Rotational Speed Unit Converter
Convert a non-negative rotational-speed magnitude between revolutions per minute, radians per second, degrees per second, revolutions per second and a carefully defined rotational frequency.
Controlled input
Enter a magnitude. Negative numbers are rejected because direction requires a declared positive axis and a signed angular-velocity model.
Reference result
Equations, quantities and boundary
Let N be the magnitude of rotational frequency in revolutions per second and ω the corresponding angular-speed magnitude in radians per second.
One revolution is exactly 2π radians and one minute is exactly 60 seconds, so the worksheet uses the mathematical factor π/30 rather than a rounded lookup factor.
| Input of 1 unit | Angular speed | Tần số quay | r/phút |
|---|---|---|---|
| 1 r/min | π/30 rad/s | 1/60 r/s | 1 |
| 1 rad/s | 1 rad/s | 1/(2π) r/s | 30/π |
| 1 °/s | π/180 rad/s | 1/360 r/s | 1/6 |
| 1 r/s | 2π rad/s | 1 r/s | 60 |
| 1 Hz rotational frequency | 2π rad/s | 1 r/s only for 1 cycle/rev | 60 |
Why Hz needs a quantity name
Hertz is the SI unit of frequency; radian per second is the SI unit of angular velocity and angular frequency. The BIPM warns that frequency and angular frequency differ numerically by 2π. This page therefore never labels rad/s as Hz. Its Hz result means rotational frequency with exactly one counted cycle per revolution.
If a shaft rotates at n, a once-per-revolution feature is n Hz, second order is 2n Hz, blade-pass for B equally spaced blades is Bn Hz, and tooth mesh for Z teeth is Zn Hz. Those are different physical quantities even though every result has dimension s⁻¹.
Signed angular velocity is outside this scalar converter
Angular velocity is a vector. A negative scalar is meaningful only after defining an axis and positive direction. This worksheet converts speed magnitudes and therefore accepts zero or positive values only.
Exact reference checks
| Đầu vào | Exact result | Decimal check | Giai đoạn |
|---|---|---|---|
| 60 r/min | 2π rad/s; 1 r/s | 6.283185307179586 rad/s | 1 s/rev |
| 1500 r/min | 50π rad/s; 25 r/s | 157.07963267948966 rad/s | 0.04 s/rev |
| 3600 r/min | 120π rad/s; 60 r/s | 376.99111843077515 rad/s | 1/60 s/rev |
Source classification
| Claim | Phân loại | Inspected source |
|---|---|---|
| Angular velocity/angular frequency use rad/s; frequency uses Hz; their numerical values differ by 2π | Current SI unit guidance | BIPM SI Brochure, 9th edition, version 4.01, June 2026, printed pages 135–136 |
| Rotational frequency is revolutions divided by time; r/s and r/min are widely used for rotating machinery | NIST SI guidance | NIST SP 811, Chapter 8.1 |
| r/min to rad/s tabulated factor 1.047198×10⁻¹ | NIST conversion table; rounded display | NIST SP 811, Appendix B.9 |
| 360° = 2π rad | Plane-angle relation | NIST SP 330, section 5.4.8 |
BIPM SI Brochure page — current edition/status and official version 4.01 PDF.
NIST SP 811 Chapter 8.1 — rotational-frequency definition and r/s/r/min usage.
NIST SP 811 Appendix B.9 — r/min to rad/s conversion table.
NIST SP 330 section 5.4.8 — radian/degree relation and unit-symbol rules.
Accessed: 14 July 2026. The official BIPM PDF was downloaded, rendered and visually inspected. The BIPM text cites ISO 80000-3 for further quantity details; no ISO clause or conformity claim is made here because licensed ISO text was not used.
