Centripetal Force Calculator

Calculate the force and acceleration needed to keep an object moving in a circle.

Please note: Results use idealised models — point masses, no air resistance, ideal gases and uniform materials. Real experiments deviate. Use these for study and estimation, not for engineering sign-off.

What the Centripetal Force Calculator does

Anything moving in a circle is constantly accelerating, because its direction keeps changing even at constant speed. That acceleration points at the centre, and the force producing it must be supplied by something real — friction, tension, gravity or a track.

Formula

  • a = v² ÷ r
  • F = m × v² ÷ r
  • v = 2πr ÷ T
  • Banking angle θ = arctan(v² ÷ (r × g))

Inputs explained

InputUnitRequiredNotes
MassnumberYes
Mass unitone of 6 optionsYes
Speed given asone of 3 optionsYes
Linear velocitynumberIn some modesShown Speed given as is Linear velocity.
Linear velocity unitone of 5 optionsIn some modesShown Speed given as is Linear velocity.
Time per revolutionnumberIn some modesShown Speed given as is Time for one revolution.
Time per revolution unitone of 6 optionsIn some modesShown Speed given as is Time for one revolution.
Revolutions per minuterpmIn some modesAccepts more than 0. Shown Speed given as is Revolutions per minute.
RadiusnumberYes
Radius unitone of 9 optionsYes

How to use it

  1. Choose Mass unit and Speed given as.
  2. Enter Mass and Radius.
  3. Fill in the remaining inputs the form shows for your choice.
  4. Select Calculate.

Worked example

A 1,000 kg car taking a 50 m radius bend at 20 m/s.

Mass
1000 kg
Velocity
20 m/s
Radius
50 m

a = 400 ÷ 50 = 8 m/s², so F = 8,000 N. That needs a friction coefficient of 0.816 — more than dry asphalt reliably gives.

Frequently asked questions

Is centrifugal force real?

Not as a force acting on the object. It is the sensation of your own inertia resisting the turn, and it only appears as a real force if you do the maths in the rotating frame.

Why are racetrack corners banked?

Tilting the surface lets the track’s normal force point partly inwards, supplying the centripetal force without relying on friction — so cars can corner faster and in the wet.

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