Centripetal Force Calculator

F_c = m × v² / r. Force required to keep object in circular motion.

Inputs

Result

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General calculation reads

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How to use this calculator

  • Enter mass, velocity, radius.
  • Read force and acceleration.

About this calculator

Centripetal force directs toward the center of circular motion. F_c = mv²/r. Doubling speed quadruples required force; halving radius doubles it. A 1500 kg car taking a 50m corner at 20 m/s (~45 mph) needs 12,000 N (1200 kg of equivalent push) — supplied by tire friction. Lateral g rises sharply with speed: tightening curve from 50m to 25m at same speed doubles g-load.

Frequently asked

Centripetal vs. centrifugal?+
Centripetal: real, toward center, is the actual physical force (friction, tension, normal). Centrifugal: apparent, in rotating reference frame.
Banked turns reduce force?+
No — they redirect the source. Highway banking lets a portion of normal force (not just friction) provide centripetal — safer at speed.
Why does it scale as v²?+
Acceleration in uniform circular motion = ω²r = v²/r. Newton's 2nd law: F = ma.
Roller coaster loops?+
At the top: normal force points down. At minimum speed, mg = mv²/r → v = √(gr). Below this, you fall away from track.
Car cornering grip?+
Max F_c = μmg (friction-limited). Solving: max v on flat curve = √(μgr). For μ=0.7, r=50m: max ≈ 18.5 m/s ≈ 41 mph.

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