Banked Curve Angle

\theta = \arctan\!\left(\frac{v^{2}}{r g}\right)

sig figs

Worked example: 25 m/s on a 150 m curve → 23.02°. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter

g_{n} = 9.80665\ \text{m/s}^{2}

Standard acceleration of gravity · exact

Where Banked Curve Angle fits

Missing an input?

rMinimum Radius of a Horizontal Curve at a Design Speed (AASHTO)

Your answer feeds

Load Factor in a Coordinated Level Turn

In this toolkit

Circular and centripetal motion7 formulas

Around the bend →

Grade 12Grade 12 Physics

Test your skills in the Exam Room: new numbers every attempt. Free lessons for students, no sign-up, just pure learning.

See your Report Card

Learning zone

Banked Curve Angle explained

Tilt a roadway and the surface's normal force gains an inward horizontal component; set the tilt so that component alone supplies mv²/r and the turn works even on ice, since mass cancels and tan θ = v²/rg. A 150 m curve designed for 25 m/s needs arctan(625 ⁄ (150 × 9.80665)) ≈ 23°. Railways call the same idea cant, and the maths dates to the 1830s when engineers first had trains fast enough to overturn.

Real tracks push it hard: Daytona banks 31°, Talladega 33°, and Bristol's short oval 28°, letting stock cars corner at speeds friction alone could never hold. The design is speed-specific: go slower than the design speed and the car tends to slide down the bank, go faster and friction has to make up the difference, which is why highway ramps combine a modest 4–8% superelevation with a posted advisory speed rather than relying on banking alone.

Banked Curve Angle formula

\theta = \arctan\!\left(\frac{v^{2}}{r g}\right)

Where

$\theta$ = Bank angle (°)
$v$ = Design speed (m/s)
$r$ = Curve radius (m)

In this toolkit

Circular and centripetal motion

7 formulasCentripetal acceleration and force in both linear and angular form, plus the curve-speed results that follow when friction or a bank supplies them.

Revised 16 October 2026

Cite this page

formula.expert. (2026, October 16). Banked Curve Angle Formula & Calculator. https://formula.expert/solvers/banked-curve-angle

https://formula.expert/solvers/banked-curve-angle