Enter your object's radius, period or frequency, and this Circular Motion Calculator computes angular velocity, tangential speed, and centripetal acceleration all at once. Plug in real-world values — like a satellite orbit or a spinning wheel — and see every key circular motion parameter laid out clearly below.
Centripetal Acceleration
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Angular Velocity
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Tangential Speed
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Period
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Frequency
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Revolutions per Minute
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Uniform circular motion describes an object moving along a circular path at a constant speed. Although the speed is constant, the velocity is always changing direction, which means the object is continuously accelerating toward the centre of the circle — this inward acceleration is called centripetal acceleration.
Start with any two known values — typically radius and either frequency, period, or angular velocity. Angular velocity ω = 2πf, tangential speed v = ωr, and centripetal acceleration a = ω²r = v²/r. This calculator handles all those relationships automatically once you enter your known values.
Frequency (f) and period (T) are simple reciprocals: f = 1/T and T = 1/f. If an object completes 2 revolutions per second (f = 2 Hz), its period is 0.5 s. Both describe how fast an object orbits, just from different perspectives.
Linear (tangential) velocity v is related to angular velocity ω by the radius r of the circular path: v = ω × r. A larger radius means a higher tangential speed for the same angular velocity, which is why the outer edge of a spinning disc moves faster than the inner edge.
Centripetal acceleration is the inward acceleration that keeps an object on its circular path. It is directed toward the centre of the circle and calculated as a = v²/r or equivalently a = ω²r, where v is tangential speed, ω is angular velocity, and r is the radius.
In uniform circular motion, the speed (magnitude of velocity), the radius, the period, the frequency, the angular velocity, and the magnitude of centripetal acceleration are all constant. What continuously changes is the direction of the velocity and the direction of the centripetal acceleration vector.
Centripetal force is the net force required to keep an object moving in a circle: F = m × a_c, where m is the object's mass and a_c is the centripetal acceleration computed by this calculator. The force always points toward the centre and is supplied by tension, gravity, friction, or a normal force depending on the scenario.
Yes. The formulas used here — ω = 2πf, v = ωr, and a = ω²r — are standard physics relationships valid for any uniform circular motion, from satellite orbits and car cornering to rotating machinery and centrifuges. Just ensure your inputs are in consistent SI units (metres, seconds, Hz) for correct SI outputs.