What is angular velocity?

Angular velocity (ω) describes how fast an object rotates or revolves relative to a central point. It is the rate of change of angular displacement over time, typically measured in radians per second (rad/s).

What formulas does this calculator use?

Mode 1 uses ω = Δθ / t, where Δθ is the angle in radians and t is the time in seconds. Mode 2 uses ω = v / r, where v is the linear (tangential) velocity in m/s and r is the radius in meters.

How is angular velocity different from linear velocity?

Linear velocity (v) measures straight-line speed in m/s, while angular velocity (ω) measures rotational speed in rad/s. They are related by v = ω × r, where r is the radius of the circular path.

How do I convert rad/s to RPM?

Multiply rad/s by (60 / 2π). For example, 10 rad/s × 60 / 6.2832 ≈ 95.49 RPM. The calculator shows all three units automatically.

What is the difference between angular velocity and angular speed?

Angular speed is the magnitude (scalar), while angular velocity is a vector that also includes the axis of rotation direction. For most calculations, they are used interchangeably as scalars.

Can I calculate angular velocity in degrees per second?

Yes. The calculator displays results in rad/s, degrees per second (deg/s), and RPM simultaneously. To convert manually: multiply rad/s by 180/π to get deg/s.

Angular Velocity Calculator

Calculate angular velocity from angle and time, or from linear velocity and radius — with unit conversion and a step-by-step breakdown.

Inputs

Select a calculation mode, enter values, then click Calculate.

Calculation Mode

Angle Change (Δθ)

Time (t)

Result

Enter values and click Calculate

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Summary

The Angular Velocity Calculator finds the rotational speed of an object in radians per second, degrees per second, or RPM. Enter an angle change and elapsed time, or provide the linear (tangential) velocity and the radius of the circular path. Instant results with a full formula breakdown make it ideal for physics problems, engineering, and motor design.

How it works

Choose a calculation mode: "Angle / Time" or "Linear Velocity / Radius".
Enter the required values with their units (degrees, radians, or revolutions for angle; seconds, minutes, or hours for time; m/s or km/h for velocity).
Click Calculate to apply the formula.
Read the angular velocity in rad/s, deg/s, and RPM simultaneously.
Use Reset to clear the form and start over.

Use cases

Physics homework involving rotational motion and circular kinematics.
Motor and gear design — converting RPM to rad/s for torque calculations.
Robotics: computing joint angular speed from encoder counts.
Astronomy: estimating the angular velocity of a planet or satellite.
Mechanical engineering: relating wheel linear speed to rotational speed.
Sports science: analysing the spin rate of a ball or gymnast.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu