Five Calculation Methods
Calculate from angle and time, RPM, frequency, period, or tangential speed and radius.
Angular Velocity Calculator
Calculate angular velocity using angular displacement and time, RPM, frequency, period, or linear velocity and radius. Get instant results in radians per second, degrees per second, RPM, and hertz.
Enter Rotation Details
Select the information you already know.
Calculator Features
Calculate Rotational Motion Your Way
Use the method that matches the data available in your physics, engineering, automotive, or machinery problem.
Automatic Conversions
Results are automatically converted into rad/s, deg/s, RPM, hertz, and rotation period.
Responsive and Fast
The calculator works directly in the browser and adapts to desktop computers, tablets, and mobile phones.
How It Works
How to Use the Angular Velocity Calculator
Select a Calculation Method
Choose angle and time, RPM, frequency, period, or linear speed and radius.
Enter Your Measurements
Type the known values and select the correct units from the available unit menus.
Review the Converted Results
Press calculate to see angular velocity and all related rotational measurements instantly.
What Is Angular Velocity?
Angular velocity measures how quickly an object rotates around a fixed point or axis. It describes the change in angular position over a specific amount of time.
The standard SI unit of angular velocity is radians per second, written as rad/s. It is commonly represented by the Greek letter omega, ω.
ω = Δθ / Δt
Angular velocity equals angular displacement divided by time.
Angular Velocity From RPM
Revolutions per minute describe how many complete rotations an object makes in one minute. Because one revolution equals 2π radians and one minute equals 60 seconds, RPM can be converted using:
ω = RPM × 2π / 60
For example, 60 RPM equals approximately 6.283185 rad/s.
Angular Velocity From Frequency
Frequency measures the number of complete rotations made every second. When frequency is provided in hertz, angular velocity is calculated by multiplying it by 2π.
ω = 2πf
Here, f represents frequency measured in hertz.
Angular Velocity and Linear Speed
For a point moving along the edge of a rotating object, angular velocity is related to tangential linear speed and radius.
ω = v / r
Linear speed and radius must use compatible measurement units.
Where Angular Velocity Is Used
- Analyzing wheels, gears, turbines, and electric motors.
- Calculating the rotational motion of fans and machinery.
- Studying planets, satellites, and orbital systems.
- Designing automotive drivetrains and rotating components.
- Solving physics and mechanical engineering problems.
Common Questions
Angular Velocity Calculator FAQs
The standard SI unit is radians per second, or rad/s. Angular velocity can also be expressed in degrees per second, revolutions per minute, or revolutions per second.
Multiply the RPM value by 2π and divide the result by 60. For example, 120 RPM equals approximately 12.5664 rad/s.
No. Angular velocity measures rotational speed, while linear velocity measures movement along a straight or curved path. They are related by the equation v = ωr.
Yes. A negative angular velocity normally represents rotation in the direction opposite to the chosen positive direction, such as clockwise instead of counterclockwise.
A speed of 60 RPM equals one complete revolution per second. Its angular velocity is 2π rad/s, or approximately 6.283185 rad/s.
Speed describes magnitude only, while velocity includes direction. In rotational motion, the sign or vector direction of angular velocity identifies the direction of rotation.