Mechanics
Angular Velocity
Rate of change of angular position.
Variables
ωrad/s
Angular velocity
Rate of rotation
Δθrad
Angular displacement
Angle swept
Δts
Time interval
Elapsed time
Allowed values: greater than 0
Derivation
Angular analog of velocity: ω = dθ/dt.
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- Δθ = 2 rad (Angular displacement)
- Δt = 3 s (Time interval)
Result: ω = 0.66666667 rad/s
Other mechanics formulas with the same quantities
- Centripetal Acceleration (Rotational Motion) shares Angular velocity
- Rotational Kinetic Energy (Rotational Motion) shares Angular velocity
- Angular Momentum (Rotational Motion) shares Angular velocity
- Rolling Kinetic Energy (Rotational Motion) shares Angular velocity
- Velocity (Kinematics) shares Time interval
- Acceleration (Kinematics) shares Time interval
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Centripetal Force, Torque, Moment of Inertia (Point Mass), Newton's Second Law (Rotation) and Rotational Kinematic 1.
- In the mechanics list it comes after Coefficient of Restitution and before Angular Acceleration.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Angular Velocity formula?
Angular Velocity is written ω = Δθ/Δt. Rate of change of angular position. It belongs to Mechanics, under Rotational Motion.
What are the units in ω = Δθ/Δt?
In SI units, ω is angular velocity, measured in rad/s; Δθ is angular displacement, measured in rad; Δt is time interval, measured in s.
How is the Angular Velocity formula derived?
Angular analog of velocity: ω = dθ/dt. The result is ω = Δθ/Δt.