Circular motion tool

Tangential Velocity Calculator

Solve tangential velocity, radius, or angular velocity using v = rω.

Enter two known values

Solve a tangential velocity problem

Free tool
m/s

This is the value being calculated.

m

Distance from the axis of rotation.

rad/s

Rate of rotation in radians per second.

Use meters per second for tangential velocity, meters for radius, and radians per second for angular velocity.

Try an example:

Your tangential velocity result will appear here

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

Calculator guide

How this calculator works

Tangential Velocity Calculator determines the linear speed of an object moving along a circular path. It helps physics students, engineers, and laboratory users understand rotational motion by connecting radius and angular velocity.

Formula explanation

Tangential velocity describes the linear speed of an object moving along a circular path.

Formula

Tangential Velocity = Radius × Angular Velocity

Worked example

Example: Points farther from the center of a rotating wheel have greater tangential velocity.

Assumptions

  • Radius and angular velocity values are measured accurately.
  • The object follows circular motion.
  • Input values use compatible units.

Examples

  • Example: Calculate tangential velocity when the radius and angular velocity of a rotating object are known.
  • Example: Engineers analyze wheels, gears, turbines, and rotating machinery by studying linear speed at different distances from the rotation center.

Common mistakes

  • Confusing angular velocity with tangential velocity.
  • Using incorrect radius values.
  • Ignoring unit conversions.

Variables

  • Radius of rotation
  • Angular velocity
  • Tangential velocity
  • Rotational speed
  • Measurement units

Limitations

  • Does not account for changing angular velocity, friction, or complex rotational forces.
  • Results depend on accurate radius and angular velocity measurements.

Scientific references

  • OpenStax University Physics: Rotational Motion
  • NIST SI Units and Measurement References
  • Engineering dynamics principles

Content review

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

Applications

  • Physics education
  • Rotational mechanics analysis
  • Engineering motion studies
  • Laboratory circular motion experiments

Frequently asked questions

How is tangential velocity calculated?

Tangential velocity is calculated by multiplying radius of rotation by angular velocity using the relationship v = rω.

What factors affect tangential velocity?

Radius of rotation and angular velocity determine the linear speed of an object moving along a circular path.

What is the difference between angular velocity and tangential velocity?

Angular velocity describes how quickly an object rotates, while tangential velocity describes the linear speed of a point on the rotating object.

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 tangential velocity?

Tangential velocity is the linear speed of an object moving along the edge of a circular path.

Formula

Tangential velocity formula

Tangential Velocityv = rω

  • v is tangential velocity in m/s.
  • r is radius in meters.
  • ω is angular velocity in rad/s.

Worked example

A point is 4 m from the axis and rotates at 3 rad/s

  1. Write the formula: v = rω.
  2. Substitute the values: v = 4 × 3.
  3. Calculate tangential velocity: v = 12 m/s.

Rearranged equations

Solve for radius or angular velocity

Radius

r = v ÷ ω

Divide tangential velocity by angular velocity.

Angular velocity

ω = v ÷ r

Divide tangential velocity by radius.

Physical relationship

Radius and rotation rate both affect v

Tangential velocity increases when radius increases, angular velocity increases, or both increase.

Units

Standard SI units

Use meters per second for tangential velocity, meters for radius, and radians per second for angular velocity.

Real-world applications

Where tangential velocity is used

  • Wheels, gears, and rotating disks.
  • Turbines and mechanical shafts.
  • Amusement rides and rotating platforms.
  • Planetary and satellite motion.
  • Motors and industrial machinery.

Calculation limits

Important assumptions

  • All entered values must be greater than zero.
  • Radius is measured from the rotation axis.
  • Angular velocity must be entered in radians per second.
  • Direction is not represented.
  • Units are not converted automatically.

Related tools

Use the Angular Velocity Calculator to calculate angular velocity, displacement, or time.

Use the Centripetal Acceleration Calculator to calculate inward acceleration in circular motion.

Questions and answers

Calculator FAQ

How is tangential velocity calculated?

Tangential velocity is calculated by multiplying radius of rotation by angular velocity using the relationship v = rω.

What factors affect tangential velocity?

Radius of rotation and angular velocity determine the linear speed of an object moving along a circular path.

What is the difference between angular velocity and tangential velocity?

Angular velocity describes how quickly an object rotates, while tangential velocity describes the linear speed of a point on the rotating object.