Road Superelevation & Minimum Radius Calculator

Understanding the road superelevation and minimum radius calculator — concept and principle

Superelevation is the cross slope that banks a road toward the inside of a curve. Together with tyre–road side friction, it provides the sideways force a vehicle needs to follow the curve. This calculator finds the minimum curve radius for a chosen design speed, maximum superelevation and side friction factor, the key number when laying out a horizontal alignment.

Tilt and grip together push the car toward the centre; together they allow a 252 m curve.

How it is calculated

R_min = V²/(127·(e + f))

V is the design speed (km/h), e the superelevation as a decimal (6% = 0.06) and f the side friction factor. The constant 127 comes from g = 9.81 m/s² and the conversion of km/h to m/s: 9.81 × 3.6² ≈ 127.

The principle

A vehicle moving at speed v on a circle of radius R needs a centripetal acceleration v²/R. On a banked road, part of this comes from the component of gravity along the tilted surface and the rest from side friction. Balancing forces gives (e + f)/(1 − e·f) = v²/(g·R); since e·f is very small, designers drop it and use e + f = v²/(gR). Rearranging for R gives the formula. The friction factor f is not the skid limit of the tyres but a comfort value: it decreases with speed because drivers feel side force more at high speed, and it leaves a margin against skidding on wet roads.

Worked example

Inputs: V = 80 km/h, e = 6%, f = 0.14.
e + f = 0.06 + 0.14 = 0.20.
127 × 0.20 = 25.4.
R_min = 80²/25.4 = 6400/25.4 = 251.97 m.

Each point is the calculator re-run with only “Design speed (km/h)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Design speed (km/h)	Minimum radius (m)
20	15.7480315
40	62.99212598
60	141.7322835
80	251.9685039
100	393.7007874
120	566.9291339
160	1,007.874016

How to read the result

Any curve at or above this radius can be driven at the design speed within the assumed friction; tighter curves need a lower design speed or more superelevation. Because R scales with V², a 20% speed increase needs about 44% more radius. AASHTO tabulates f = 0.14 at 80 km/h, decreasing to about 0.08 at 130 km/h. Maximum superelevation is usually limited to 4–12%, with lower values in urban areas and where snow and ice make slow vehicles slide inward.

Common mistakes

Entering e as 6 instead of 0.06 in hand calculations (the calculator divides by 100).
Using a tyre skid coefficient (0.5 or more) as f, which gives unsafe radii.
Using the minimum radius everywhere; designers prefer flatter curves where terrain allows.

Keep in mind: This is the basic point-mass model. Actual design values for e, f and radius come from your national road standard and must be checked by a qualified highway engineer.

Frequently asked questions

Why not simply bank curves more steeply?

Slow or stopped vehicles would slide inward on ice and trucks could become unstable, so e is capped.

What is superelevation runoff?

The length over which the cross slope changes from normal crown to full superelevation, so drivers are not jolted.

Can I calculate the safe speed of an existing curve?

Yes, rearrange to V = √(127·R·(e + f)), but advisory speeds also consider sight distance and crash history.

Sources: AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book) · N. J. Garber and L. A. Hoel, Traffic and Highway Engineering, Cengage Learning

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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