MihsabaShare this free calculator
Send this tool to someone who needs the calculation.
How to use
Angular velocity describes the rate of angular change. It can be expressed in rad/s, degrees/s, RPM or revolutions/s; every conversion follows one full turn = 2π radians = 360 degrees. To convert RPM to angular velocity in radians per second, use ω = RPM × 2π/60. For example, 1,500 RPM ≈ 157.0796 rad/s. In reverse, RPM = ω × 60/(2π), so 10 rad/s ≈ 95.493 RPM. Radians per second and revolutions per second differ by a factor of 2π.
- Enter angular velocity; negative values may represent reverse direction.
- Choose source and target units.
- Review the converted result and common equivalent units.
How it is calculated
Example
1500 RPM = 1500×2π÷60 ≈ 157.0796 rad/s = 9000°/s = 25 rev/s.
Important notes
This converter handles angular velocity only. Converting it to linear speed also requires a radius through v=ωr.
Worked examples and interpreting results
Rotation of 60 revolutions per minute equals one revolution per second or 2π rad/s. Angular velocity describes angle change per time; rim speed also requires the radius.
| Case | Calculation | Result |
|---|---|---|
| Revolutions/minute to radians/second | 60 × 2π ÷ 60 | 6.283185 rad/s |
| Revolutions/minute to degrees/second | 60 × 360 ÷ 60 | 360 °/s |
| 1500 RPM to radians per second | 1500 × 2π ÷ 60 | 157.079633 rad/s |
| 10 rad/s to revolutions per minute | 10 × 60 ÷ (2π) | 95.492966 RPM |
How to check the result
For linear speed use v=ωr with ω in radians per second. Frequency in hertz counts cycles; angular velocity in rad/s includes the factor 2π for each cycle.
Convert RPM to rad/s, revolutions per second and degrees
One complete revolution equals 2π radians or 360 degrees. Multiply revolutions per minute by 2π and divide by 60 to obtain angular speed in radians per second; keep a negative sign if direction matters.
- 60 RPM to radians per second: 60 × 2π ÷ 60 = 2π rad/s
- 120 RPM to revolutions per second: 120 ÷ 60 = 2 RPS
- 180 degrees per second to rad/s: 180 × π ÷ 180 = π rad/s
Important note
Hertz measures cycles per second while rad/s measures angular displacement per second. Do not assume their numerical values agree without the 2π conversion factor.
Related calculators
Frequently asked questions
How many rad/s is 1 RPM?
1 RPM = 2π/60 ≈ 0.104719755 rad/s.
Can angular velocity be negative?
Yes. The converter preserves the sign as a rotation-direction convention.
Is Hz the same as rad/s?
Not directly. If Hz means revolutions per second, angular velocity is ω=2πf.
How is angular velocity related to linear speed?
At radius r, tangential speed is v=ωr when ω is expressed in radians per unit time. Two points on one rotating body can therefore share angular velocity but have different linear speeds.
What is the angular velocity at 3,000 RPM?
3,000 × 2π/60 = 100π ≈ 314.1593 rad/s. The rotational rate is 3,000/60 = 50 revolutions per second.