Centripetal Force Calculator
Centripetal force, acceleration, g-force and banking angle.
About this tool
Enter the mass, the speed (in m/s, km/h, mph or rpm) and the radius of the circle. The tool gives the centripetal force and acceleration, g-force, angular velocity, the friction coefficient needed and the ideal banking angle.
Why circular motion needs a force
Even at constant speed, an object moving in a circle accelerates towards the centre because its direction keeps changing. The centripetal acceleration is a = v² ÷ r = ω² r, and the force that provides it is F = m v² ÷ r. That force is supplied by something real: tyre friction on a bend, string tension for a whirled ball, gravity for a satellite. A 1,000 kg car on a 50 m radius curve at 20 m/s (72 km/h) needs 8,000 N, an acceleration of 8 m/s² or 0.82 g. On a flat road that requires a tyre-road friction coefficient of at least 0.82, near the limit for dry tarmac and well beyond wet roads. Banking the road at tan θ = v² ÷ (r g), about 39° here, would provide the force with no friction at all. Because force scales with speed squared, doubling speed quadruples it. For spinning parts, enter rpm and radius. Honest limits: this assumes uniform circular motion and ignores aerodynamic downforce and load transfer. Not driving advice. The force calculator and the momentum calculator are related.
Frequently asked questions
What is the formula for centripetal force?
F = m v² ÷ r, where m is mass, v speed and r the radius of the circle.
What is centripetal acceleration?
a = v² ÷ r, directed towards the centre of the circle.
How do I convert rpm to speed?
v = 2πr × rpm ÷ 60, giving metres per second with r in metres.
What is the ideal banking angle?
tan θ = v² ÷ (r g). At that angle no friction is needed to take the curve.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.