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Centripetal Acceleration Calculator

Find the centripetal acceleration of circular motion.

How it is calculated

For motion at constant speed on a circle, the acceleration points toward the centre and has size a = v² ÷ r. Here v is the speed in m/s and r is the radius of the circle in m, so a is in m/s². The tool also divides by standard gravity, a ÷ 9.80665, to express it in g. The radius must be greater than zero. Speed is squared, so the sign does not matter and doubling the speed quadruples the acceleration, while doubling the radius halves it. It assumes uniform circular motion, not a speed that is changing.

Worked example

A car takes a curve of radius 100 m at 25 m/s (90 km/h). Square the speed: 25² = 625. Divide by the radius: 625 ÷ 100 = 6.25 m/s². In g: 6.25 ÷ 9.80665 = 0.64 g. The centripetal acceleration is 6.25 m/s², or 0.64 g.

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Common mistakes

  • Entering speed in km/h. The formula needs m/s; divide km/h by 3.6 first (90 km/h is 25 m/s).
  • Using the diameter as the radius, which makes the acceleration twice too small.
  • Expecting a linear relation with speed. Because v is squared, 50 m/s on the same curve needs four times the acceleration, not twice.
  • Treating the result as a force. It is an acceleration; multiply by the mass to obtain the centripetal force in newtons.

Sources

About this calculator

Centripetal acceleration is the acceleration directed toward the center of a circular path that keeps an object moving in that circle rather than flying off in a straight line, calculated as a = v² / r, where v is the object's speed and r is the radius of the circular path. It can equivalently be written as a = ω²r using angular velocity ω, and this calculator also expresses the result as a multiple of g (9.8 m/s²) for intuitive comparison.

Physics students, engineers, and ride designers use this formula to calculate the forces experienced in a car rounding a curve, a satellite in orbit, a centrifuge spinning a sample, or a passenger on a roller-coaster loop — amusement park engineers specifically check that centripetal acceleration (as "g-force") stays within safe and comfortable limits for riders.

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Comments (1)

  • Editorial team

    The g figure doubles as a grip check for an unbanked, flat curve: the tires need a friction coefficient at least as large as the acceleration in g. A car at 20 m/s on a 50 m radius gives 8.00 m/s², or 0.82 g, which asks a lot of the tires. Banking, speed changes and the car's weight transfer are not part of this number. What kind of motion are you checking, a road bend, a centrifuge or something else?

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