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Rotation · Mechanics

Uniform Circular Motion Calculator

Connect radius, tangential and angular speed, period, frequency, centripetal acceleration, and optional centripetal force for uniform circular motion.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Constant speed magnitude on a circular path of fixed radius

Linear and angular motion

v = ωrω = 2πf = 2π/T

Centripetal acceleration

ac = v²/r = ω²r

Net radial force

Fc = mac
Circular motion

Connect one revolution to its inward acceleration

The speed magnitude and radius are constant; acceleration points toward the centre. Inputs accept up to three decimal places, and displayed results are rounded to at most three decimal places.

ac = v²/r

Enter the radius and one motion quantity.

Using the model

Symbols, assumptions and limitations

Interpretation notes

The object moves on a circle of constant radius with constant speed magnitude. Velocity remains tangent to the path while centripetal acceleration and the net radial force point toward the centre. The force result requires the object’s mass.

Worked examples

See the method in practice

01

Known tangential speed

At 10 m/s on a 2 m radius, the angular speed is 5 rad/s and centripetal acceleration is 50 m/s².

02

Known period

A 3 m radius with a 2 s period gives a speed of about 9.425 m/s and a frequency of 0.5 Hz.

Questions

Frequently asked

Is centripetal force a new type of force?

No. It is the name for the net inward force, which may be supplied by tension, gravity, friction, a normal force, or their combination.

Why is there acceleration at constant speed?

Velocity includes direction. Its continuously changing direction produces an inward acceleration even when its magnitude stays constant.

Can I use rpm?

Yes. Revolutions per minute are converted internally to angular speed or frequency in SI units.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — Uniform Circular Motion

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology