Circular Velocity Calculator

Physics overview

What is circular velocity?

Circular velocity is the tangential speed of an object moving around a circular path. It equals the distance traveled in one revolution divided by the time required.

Formula

Circular velocity formula

Circular Velocityv = 2πr ÷ T

v is circular velocity in meters per second.
r is radius in meters.
T is period in seconds.

Worked example

A 5 m radius circle has a 10 s period

Write the formula: v = 2πr ÷ T.
Substitute the values: v = 2 × π × 5 ÷ 10.
Calculate the velocity: v ≈ 3.1416 m/s.

Rearranged equations

Solve for radius or period

Radius

r = vT ÷ 2π

Multiply velocity by period, then divide by 2π.

Period

T = 2πr ÷ v

Divide the circumference by circular velocity.

Distance traveled

Why the formula uses 2πr

The expression 2πr is the circumference of the circular path. An object traveling one complete revolution covers this distance during one period.

Units

Standard SI units

Use meters per second for circular velocity, meters for radius, and seconds for period.

Real-world applications

Where circular velocity is used

Rotating laboratory equipment.
Wheels, pulleys, and turntables.
Circular tracks and amusement rides.
Planetary and satellite motion.
Circular-motion experiments.

Calculation limits

Important assumptions

Velocity, radius, and period must be greater than zero.
Motion is assumed to follow a circular path.
Velocity represents tangential speed.
Period represents one complete revolution.
Units are not converted automatically.

Related tools

Use the Centripetal Force Calculator to calculate inward force, mass, velocity, or radius.

Use the Kinetic Energy Calculator to calculate energy from mass and velocity.

Questions and answers