Convert BPM to Radians per Second (bpm to rad/s)
1 beat per minute (bpm) = 0.1047197551 radians per second (rad/s). 1 rad/s = 9.549296586 bpm. Example: 15 bpm = 15 × 0.1047197551 = 1.570796327 rad/s.
Also searched as beats per minute to rad/s, beats per minute in rad/s, beats per minute into radians per second, bpm to rad/s, bpm in radians per second, bpm into radian per second, beat per minute to radian per second, bpm to radians per second converter and how many radians per second in a beat per minute.
1 bpm = 0.1047197551 rad/s
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk beat per minute to radian per second converter to paste a column from Excel.
How to Convert BPM to Radian per Second
- 1 bpm = 0.1047197551 rad/s
- 1 rad/s = 9.549296586 bpm
- Example: convert 15 bpm to rad/s: 15 bpm = 15 × 0.1047197551 rad/s = 1.570796327 rad/s
Formula
rad/s = bpm × 0.1047197551197
or rad/s = bpm ÷ 9.549296585514
Derivation from SI units:
- 1 bpm = 1/60 Hz.
- ω = 2πf, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.
- 1 bpm = 0.01666666666667 Hz ÷ 0.1591549430919 Hz per rad/s = 0.1047197551197 rad/s
Both units are defined exactly, so the factor is exact. BPM definition: beat per minute; Radian per Second definition: radian per second.
Worked examples
- A reading of 90 bpm converts to 9.424777961 rad/s.
90 bpm × 0.1047197551 = 9.424777961 rad/s - A value of 140 bpm is 14.66076572 rad/s.
140 bpm × 0.1047197551 = 14.66076572 rad/s
BPM to Radian per Second conversion table
| BPM | Radians per Second (rad/s) |
|---|---|
| 40 bpm | 4.188790205 rad/s |
| 60 bpm | 6.283185307 rad/s |
| 72 bpm | 7.539822369 rad/s |
| 90 bpm | 9.424777961 rad/s |
| 100 bpm | 10.47197551 rad/s |
| 120 bpm | 12.56637061 rad/s |
| 140 bpm | 14.66076572 rad/s |
| 160 bpm | 16.75516082 rad/s |
| 180 bpm | 18.84955592 rad/s |
| 200 bpm | 20.94395102 rad/s |
Where it's used
BPM are used for heart rate, 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.
BPM to other frequency units
| Conversion | 1 bpm equals |
|---|---|
| beat per minute to radian per second | 0.1047197551 rad/s |
| beat per minute to hertz | 0.01666666667 Hz |
| beat per minute to megahertz | 1.666666667 × 10⁻⁸ MHz |
| beat per minute to gigahertz | 1.666666667 × 10⁻¹¹ GHz |
| beat per minute to revolution per minute | 1 rpm |
| beat per minute to kilohertz | 0.00001666666667 kHz |
| beat per minute to revolution per second | 0.01666666667 rps |
| beat per minute to degree per second | 6 °/s |
Show 1 more units
| beat per minute to terahertz | 1.666666667 × 10⁻¹⁴ THz |
|---|
Frequently asked questions
How many radians per second are in 1 beat per minute?
1 bpm = 0.1047197551 rad/s.
How do I convert beats per minute to radians per second?
Multiply the value in bpm by 0.1047197551, or divide it by 9.549296586. For example, 15 bpm × 0.1047197551 = 1.570796327 rad/s.
Is the bpm 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). Convert BPM to Radians per Second (bpm to rad/s). Retrieved October 25, 2026, from https://scientificconverters.com/frequency/bpm-to-radians-per-second/
IEEE
Scientific Converters, "Convert BPM to Radians per Second (bpm to rad/s)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/frequency/bpm-to-radians-per-second/