Conversion method
Angular velocity uses radians per second. A full revolution is 2π radians; numerical π is approximate. Signed values can represent opposite directions.
rpm = x × 9.549296585513721
10 rad/s = 95.492966 rpm.
| rad/s | rpm |
|---|---|
| 1 | 9.549297 |
| 5 | 47.746483 |
| 10 | 95.492966 |
| 25 | 238.732415 |
| 50 | 477.464829 |
| 100 | 954.929659 |
Unit definitions and sources
Angular velocity uses radians per second. A full revolution is 2π radians; numerical π is approximate. Signed values can represent opposite directions.
| Unit and system | Use | Definition | Relationship |
|---|---|---|---|
| Radian per second (rad/s); si | Common units | Radian per second: base (rad-s) = value × 1. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Revolution per minute (rpm); si | Common units | Revolution per minute: base (rad-s) = value × 0.10471975511965977. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Revolution per second (rev/s); si | Specialist units | Revolution per second: base (rad-s) = value × 6.283185307179586. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Degree per second (°/s); si | Specialist units | Degree per second: base (rad-s) = value × 0.017453292519943295. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Degree per minute (°/min); si | Specialist units | Degree per minute: base (rad-s) = value × 0.0002908882086657216. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Radian per minute (rad/min); si | Specialist units | Radian per minute: base (rad-s) = value × 0.016666666666666666. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Radian/day (rad/(d)); other | Specialist units | radian/day = 1.1574074074074073e-05 rad-s, derived from the component SI/customary definitions. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Radian/hour (rad/(h)); other | Specialist units | radian/hour = 0.0002777777777777778 rad-s, derived from the component SI/customary definitions. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Degree/day (°/(d)); other | Specialist units | degree/day = 2.0200570046230665e-07 rad-s, derived from the component SI/customary definitions. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Degree/hour (°/(h)); other | Specialist units | degree/hour = 4.84813681109536e-06 rad-s, derived from the component SI/customary definitions. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Revolution/day (rev/(d)); other | Specialist units | revolution/day = 7.27220521664304e-05 rad-s, derived from the component SI/customary definitions. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
| Revolution/hour (rev/(h)); other | Specialist units | revolution/hour = 0.0017453292519943296 rad-s, derived from the component SI/customary definitions. Common use: Angular Velocity. Source checked 2026-09-20 (implementation review). | Exact definition; numerical display may be rounded |
Sources: NIST: SP 811 Appendix B.8: conversion factors; BIPM: SI prefixes
Precision of angular velocity conversions
All 12 angular velocity units convert through Radian per second (rad/s). 12 have an exact defined relationship to the base unit and 0 are conventional or measured values. Results and the tables on this page come from the same engine, so a table value can be checked against the converter directly.
Standard display shows up to six decimal places, switching to scientific notation for very large or small values. Calculation uses JavaScript binary floating point independently of display rounding, so extra digits are not a claim about measurement accuracy. Each unit lists its own source; a citation records where the definition comes from, not an independent review. See Conversion methodology for the review and correction process.