermann (outer wheel turned more than inner) to equalize tire slip angles under high lateral load, trading low-speed scrub for better high-speed grip balance.
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.
This is the angle the front wheels are turned from straight ahead. Most passenger cars achieve a maximum lock of 30 to 40 degrees. For this example, the steering angle is 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 below shows typical turning circle diameters (curb-to-curb) for common vehicle classes. Manufacturers measure curb-to-curb at maximum steering lock. Wall-to-wall adds roughly 0.4–0.8 m per side for body overhang.
| Vehicle Class | Typical Wheelbase | Max Steer Angle | Turning Circle (curb-to-curb) |
|---|---|---|---|
| City car (e.g., Smart ForTwo) | 1.9 m / 6.2 ft | ~38° | ~8.7 m / 28.5 ft |
| Compact car | 2.5–2.7 m / 8.2–8.9 ft | 34–37° | 10.0–11.0 m / 33–36 ft |
| Mid-size sedan | 2.7–2.9 m / 8.9–9.5 ft | 33–36° | 10.6–11.8 m / 35–39 ft |
| Compact SUV / crossover | 2.6–2.7 m / 8.5–8.9 ft | 33–36° | 10.8–11.8 m / 35–39 ft |
| Full-size SUV / truck | 3.2–3.7 m / 10.5–12.1 ft | 30–33° | 12.8–14.5 m / 42–47.5 ft |
| School bus (Type C/D) | ~5.5–6.5 m / 18–21 ft | 25–30° | 13.7–15.8 m / 45–52 ft |
| City transit bus (articulated) | ~5.8 m / 19 ft (tractor) | varies | ~22–24 m / 72–79 ft |
Road and Parking Design Standards
Civil engineers use minimum turning radius values from AASHTO (American Association of State Highway and Transportation Officials) and local design manuals to size intersection corner radii, ramp curves, and parking aisles. The values below reflect AASHTO Green Book guidance and TxDOT design standards for new construction:
| Application | Minimum Turning Radius | Design Vehicle |
|---|---|---|
| Residential street intersection | 4.5 m (15 ft) | Passenger car (P) |
| Urban minor cross-street | 7.6 m (25 ft) | Single-unit truck (SU) |
| Urban arterial intersection | 9.1 m (30 ft) | Semi-trailer (WB-12) |
| Frequent heavy truck route | 12.2 m (40 ft) | Combination truck (WB-19) |
| Arterial-arterial (large truck combinations) | 22.9 m (75 ft) | Long combination (WB-67) |
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 curb-to-curb turning circle under 10.5 m (34 ft) is considered tight for a passenger car and aids parking in urban environments. City cars like the Smart ForTwo achieve roughly 8.7 m. Most family sedans and crossovers fall in the 10.5–12 m range. Full-size pickups typically require 13–14.5 m. Anything over 13 m starts to create difficulty in standard 90° parking lots designed around 6 m drive aisles.
Is a smaller or larger turning radius better?
Smaller is better for parking, tight intersections, and urban maneuverability. Larger turning radii generally improve high-speed directional stability because the steering geometry is less sensitive near center. Sports cars tuned for track use optimize for minimum turning radius at low speed; long-distance touring vehicles prioritize stability at highway speeds.
Do bigger tires affect turning radius?
Yes, in two ways. Larger diameter tires reduce the available steering lock angle because the tire contacts the wheel arch sooner, which increases the minimum turning radius. Wider tires also increase the effective track width (TW), raising the curb-to-curb turning circle by approximately TW/2 per the formula TR₂ = WB / sin(a) + TW/2. A 20 mm increase in tire width alone adds roughly 10 mm to the curb-to-curb radius.
What is the difference between turning radius and turning circle?
Turning circle is the full diameter of the circular path (radius x 2). Manufacturers publish two turning circle figures: curb-to-curb (measured to the inside face of the curb, excluding sidewall bulge) and wall-to-wall (the swept diameter of the widest body point). Wall-to-wall is always larger. For parking and road design, curb-to-curb is the standard reference.
How does wheelbase affect turning radius?
Wheelbase is the dominant variable. Because TR = WB / sin(a), a 10% increase in wheelbase raises the turning radius by exactly 10% for the same steering angle. This is why compact cars with short wheelbases turn tighter than full-size trucks even when both share a similar maximum steering lock angle. Engineers seeking a smaller turning radius without changing package size must increase the maximum steering lock angle, which requires redesigning the steering knuckle geometry.
How is turning radius measured on a real vehicle?
The standard test drives the vehicle in a full lock circle on a flat surface and measures the diameter of the outer tire path with a tape measure or chalk line. Dividing by 2 gives the curb-to-curb turning radius. SAE J695 defines the formal test procedure used by manufacturers. The test is performed at low speed (under 5 km/h) to eliminate centripetal force effects on steering geometry.
