How to use this calculator
Enter the mass, the speed and the radius of the circular path. The force is the net inward force needed to keep the object on the circle.
Formulas
Centripetal accelerationac = v²r = ω²r
Centripetal forceFc = mv²r
Angular velocity and periodω = vr T = 2πrv
Worked example
1,200 kg car at 72 km/h around a 50 m curve (the default)
- v = 72/3.6 = 20 m/s.
- ac = 20²/50 = 8 m/s² (0.82 g).
- Fc = 1,200 × 8 = 9.6 kN, supplied by tire friction.
- T = 2π × 50/20 = 15.7 s per lap.
On a flat road that friction needs μ ≥ 8/9.81 = 0.82, which is why curves are banked.
Frequently asked questions
Is there an outward centrifugal force?
Not in an inertial frame. What you feel pushing you outward is your body’s tendency to go straight while the car turns.
What supplies the centripetal force?
Whatever acts inward: string tension, friction, gravity for orbits, or the normal force on a banked track.