Centripetal Force Calculator
By Santaji GadepatilinUpdated October 27, 2026
Anything moving in a circle needs a force pulling it towards the centre — centripetal force. It keeps cars on curves, satellites in orbit and water in a spinning bucket.
How to use the centripetal force calculator
Enter the mass, speed and radius to get the centripetal acceleration and force. Or find the maximum safe speed for a given radius and force.
Centripetal force formulas
a = v² ÷ r F = m v² ÷ r
Worked example
A 1,200 kg car takes a 50 m radius bend at 60 km/h (16.67 m/s):
- a = 16.67² ÷ 50 = 5.56 m/s² (0.57 g)
- F = 1,200 × 5.56 = 6.67 kN
Centripetal acceleration on curves
| Speed | Radius 50 m | Radius 100 m | Radius 250 m |
|---|---|---|---|
| 30 km/h | 1.39 m/s² (0.14 g) | 0.69 m/s² | 0.28 m/s² |
| 50 km/h | 3.86 m/s² (0.39 g) | 1.93 m/s² | 0.77 m/s² |
| 80 km/h | 9.88 m/s² (1.01 g) | 4.94 m/s² | 1.98 m/s² |
| 100 km/h | 15.43 m/s² (1.57 g) | 7.72 m/s² | 3.09 m/s² |
| 120 km/h | 22.22 m/s² (2.27 g) | 11.11 m/s² | 4.44 m/s² |
Doubling the speed quadruples the force needed, which is why speed limits drop on tight bends.
Banked curves
Roads and racetracks are banked so that part of the normal force supplies the turning force. With no friction, the ideal banking angle is:
tan θ = v² ÷ (r × g)
For 80 km/h on a 200 m curve, θ = atan(493.8 ÷ 1961) = about 14°.
Angular speed form
If you know revolutions per minute instead of speed:
a = ω² × r, with ω = 2π × rpm ÷ 60
A centrifuge spinning at 3,000 rpm with a 10 cm radius produces about 9,870 m/s², or roughly 1,006 g.
Centripetal vs centrifugal
Centripetal force is the real force pointing towards the centre (friction, tension, gravity). Centrifugal force is the outward push you feel in a turning car, which comes from your body’s inertia in a rotating frame of reference.
Grip limit
On a dry road, tyres can typically provide around 0.7–0.9 g of sideways acceleration; on wet roads much less. At 0.7 g, the maximum speed for a 50 m bend is about √(0.7 × 9.81 × 50) = 67 km/h.
Frequently asked questions
What is centripetal force?
The inward force needed to keep an object moving in a circle. For a car, it is supplied by tyre friction.
Why is taking a bend fast dangerous?
Force rises with the square of speed. Doubling speed needs four times the grip.
What is centrifugal force?
The outward push you feel inside a turning car. It is an effect of your inertia, not a real outward force.
What provides centripetal force for a car turning?
Friction between the tyres and the road. On ice there is little friction, so the car slides outward.
What is the centripetal force formula?
F = m × v² ÷ r, where m is mass, v is speed and r is the radius of the circular path.