Use this angular velocity calculator to find average angular velocity from angle and time or convert between rad/s, deg/s, RPM, and Hz.
Advanced options
How to use our Angular Velocity Calculator
- Choose a mode in What do you want to calculate?.
- For average motion, enter Angular displacement (selected unit), pick Angular displacement unit, enter Time interval (selected unit), and choose Time unit.
- For conversion, enter Known angular speed value and select Known angular speed unit.
- If needed, open Advanced options and set Direction convention, Display format, and Significant figures.
- Click Calculate.
- Read Angular velocity (rad/s) as the standard SI-style result, then compare the same speed in Angular velocity (deg/s), Angular velocity (RPM), and Frequency (Hz).
- Check Period (s) to see the time for one full turn. If it shows N/A, the matching frequency is zero so one-turn time is undefined.
- Use Result note to interpret the sign. A negative value means the rotation is in the negative direction under your chosen convention.
- Sanity-check the answer: one full turn in 2 seconds should be about 3.14 rad/s, 180 deg/s, 30 RPM, and 0.5 Hz.
Definitions
Angular displacement: The change in angle during the motion. In this calculator, it is entered in Angular displacement (selected unit).
Angular velocity: The rate of change of angle with time, often written as ω [3].
Average angular velocity: Angular displacement divided by the time interval, so it tells how fast the angle changed on average over that interval [3].
Radians per second (rad/s): A standard unit for angular velocity based on radians, which are commonly used in physics [2].
Frequency (Hz): The number of full revolutions each second. It is linked to angular velocity, but it counts cycles instead of radians.
Period (s): The time for one full revolution. A smaller period means faster rotation.
Common mistakes and quick fixes
Mistake: Entering 360 in Angular displacement (selected unit) but leaving Angular displacement unit on radians.
Fix: Match the number to the unit you actually mean. For 360 degrees, set Angular displacement unit to degrees.
Mistake: Using 0 or a negative value in Time interval (selected unit) for average mode.
Fix: Enter a time greater than zero and confirm the correct Time unit .
Mistake: Typing a value into Known angular speed value while still using average mode and expecting it to affect the result.
Fix: Switch What do you want to calculate? to unit conversion if you want to use Known angular speed value .
Mistake: Reading Frequency (Hz) and Angular velocity (RPM) as the same unit.
Fix: Remember that Frequency (Hz) is revolutions per second, while Angular velocity (RPM) is revolutions per minute.
Mistake: Entering a decimal or out-of-range value for Significant figures .
Fix: Use a whole number from 2 to 8 so the displayed outputs round correctly.
Mistake: Thinking a negative Angular velocity (rad/s) means the speed is impossible.
Fix: Check Result note and Direction convention . Negative means the opposite rotation direction, not a math error.
Limitations & Key Assumptions / Boundary Conditions
- This tool calculates average angular velocity from total angle change over a time interval. It does not show how the angular speed may have changed during the motion.
- Time interval (selected unit) must be greater than zero in average mode, or the result is not defined.
- Period (s) is shown as undefined or N/A when Frequency (Hz) is zero, because one full revolution would never be completed.
- Negative outputs are allowed and mean rotation in the negative direction under the selected Direction convention.
- Displayed values are rounded by Display format and Significant figures, so the shown number may differ slightly from the full internal value.
- Unit conversion assumes standard relationships among degrees, radians, revolutions, seconds, minutes, and hours. It does not include special machine-specific definitions or sensor filtering.
Methodology
Core idea
Angular velocity compares how much angle changes to how much time passes. A larger angle in the same time means a larger angular velocity [1][3].
ω (angular velocity) = Δθ (angular displacement) / Δt (time interval)
Unit conversions used
If the angle is entered in degrees, it is converted to radians before calculating rad/s.
θ_rad = θ_deg * pi / 180
If the angle is entered in revolutions, one full revolution is converted to 2 pi radians [2].
θ_rad = θ_rev * 2 * pi
Time is converted to seconds when needed.
1 min = 60 s, 1 h = 3600 s
For unit conversion mode, the calculator first converts the known value to rad/s, then converts that result into the other units.
ω_rad/s = RPM * 2 * pi / 60
ω = 2 * pi * f
T = 1 / f
Worked mini-example
Suppose an object turns 360 degrees in 2 seconds. First convert 360 degrees to 2 pi radians. Then divide by 2 seconds.
ω = 2*pi / 2 = pi rad/s = 3.1416 rad/s
That same result is 180 deg/s, 30 RPM, and 0.5 Hz. The period is 2 seconds for one full revolution.
Signed results
If the angular displacement or known angular speed is negative, the outputs stay negative. The sign shows direction based on your selected convention, not an error.
Assumptions behind the results
This calculator uses average angular velocity, standard angle-unit conversions, and standard time-unit conversions. It does not model changing angular acceleration, friction, or real machine slip. If frequency is zero, period is not displayed as Infinity because one-turn time is undefined.