Circular motion speed tool

Circular Velocity Calculator

Solve circular velocity, radius, or period using v = 2πr ÷ T.

Enter two known values

Solve a circular velocity problem

Free tool
m/s

This is the value being calculated.

m

Positive radius of the circular path.

s

Positive time required for one complete revolution.

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

Try an example:

Your circular velocity result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Circular Velocity Calculator determines the speed of an object moving along a circular path. It helps physics students, engineers, and laboratory users analyze rotating systems, orbital motion, wheels, machines, and mechanical components using radius and period relationships.

Formula explanation

Circular velocity calculates the speed required for an object to complete circular motion under given conditions.

Formula

Circular Velocity = 2π × Radius ÷ Period

Worked example

Example: Satellites require specific circular velocity to maintain orbit.

Assumptions

  • Radius and period measurements are accurate.
  • The object follows circular motion with consistent speed.
  • Input values use compatible units.
  • The calculated velocity represents ideal circular motion.

Examples

  • Example: Calculate circular velocity when radius and rotation period are known.
  • Example: Engineers analyze rotating systems and orbital motion using circular velocity calculations.

Common mistakes

  • Using incorrect radius values.
  • Ignoring gravitational conditions.
  • Mixing speed and velocity.

Variables

  • Radius of circular path
  • Orbital or rotation period
  • Circular velocity
  • Distance traveled per rotation
  • Circular motion conditions
  • Measurement units

Limitations

  • Results assume constant circular motion conditions.
  • Variable-speed or complex orbital systems may require advanced motion analysis methods.

Scientific references

  • OpenStax University Physics: Circular Motion
  • NIST SI Units and Measurement References
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Circular motion analysis
  • Engineering rotating system studies
  • Orbital mechanics calculations
  • Vehicle and wheel motion analysis
  • Laboratory circular motion experiments

Frequently asked questions

How is circular velocity calculated?

Circular velocity is calculated by multiplying 2π by the radius and dividing the result by the period using the relationship v = 2πr ÷ T.

What factors affect circular velocity?

Circular velocity depends on the radius of the circular path and the time required to complete one rotation.

What is the SI unit of circular velocity?

The SI unit of circular velocity is meters per second (m/s), representing the speed of an object traveling along a circular path.

What is the difference between circular velocity and angular velocity?

Circular velocity describes the linear speed along the circular path, while angular velocity describes the rate of rotation around an axis.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

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

  1. Write the formula: v = 2πr ÷ T.
  2. Substitute the values: v = 2 × π × 5 ÷ 10.
  3. 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

Calculator FAQ

How is circular velocity calculated?

Circular velocity is calculated by multiplying 2π by the radius and dividing the result by the period using the relationship v = 2πr ÷ T.

What factors affect circular velocity?

Circular velocity depends on the radius of the circular path and the time required to complete one rotation.

What is the SI unit of circular velocity?

The SI unit of circular velocity is meters per second (m/s), representing the speed of an object traveling along a circular path.

What is the difference between circular velocity and angular velocity?

Circular velocity describes the linear speed along the circular path, while angular velocity describes the rate of rotation around an axis.