A Centripetal Force Calculator

Anything moving in a circle needs a force pointing at the centre, and its size depends on speed squared, mass and how tight the turn is.

MassIn kilograms. Enter 0.15 for 150 grams.Tangential speedSpeed along the circular path, in metres per second.RadiusRadius of the circle in metres, not the diameter.

Centripetal force

Centripetal acceleration: 180
Angular velocity: 15
Revolution period: 0.4189

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

F = m x v squared / r

F: Centripetal force
m: Mass
v: Tangential speed
r: Radius

How to check the result by hand

1
Get the mass in kilograms
Convert grams to kilograms by dividing by 1,000. A 150 gram mass is 0.15 kilograms, and forgetting this step overstates the answer by a factor of 1,000.
2
Square the speed
Multiply the speed by itself. Twelve metres per second squared is 144, and this is where the strong speed dependence enters.
3
Multiply by the mass
Multiply the squared speed by the mass. For 0.15 kilograms and 144 that is 21.6.
4
Divide by the radius
Divide by the radius in metres. Twenty-one point six divided by 0.8 gives 27 newtons, the inward force needed.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Centripetal Force page.