RPM to rad/s Converter
Convert rpm, rev/s, rad/s and deg/s into one another at once.
The size of each unit in rpm is listed below. The converter first turns your value into rpm, then divides by the size of each unit.
| Unit | Size of one unit | Definition and source |
|---|---|---|
| Rotational speed (revolutions) | ||
| rpm (revolutions per minute) | 1 rpm | One full turn per minute |
| rev/s (hertz) | 60 rpm | One full turn per second = 60 rpm |
| Angular velocity | ||
| rad/s (radians per second) | 937500000000000000000000000000000000000000000000000000000000/98174770424681038701957605727484465131161543730472056905467 rpm (about 9.549297 rpm) | One radian per second. 1 revolution = 2π rad, so 1 rad/s = 30/π rpm (about 9.549297 rpm), calculated with an approximation of π |
| deg/s (degrees per second) | 1/6 rpm (about 0.1666667 rpm) | 1 revolution = 360°, so 1 deg/s = 1/6 rpm |
How rpm and rad/s are related
- One full revolution is 2π radians (360°). One minute is 60 seconds. So 1 rpm = 2π ÷ 60 rad/s = π/30 rad/s (about 0.1047198 rad/s), and 1 rad/s = 30/π rpm (about 9.549297 rpm).
- Any value in rad/s involves π and cannot be exact. The tool calculates with an approximation of π (to the 60th decimal place) and labels every value that involves rad/s as a "rounded value". Conversions among rpm, rev/s and deg/s use only whole numbers and fractions and are exact (1 rev/s = 60 rpm, 1 rpm = 6 deg/s).
- The result is rounded only once, when it is displayed, to 7 significant digits. The 15-digit copy uses the same calculation with more digits shown.
- This tool converts a speed of rotation. It does not turn it into linear speed, which also needs the radius, and it does not convert frequency of a signal or period; for those see the Degrees to Radians Converter for angles and the Speed Converter for linear speeds.
Examples
- 1,000 rpm = about 104.7198 rad/s
- 3,000 rpm = about 314.1593 rad/s = 50 rev/s = 18,000 deg/s
- 100 rad/s = about 954.9297 rpm
- 60 rpm = 1 rev/s = about 6.283185 rad/s
Notes
- You can enter decimals (up to 12 digits before the decimal point and 6 decimal places). Use a period as the decimal separator. Commas are accepted only as thousands separators, for example 1,234.5. Negative values cannot be entered.
- Rotational speed is a rate, so it is not a frequency of oscillation measured in hertz in the usual sense; "rev/s" is shown with the hertz name only because one revolution per second is a common way to write it.
Sources
The factors on this page follow from the definitions of the minute (60 s), the revolution (one full turn, 360° or 2π rad) and the radian. The row "revolution (r) = 6.283 185 rad" of NIST SP 811 Appendix B.9 was read word for word (NIST SP 811, Appendix B.9); the table does not mark it as exact, and this tool derives it from π. The rpm row of Appendix B.8 was not read word for word and is not relied on. The radian itself was not checked in a primary document.
Frequently asked questions
How many rad/s is 1,000 rpm?
About 104.7198 rad/s (1,000 × 2π ÷ 60).
How many rpm is 1 rad/s?
About 9.549297 rpm (30 ÷ π).
Is rad/s the same as Hz?
No. Hertz counts cycles per second and rad/s counts radians per second. One revolution per second is 1 Hz and about 6.283185 rad/s.
Why is the result labeled "rounded value"?
Because it involves π, which cannot be written exactly. The tool uses an approximation of π with 60 decimal places.