Angular Velocity Calculator
Find angular velocity in rad/s and rpm from angle and time.
Results update as you type.
How it works
Angular velocity describes how fast something spins, and this calculator finds it in both radians per second and the more familiar revolutions per minute. You enter the angle rotated in radians and the time it took, and it returns the angular velocity and its equivalent in rpm. Angular velocity is the rotational counterpart of ordinary speed: instead of distance per time, it is angle per time. Radians per second is the scientific unit, while rpm is used everywhere from car engines and record players to hard drives and industrial motors. To convert, remember that one full turn is two pi radians, so an angular velocity of two pi radians per second equals exactly 60 rpm. Angular velocity is central to rotational dynamics, linking to linear speed at the rim of a wheel, to centripetal acceleration, and to rotational kinetic energy. Engineers use it to specify motors and turbines, and physicists use it to analyse everything from spinning tops to planetary rotation. It connects directly to frequency and period: an object completing more turns per second has a higher angular velocity. The calculation assumes constant rotation over the interval. Enter the angle in radians and the time to compute the angular velocity and rpm.
ω = θ / t; rpm = ω × 60 / 2π
Angular velocity is the rate at which an object rotates, found by dividing the angle turned, in radians, by the time taken, giving radians per second. To express this as revolutions per minute, multiply the angular velocity by 60 to convert seconds to minutes and divide by two pi, since one full revolution equals two pi radians. The two forms describe the same rotation in different units.
Source:Classical mechanics (rotational motion)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter angle rotated and time taken.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Angular velocity updates instantly as you type — no button to press.
Frequently asked questions
What is angular velocity?
Angular velocity is the rate at which an object rotates, measured as the angle swept per unit time, typically in radians per second. It is the rotational equivalent of linear velocity. A higher angular velocity means faster spinning. It underpins the analysis of wheels, gears, motors, and any rotating system in physics and engineering.
How do I convert rad/s to rpm?
Multiply the angular velocity in radians per second by 60 to convert to per minute, then divide by two pi because one revolution is two pi radians. So an angular velocity of one radian per second is about 9.55 rpm, and two pi radians per second is exactly 60 rpm. The calculator performs this conversion automatically.
Why use radians instead of degrees?
Radians are the natural unit for rotational physics because they directly relate angle to arc length: an arc equal to the radius subtends one radian. This makes formulas for linear speed, acceleration, and energy at a distance from the axis clean and free of conversion factors. Degrees are more intuitive for everyday angles, but radians simplify the mathematics of rotation.
How does angular velocity relate to linear speed?
The linear speed of a point on a rotating object equals its angular velocity multiplied by its distance from the axis. So a point on the rim of a wheel moves faster than one near the hub, even though both share the same angular velocity. This relationship connects rotational motion to the straight-line speed you would measure at the edge.
What is the difference from frequency?
Frequency counts complete revolutions per second in hertz, while angular velocity measures radians per second. They differ by a factor of two pi, since each revolution is two pi radians. Angular velocity in radians per second equals two pi times the frequency in hertz. Both describe rotational rate; angular velocity is preferred in physics equations, frequency in everyday contexts.