Degrees per Second to Radians per Second (°/s to rad/s)
1 degree per second (°/s) = 0.01745329252 radians per second (rad/s). 1 rad/s = 57.29577951 °/s. Example: 15 °/s = 15 × 0.01745329252 = 0.2617993878 rad/s.
Also searched as degrees per second to rad/s, degrees per second in rad/s, degrees per second into radians per second, °/s to rad/s, °/s in radians per second, °/s into radian per second, degree per second to radian per second, °/s to radians per second converter and how many radians per second in a degree per second.
1 °/s = 0.01745329252 rad/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk degree per second to radian per second converter to paste a column from Excel.
How to Convert Degree per Second to Radian per Second
- 1 °/s = 0.01745329252 rad/s
- 1 rad/s = 57.29577951 °/s
- Example: convert 15 °/s to rad/s: 15 °/s = 15 × 0.01745329252 rad/s = 0.2617993878 rad/s
Formula
rad/s = °/s × 0.01745329251994
or rad/s = °/s ÷ 57.29577951308
Derivation from SI units:
- 360°/s is one revolution per second, so 1 °/s = 1/360 Hz.
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 °/s = 0.002777777777778 Hz ÷ 0.1591549430919 Hz per rad/s = 0.01745329251994 rad/s
Both units are defined exactly, so the factor is exact. Degree per Second definition: degree per second; Radian per Second definition: radian per second.
Worked examples
- A reading of 30 °/s converts to 0.5235987756 rad/s.
30 °/s × 0.01745329252 = 0.5235987756 rad/s - A value of 250 °/s is 4.36332313 rad/s.
250 °/s × 0.01745329252 = 4.36332313 rad/s
Degree per Second to Radian per Second conversion table
| Degrees per Second (°/s) | Radians per Second (rad/s) |
|---|---|
| 1 °/s | 0.01745329252 rad/s |
| 6 °/s | 0.1047197551 rad/s |
| 15 °/s | 0.2617993878 rad/s |
| 30 °/s | 0.5235987756 rad/s |
| 90 °/s | 1.570796327 rad/s |
| 180 °/s | 3.141592654 rad/s |
| 250 °/s | 4.36332313 rad/s |
| 360 °/s | 6.283185307 rad/s |
| 500 °/s | 8.72664626 rad/s |
| 2000 °/s | 34.90658504 rad/s |
Where it's used
Degrees per Second are used for gyroscopes and IMU sensors (±250 to ±2000 dps), while radians per second appear in angular velocity in physics and dynamics. Both measure frequency and rotational speed, so the conversion is a fixed factor.
Degree per Second to other frequency units
| Conversion | 1 °/s equals |
|---|---|
| degree per second to radian per second | 0.01745329252 rad/s |
| degree per second to hertz | 0.002777777778 Hz |
| degree per second to megahertz | 2.777777778 × 10⁻⁹ MHz |
| degree per second to gigahertz | 2.777777778 × 10⁻¹² GHz |
| degree per second to revolution per minute | 0.1666666667 rpm |
| degree per second to kilohertz | 0.000002777777778 kHz |
| degree per second to revolution per second | 0.002777777778 rps |
| degree per second to beat per minute | 0.1666666667 bpm |
Show 1 more units
| degree per second to terahertz | 2.777777778 × 10⁻¹⁵ THz |
|---|
Frequently asked questions
How many radians per second are in 1 degree per second?
1 °/s = 0.01745329252 rad/s.
How do I convert degrees per second to radians per second?
Multiply the value in °/s by 0.01745329252, or divide it by 57.29577951. For example, 15 °/s × 0.01745329252 = 0.2617993878 rad/s.
Is the °/s to rad/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). Degrees per Second to Radians per Second (°/s to rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/degrees-per-second-to-radians-per-second/
IEEE
Scientific Converters, "Degrees per Second to Radians per Second (°/s to rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/degrees-per-second-to-radians-per-second/