MotionLab

Centripetal Force Calculator

The inward force required to keep anything moving in a curve, from cars on a track to planets in orbit.

Mass (kg)

Speed (m/s)

Radius (m)

Centripetal force (N)

F = mv² / r

What you entered

Mass (kg): 2Speed (m/s): 5Radius (m): 1

1
F = mv² ÷ r
2 × 5² ÷ 1= 50 N

Result

Centripetal force (N): 50

A 2kg mass moving at 5 m/s in a 1m circle needs 50 N of centripetal force.

Centripetal force needed to hold a circular path

Centripetal force is mass times velocity squared divided by radius. It always points toward the centre of the circle.

Mass (kg)	Velocity (m/s)	Radius (m)	Force (N)
0.5	10	1	50.00
70	5	2	875.00
1000	20	50	8000.00
1000	30	100	9000.00
1500	25	80	11718.75

Velocity is squared while radius is not, which is why a modest speed increase demands so much more grip: rows three and four show that going from 20 to 30 m/s on double the radius still needs more force. For a car this force must come entirely from tyre friction, so the maximum cornering speed is set by the friction coefficient and the radius - which is why corners have advisory speeds and why banking a track lets vehicles corner faster without relying on grip alone. There is no outward centrifugal force in an inertial frame; what passengers feel is their own inertia.

Not a separate force, but a role

Centripetal force isn't a distinct type of force like gravity or friction — it's the name for whatever force (tension, friction, gravity) is actually causing the circular motion in a given situation. A car turning relies on friction; a satellite orbiting relies on gravity.

Why tighter turns need more force

Force scales inversely with radius — halving the turning radius at the same speed doubles the required centripetal force, which is why tight highway curves have lower speed limits than gentle ones.

Frequently asked questions

A 1,200 kg car takes a curve of radius 50 m at 20 m/s. What centripetal force is needed?

F = mv²/r = 1200 × 400/50 = 9,600 N. This force comes from tire friction. If the road is wet and friction drops below 9,600 N, the car skids outward — it literally can't turn that fast.

Why do race tracks have banked curves?

Banking adds a component of the normal force toward the center, supplementing friction. At the ideal banking angle, a car can turn without any friction at all — useful on icy roads too. The angle depends on speed and radius: tan(θ) = v²/(rg).

Is centrifugal force real?

In a rotating reference frame, centrifugal force feels real (you're pushed outward on a merry-go-round). In an inertial frame, it's not a real force — your body just wants to go straight (Newton's first law), and the centripetal force is what curves your path inward.

How is centripetal force related to gravity for orbits?

For orbiting bodies, gravity IS the centripetal force: GMm/r² = mv²/r. This sets orbital velocity at v = √(GM/r). The ISS orbits at ~7.66 km/s to balance gravity at 400 km altitude. See the gravitational force calculator.