Revolutions per Second to Radians per Second (rps to rad/s)
1 revolution per second (rps) = 6.283185307 radians per second (rad/s). 1 rad/s = 0.1591549431 rps. Example: 15 rps = 15 × 6.283185307 = 94.24777961 rad/s.
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1 rps = 6.283185307 rad/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk revolution per second to radian per second converter to paste a column from Excel.
How to Convert Revolution per Second to Radian per Second
- 1 rps = 6.283185307 rad/s
- 1 rad/s = 0.1591549431 rps
- Example: convert 15 rps to rad/s: 15 rps = 15 × 6.283185307 rad/s = 94.24777961 rad/s
Formula
rad/s = rps × 6.28318530718
Derivation from SI units:
- 1 rev/s = 1 Hz.
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 rps = 1 Hz ÷ 0.1591549430919 Hz per rad/s = 6.28318530718 rad/s
Both units are defined exactly, so the factor is exact. Revolution per Second definition: revolution per second; Radian per Second definition: radian per second.
Worked examples
- A reading of 10 rps converts to 62.83185307 rad/s.
10 rps × 6.283185307 = 62.83185307 rad/s - A value of 100 rps is 628.3185307 rad/s.
100 rps × 6.283185307 = 628.3185307 rad/s
Revolution per Second to Radian per Second conversion table
| Revolutions per Second (rps) | Radians per Second (rad/s) |
|---|---|
| 1 rps | 6.283185307 rad/s |
| 5 rps | 31.41592654 rad/s |
| 10 rps | 62.83185307 rad/s |
| 25 rps | 157.0796327 rad/s |
| 50 rps | 314.1592654 rad/s |
| 100 rps | 628.3185307 rad/s |
| 200 rps | 1256.637061 rad/s |
| 1000 rps | 6283.185307 rad/s |
Where it's used
Revolutions per Second are used for turbines and centrifuges, 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.
Revolution per Second to other frequency units
| Conversion | 1 rps equals |
|---|---|
| revolution per second to radian per second | 6.283185307 rad/s |
| revolution per second to hertz | 1 Hz |
| revolution per second to megahertz | 0.000001 MHz |
| revolution per second to gigahertz | 1 × 10⁻⁹ GHz |
| revolution per second to revolution per minute | 60 rpm |
| revolution per second to kilohertz | 0.001 kHz |
| revolution per second to degree per second | 360 °/s |
| revolution per second to beat per minute | 60 bpm |
Show 1 more units
| revolution per second to terahertz | 1 × 10⁻¹² THz |
|---|
Frequently asked questions
How many radians per second are in 1 revolution per second?
1 rps = 6.283185307 rad/s.
How do I convert revolutions per second to radians per second?
Multiply the value in rps by 6.283185307. For example, 15 rps × 6.283185307 = 94.24777961 rad/s.
Is the rps 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). Revolutions per Second to Radians per Second (rps to rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/revolutions-per-second-to-radians-per-second/
IEEE
Scientific Converters, "Revolutions per Second to Radians per Second (rps to rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/revolutions-per-second-to-radians-per-second/