Hertz to Radians per Second Converter
Convert hertz (cycles per second) (Hz) to radians per second (rad/s), with the formula, a conversion table and exact factors.
Change the values and press Calculate to work out your own figures.
Enter a frequency, choose its unit and the unit you want. The answer is exact until it is shown, and the same value appears in every other unit.
Show the working
- 1 Hz = 6.28318530718 rad/s
- 1 × 6.28318530718 = 6.28318530718 rad/s
How to convert hertz to radians per second
1 Hz = 6.28318530718 rad/s, so multiply by 6.28318530718 to go from hertz (cycles per second) to radians per second. Going the other way, 1 rad/s = 0.159154943092 Hz.
rad/s = Hz × 6.28318530718 Hz = rad/s × 0.159154943092
Worked example:
1 Hz = 6.28318530718 rad/s 5 × 6.28318530718 = 31.4159265359 rad/s
Hertz to radians per second table
| Hertz | Radians per Second |
|---|---|
| 1 Hz | 6.28318530718 rad/s |
| 2 Hz | 12.5663706144 rad/s |
| 3 Hz | 18.8495559215 rad/s |
| 4 Hz | 25.1327412287 rad/s |
| 5 Hz | 31.4159265359 rad/s |
| 6 Hz | 37.6991118431 rad/s |
| 7 Hz | 43.9822971503 rad/s |
| 8 Hz | 50.2654824574 rad/s |
| 9 Hz | 56.5486677646 rad/s |
| 10 Hz | 62.8318530718 rad/s |
| 15 Hz | 94.2477796077 rad/s |
| 20 Hz | 125.663706144 rad/s |
| 25 Hz | 157.079632679 rad/s |
| 30 Hz | 188.495559215 rad/s |
| 40 Hz | 251.327412287 rad/s |
| 50 Hz | 314.159265359 rad/s |
| 75 Hz | 471.238898038 rad/s |
| 100 Hz | 628.318530718 rad/s |
| 250 Hz | 1,570.79632679 rad/s |
| 500 Hz | 3,141.59265359 rad/s |
| 1000 Hz | 6,283.18530718 rad/s |
About the units
- Hertz (Hz)
- Hertz (cycles per second), a metric unit. Definition: BIPM SI Brochure, 9th edition (SI units, prefixes and units accepted for use with the SI).
- Radians per Second (rad/s)
- Radians per second, a metric unit. Involves π, which no fraction equals exactly; this converter uses π to 50 significant digits, far beyond the 12 digits shown. Definition: BIPM SI Brochure, 9th edition (SI units, prefixes and units accepted for use with the SI).