Road Banking Angle Calculator
When a road or racetrack curves, engineers tilt the surface inward so that vehicles lean into the bend rather than sliding outward. This sideways tilt is the banking angle, also called superelevation, and at the right value a vehicle travelling at the design speed is held on the curve by gravity and the road's support alone, with no need for tire friction at all. That makes the curve safe even when the surface is wet or icy. This calculator finds that ideal angle. You enter the design speed and the radius of the curve, and it returns the banking angle in degrees, using standard gravity. The relationship rises with speed, which appears as a square, and falls as the radius grows, so a fast, tight curve needs a steep bank while a gentle, wide one barely tilts. The vehicle's mass never enters: the ideal angle is the same for a motorcycle and a loaded truck. The defaults describe a 100 meter radius curve at 25 meters per second, which is 90 kilometers per hour. Every figure here is computed deterministically from the standard physics formula shown below, with a worked example that reconciles exactly to the calculator defaults.
The ideal banking angle is the arctangent of the speed squared divided by the radius times gravity: theta = atan(v^2 / (r x g)), with g fixed at 9.81 m/s^2. For a speed of 25 m/s (90 km/h) on a radius of 100 m, the banking angle is 32.50 degrees.
Banking angle formula
theta = atan(v^2 / (r x g))
v = design speed (m/s)
r = curve radius (m)
g = 9.81 m/s^2 (fixed standard gravity)
theta = ideal banking angle (degrees)
This is the no-friction ideal: the angle at which the horizontal component of the road's support exactly provides the centripetal force. Speed enters as a square, so faster design speeds tilt the curve more steeply, while a larger radius needs a gentler bank.
Worked example
Take a design speed of 25 meters per second (90 kilometers per hour) on a curve of radius 100 meters, with g fixed at 9.81 meters per second squared.
- Square the speed: 25^2 = 625
- Denominator: r x g = 100 x 9.81 = 981
- Ratio: 625 / 981 = 0.6371
- theta = atan(0.6371) = 0.5673 rad = 32.50 degrees
The banking angle is 32.50 degrees. These are the calculator's default inputs, so the result above matches the widget exactly.
Banking angle at a 100 m radius
| Speed | v in m/s | Banking angle |
|---|---|---|
| 36 km/h | 10 | 5.82 degrees |
| 54 km/h | 15 | 12.92 degrees |
| 72 km/h | 20 | 22.18 degrees |
| 90 km/h | 25 | 32.50 degrees |
Ideal no-friction angles for a fixed 100 m radius and g = 9.81 m/s^2. Real roads add a friction margin and rarely bank this steeply at the higher speeds.
Road banking angle calculator: frequently asked questions
What is the banking angle of a road?
The banking angle is the sideways tilt, or superelevation, built into a curved road or track so that a vehicle at the design speed is held on the curve by gravity and the normal force alone, with no reliance on friction. It is the angle at which the road surface leans inward toward the center of the curve.
Does the ideal banking angle depend on the vehicle's mass?
No. The formula theta equals the arctangent of v squared divided by r times g contains only the speed, the radius and gravity. The vehicle's mass cancels out, so a motorcycle and a truck share the same ideal banking angle for a given speed and curve radius.
What value of g does the calculator use?
It uses standard gravity, g equal to 9.81 meters per second squared. This is fixed in the calculation, so you only enter the design speed and the curve radius. The result is the ideal angle for those conditions, ignoring friction.
Is the speed in meters per second or km/h?
The calculator takes the speed in meters per second to match SI units throughout. The default of 25 meters per second is 90 kilometers per hour. To convert from km/h, divide by 3.6 before entering the value, or from mph multiply by about 0.447.
Why ignore friction in the ideal angle?
The ideal banking angle is the design case where a vehicle needs no sideways friction at all, which keeps the curve safe even on a wet or icy surface. Real roads add a friction margin so vehicles can travel a range of speeds, but the no-friction ideal sets the baseline geometry.
Official sources
- Highway geometry and physics references: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.