Radians per Second to Degrees per Second (rad/s to °/s)
1 radian per second (rad/s) = 57.29577951 degrees per second (°/s). 1 °/s = 0.01745329252 rad/s. Example: 15 rad/s = 15 × 57.29577951 = 859.4366927 °/s.
Also searched as radians per second to °/s, radians per second in °/s, radians per second into degrees per second, rad/s to °/s, rad/s in degrees per second, rad/s into degree per second, radian per second to degree per second, rad/s to degrees per second converter and how many degrees per second in a radian per second.
1 rad/s = 57.29577951 °/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian per second to degree per second converter to paste a column from Excel.
How to Convert Radian per Second to Degree per Second
- 1 rad/s = 57.29577951 °/s
- 1 °/s = 0.01745329252 rad/s
- Example: convert 15 rad/s to °/s: 15 rad/s = 15 × 57.29577951 °/s = 859.4366927 °/s
Formula
°/s = rad/s × 57.29577951308
Derivation from SI units:
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 360°/s is one revolution per second, so 1 °/s = 1/360 Hz.
- 1 rad/s = 0.1591549430919 Hz ÷ 0.002777777777778 Hz per °/s = 57.29577951308 °/s
Both units are defined exactly, so the factor is exact. Radian per Second definition: radian per second; Degree per Second definition: degree per second.
Worked examples
- A reading of 6.28318 rad/s converts to 359.9996959 °/s.
6.28318 rad/s × 57.29577951 = 359.9996959 °/s - A value of 100 rad/s is 5729.577951 °/s.
100 rad/s × 57.29577951 = 5729.577951 °/s
Radian per Second to Degree per Second conversion table
| Radians per Second (rad/s) | Degrees per Second (°/s) |
|---|---|
| 1 rad/s | 57.29577951 °/s |
| 2 rad/s | 114.591559 °/s |
| 3.14159 rad/s | 179.999848 °/s |
| 6.28318 rad/s | 359.9996959 °/s |
| 10 rad/s | 572.9577951 °/s |
| 50 rad/s | 2864.788976 °/s |
| 100 rad/s | 5729.577951 °/s |
| 314.159 rad/s | 17999.9848 °/s |
| 376.991 rad/s | 21599.99321 °/s |
| 1000 rad/s | 57295.77951 °/s |
Where it's used
Radians per Second are used for angular velocity in physics and dynamics, while degrees per second appear in gyroscopes and IMU sensors (±250 to ±2000 dps). Both measure frequency and rotational speed, so the conversion is a fixed factor.
Radian per Second to other frequency units
| Conversion | 1 rad/s equals |
|---|---|
| radian per second to degree per second | 57.29577951 °/s |
| radian per second to hertz | 0.1591549431 Hz |
| radian per second to megahertz | 1.591549431 × 10⁻⁷ MHz |
| radian per second to gigahertz | 1.591549431 × 10⁻¹⁰ GHz |
| radian per second to revolution per minute | 9.549296586 rpm |
| radian per second to kilohertz | 0.0001591549431 kHz |
| radian per second to revolution per second | 0.1591549431 rps |
| radian per second to beat per minute | 9.549296586 bpm |
Show 1 more units
| radian per second to terahertz | 1.591549431 × 10⁻¹³ THz |
|---|
Frequently asked questions
How many degrees per second are in 1 radian per second?
1 rad/s = 57.29577951 °/s.
How do I convert radians per second to degrees per second?
Multiply the value in rad/s by 57.29577951. For example, 15 rad/s × 57.29577951 = 859.4366927 °/s.
Is the rad/s to °/s conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
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). Radians per Second to Degrees per Second (rad/s to °/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/radians-per-second-to-degrees-per-second/
IEEE
Scientific Converters, "Radians per Second to Degrees per Second (rad/s to °/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/radians-per-second-to-degrees-per-second/