Radian per Second (rad/s)
The radian per second is the SI unit of angular velocity: a full turn is 2π radians, so 1 Hz of rotation equals 2π rad/s. Physics formulas such as v = ωr and P = Tω use rad/s.
Symbol: rad/s
Quantity: frequency and rotational speed
SI relation: 1 rad/s = 0.1591549430919 Hz (exact)
Derivation: ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
Exact: yes, by definition
Typical uses
- Angular velocity in physics and dynamics
- Motor power P = Tω
- AC circuits (ω = 2πf, 314.16 rad/s at 50 Hz)
Convert radians per second to other units
| Conversion | 1 rad/s equals | Reverse |
|---|---|---|
| radian per second to hertz | 0.1591549431 Hz | hertz to radian per second |
| radian per second to megahertz | 1.591549431 × 10⁻⁷ MHz | megahertz to radian per second |
| radian per second to gigahertz | 1.591549431 × 10⁻¹⁰ GHz | gigahertz to radian per second |
| radian per second to revolution per minute | 9.549296586 rpm | revolution per minute to radian per second |
| radian per second to kilohertz | 0.0001591549431 kHz | kilohertz to radian per second |
| radian per second to revolution per second | 0.1591549431 rps | revolution per second to radian per second |
| radian per second to degree per second | 57.29577951 °/s | degree per second to radian per second |
| radian per second to beat per minute | 9.549296586 bpm | beat per minute to radian per second |
| radian per second to terahertz | 1.591549431 × 10⁻¹³ THz | terahertz to radian per second |
Open the Frequency & RPM Converter to convert any value between all units.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 7 (SI prefixes); hertz, Table 4.
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Radian per Second (rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/units/radian-per-second/
IEEE
Scientific Converters, "Radian per Second (rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/units/radian-per-second/