Revolutions per second to radians per second
Type a value in revolutions per second to see it in radians per second straight away, or type in the second box to convert back.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Type the value in the revolutions per second box.
- Read the result in radians per second as you type, and pick the precision you need.
- Swap the direction to convert back, or copy the result.
How it is calculated
rad/s = rps × 6.283185307
Multiply the value in revolutions per second by 6.283185307 to get radians per second.
Example
To convert 25 rps to radians per second: 25 × 6.283185307 = 157.08 rad/s.
Conversion table
| Revolutions per second (rps) | Radians per second (rad/s) |
|---|---|
| 1 | 6.28319 |
| 2 | 12.5664 |
| 3 | 18.8496 |
| 5 | 31.4159 |
| 10 | 62.8319 |
| 20 | 125.664 |
| 25 | 157.08 |
| 50 | 314.159 |
| 100 | 628.319 |
| 250 | 1,570.8 |
| 500 | 3,141.59 |
| 1,000 | 6,283.19 |
About the units
- Revolution per second
- Full turns per second, so 1 rps is exactly 2π rad/s and 60 rpm.
- Radian per second
- The SI unit of angular speed: turning through one radian each second. A full turn is 2π radians.
Limits and caveats
- Results are rounded for display and computed with the browser's floating point precision (about 15 significant digits).
- Both unit factors are exact by their official definitions.
Questions about this tool
How many radians per second are in one revolution per second?
1 rps = 6.28319 rad/s exactly.
How do I convert revolutions per second to radians per second?
Use rad/s = rps × 6.283185307. For example, 25 rps = 157.08 rad/s.
How many revolutions per second are in one radian per second?
1 rad/s = 0.159155 rps.
How do I convert rpm to radians per second?
Multiply the rpm by 2π and divide by 60. For example 3000 rpm is 100π, about 314.16 rad/s.
Is angular speed the same as frequency in hertz?
No. Frequency counts turns per second, while angular speed in rad/s is the frequency times 2π. So a rotation at 1 Hz is 6.2832 rad/s.