What is angular acceleration?

Angular acceleration (α) is the rate of change of angular velocity with respect to time. Its SI unit is radians per second squared (rad/s²). A positive value means the rotation is speeding up; a negative value means it is slowing down.

What formula does this tool use?

α = (ω_final − ω_initial) / t, where ω values are in rad/s and t is in seconds. If you enter deg/s or RPM, the tool converts them to rad/s before computing.

How do I convert RPM to rad/s?

Multiply RPM by 2π/60 (approximately 0.10472). For example, 60 RPM = 60 × 2π/60 = 2π ≈ 6.283 rad/s.

Can angular acceleration be negative?

Yes. A negative result means the object is decelerating rotationally — its angular speed is decreasing over the given time interval.

What if time is zero?

Division by zero is undefined in physics. The tool will show an error if you enter t = 0.

Angular Acceleration Calculator

Enter initial and final angular velocity plus elapsed time to compute angular acceleration in rad/s².

Input Values

Initial Angular Velocity (ω₀)

Final Angular Velocity (ω)

Time Interval (t) — seconds

Results

Enter values and click Calculate

Formula Reference

α = Δω / t

Core definition

Δω = ω − ω₀

Change in angular velocity

1 RPM = 2π/60 rad/s

Unit conversion

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Summary

Angular acceleration (α) measures how quickly an object's rotational speed changes. It is defined as the change in angular velocity (Δω) divided by the elapsed time (Δt). This calculator accepts angular velocities in rad/s, deg/s, or RPM, converts them automatically, and returns the angular acceleration in rad/s² along with supporting values.

How it works

Enter the initial angular velocity (ω₀) and select its unit.
Enter the final angular velocity (ω) and select its unit.
Enter the elapsed time interval (t) in seconds.
Click Calculate — the tool computes α = (ω − ω₀) / t.
Results are shown in rad/s², deg/s², and rev/s².

Use cases

Physics homework and lab reports on rotational dynamics.
Engineering analysis of motors, turbines, and rotating machinery.
Robotics — calculating servo or wheel acceleration profiles.
Automotive — analyzing crankshaft or wheel angular acceleration.
Sports science — computing bat, racket, or discus spin-up rates.
Simulation and game physics for rotating rigid bodies.

Frequently Asked Questions

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