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Centripetal Force (F = mv²/r)

Also known as circular motion force

Fc=mv2rF_c = \frac{m v^2}{r}
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Worked example: 1200 kg at 20 m/s, r = 100 m → F = 4800 N. Press Try an example to run it live, then adjust anything.

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Where Centripetal Force (F = mv²/r) fits

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See also

Centripetal Acceleration (a = v²/r): Both use tangential speed and circular path radius.Speed in Circular Motion (v = 2πr/T): Both use tangential speed and circular path radius.Centripetal Acceleration (a = ω²r): Both use circular path radius.Linear Speed from Rotation (v = ωr): Both use tangential speed.
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Centripetal Force (F = mv²/r) explained

rmvFc

An object moving in a circle is accelerating even at constant speed, because its direction keeps changing, and sustaining that requires a net inward force of mv²/r. Swing a ball on a string and the string's tension supplies it; drive through a curve and tire friction does. A 1,200 kg car rounding a 50 m curve at 20 m/s needs FcF_c = (1200)(20²)/50 = 9,600 N of sideways grip: nearly the car's own weight.

The v² is the part engineers respect: doubling speed quadruples the required force, which is why exit ramps post low advisory speeds and why racetracks bank their turns. Banking tilts the road's normal force inward so friction isn't doing all the work. Solving for v takes the principal positive square root, since speed is a magnitude. And centripetal force is not a new kind of force; it's simply the name for whatever real force happens to point toward the centre.

Centripetal Force (F = mv²/r) formula

Fc=mv2rF_c = \frac{m v^2}{r}
Where
  • FcF_c= Centripetal force (N)
  • mm= Mass (kg)
  • vv= Speed (m/s)
  • rr= Radius (m)
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Circular and centripetal motion

7 formulasCentripetal acceleration and force in both linear and angular form, plus the curve-speed results that follow when friction or a bank supplies them.

Revised 16 October 2026
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formula.expert. (2026, October 16). Centripetal Force (F = mv²/r) Formula & Calculator. https://formula.expert/solvers/centripetal-force

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