AmesWeb

Circular Motion Calculator

Use this circular motion calculator to find centripetal acceleration, angular velocity, speed, radius, period, and frequency for uniform circular motion. It works as a centripetal acceleration calculator, uniform circular motion calculator, and radial acceleration calculator.

Uniform Circular Motion Calculator

Select two known parameters. The calculator solves the remaining circular motion quantities automatically.

Calculator Inputs

Use “.” as the decimal separator. Default rounding is 5 decimal places.

Results

f = 1 / T
ω = 2π / T
v = 2πr / T = ωr
ac = v² / r = ω²r
Radius [r]
—
Angular Velocity [ω]
—
Speed [V]
—
Period [T]
—
Frequency [f]
—
Centripetal Acceleration [ac]
—
Meaning of the result

Select two known circular motion quantities and the calculator will solve the rest.

Uniform Circular Motion Diagram

In uniform circular motion, the object moves around a circle at constant speed. Its velocity v is tangent to the circular path, while its centripetal acceleration ac points inward toward the center. The distance from the center to the object is the radius r, and ω represents angular velocity.

Center r ac v ω rotation direction radius r velocity v centripetal ac

Circular Motion Formulas

f = 1 / T
ω = 2π / T
v = 2πr / T = ωr
ac = v² / r = ω²r
  • r = radius
  • ω = angular velocity
  • v = tangential speed
  • T = period
  • f = frequency
  • ac = centripetal acceleration

How to Use the Circular Motion Calculator

  1. Select the two known parameters from the dropdown list.
  2. Enter the corresponding values.
  3. Select the correct units for radius, speed, angular velocity, period, and acceleration.
  4. The calculator solves radius, angular velocity, speed, period, frequency, and centripetal acceleration automatically.
  5. You can also use the Calculate button for a manual refresh.

Examples

Example 1: Find radius from speed and centripetal acceleration

If v = 20 m/s and ac = 5 m/s², then:

r = v² / ac = 20² / 5 = 80 m

Example 2: Find speed from radius and period

If r = 2 m and T = 4 s, then:

v = 2πr / T = 2π(2) / 4 = π ≈ 3.14159 m/s

What This Calculator Helps You Find

This page is useful for searches such as circular motion calculator, centripetal acceleration calculator, uniform circular motion calculator, radial acceleration calculator, tangential velocity calculator, tangential speed calculator, and centripetal acceleration calculator rpm.

FAQ

What is the centripetal acceleration formula?

For uniform circular motion, centripetal acceleration is ac = v²/r = ω²r.

How do you find angular velocity?

You can use ω = 2π/T or ω = v/r.

What is the relation between period and frequency?

Frequency and period are reciprocals: f = 1/T.

Can this calculator solve for radius?

Yes. Several solve modes calculate radius directly from the selected known parameters.

Definitions

Centripetal acceleration (ac): The inward acceleration that continuously changes the direction of velocity in circular motion.

Frequency (f): The number of revolutions per second.

Period (T): The time required for one complete revolution.

Speed (v): How fast the object moves along the circular path.

Velocity: A vector quantity that includes both speed and direction.

Related Physics Calculators

Physics Calculators Acceleration Calculator Free Fall Calculator Projectile Motion Calculator Simple Harmonic Motion Calculator Simple Pendulum Calculator

References

  • Giancoli, Douglas C. Physics: Principles with Applications. Pearson.
  • Standard introductory physics treatment of uniform circular motion and centripetal acceleration.
  • Your current AmesWeb page solves twelve combinations of known circular-motion parameters using these same relationships.