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

Name: Angular Velocity Calculator
Availability: InStock
Author: Nham Vu

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

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

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: 2026-06-11 · Reviewed by Nham Vu