Centripetal Force & Acceleration Calculator

Inward acceleration and force for any object moving in a circle.

Formulas

From linear velocity: ac = v² / r, F = m·v² / r
From angular velocity: ac = ω²·r, F = m·ω²·r
Relation: v = ω·r

How to use

  1. Enter mass and radius.
  2. Pick whether you know linear speed v or angular speed ω and enter the value.
  3. Calculate.

Physics behind circular motion

An object moving in a circle at constant speed is still accelerating — its velocity vector keeps changing direction. The acceleration always points toward the centre and has magnitude v²/r. By Newton's second law, a net inward force of size m·v²/r is required. For a car taking a corner, that force is friction. For a satellite, it is gravity. For a ball on a string, it is tension.

Worked example

m = 1 kg, r = 2 m, v = 4 m/s

a = v²/r = 16/2 = 8 m/s²
F = m·a = 8 N

Related tools

Angular Velocity Torque Moment of Inertia Newton's 2nd Law

FAQs

What is centripetal force?

The net inward force that keeps an object on a circular path.

Is centrifugal force real?

Only in a rotating reference frame (where it's a fictitious force).

How do ω and v relate?

v = ω·r, so ac = v²/r = ω²·r.