By Zencalcy Editorial TeamLast reviewed About us
Any object moving in a circle is accelerating toward the centre even if its speed is constant, because its direction keeps changing. That centripetal acceleration is v²/r, and the force needed to produce it is m v²/r — supplied by friction, tension, gravity or whatever constraints the object.
Force, speed or radius for motion in a circle.
F = m v² / r a = v² / r
v is the tangential speed and r is the radius of the circular path. The force points toward the centre; it is not a new kind of force but the net inward force from real interactions.
| Symbol | Meaning |
|---|---|
| F | Centripetal force, in newtons. |
| m | Mass, in kilograms. |
| v | Tangential speed, in metres per second. |
| r | Radius of the circular path, in metres. |
A 2 kg object moving at 10 m/s on a 5 m circle needs 2 × 100 / 5 = 40 N toward the centre. Its centripetal acceleration is 20 m/s², about 2 g.
Continue with the Coefficient of Restitution Calculator, Drag Force Calculator, or the Force Calculator — or browse more dynamics tools and all physics calculators.
Yes, and disproportionately so: force scales with the square of speed. Doubling speed quadruples the centripetal force for the same radius.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026