Cycles per Second to Radians per Second: 1 cps equals 6.283183 rad/s. To convert cycles per second to radians per second, multiply by 6.283183 (rad/s = cps × 6.28318). For example, 10 cps = 62.831831 rad/s.
How to Convert Cycles per Second to Radians per Second
To convert from cycles per second to radians per second, multiply the value by 6.283183. The conversion is linear, meaning doubling the input doubles the output.
Conversion Formula
- Cycles per Second to Radians per Second:
rad/s = cps × 6.28318 - Radians per Second to Cycles per Second:
cps = rad/s ÷ 6.28318
Cycles per Second to Radians per Second Conversion Chart
| Cycles per Second (cps) | Radians per Second (rad/s) |
|---|---|
| 0.1 | 0.628318 |
| 0.25 | 1.570796 |
| 0.5 | 3.141592 |
| 1 | 6.283183 |
| 2 | 12.566366 |
| 3 | 18.849549 |
| 5 | 31.415915 |
| 10 | 62.831831 |
| 20 | 125.663662 |
| 25 | 157.079577 |
| 50 | 314.159155 |
| 100 | 628.31831 |
| 250 | 1570.795775 |
| 1000 | 6283.1831 |
Understanding the Units
What is a Cycles per Second?
The hertz is the SI derived unit of frequency, equal to one cycle per second (1 Hz = 1/s).
Named after Heinrich Hertz (1857–1894), German physicist who experimentally demonstrated electromagnetic waves.
Common contexts: audio, radio, computing clock speeds.
Real-World Reference Points
| Item | Cycles per Second (cps) | Radians per Second (rad/s) |
|---|---|---|
| US power-grid frequency | 60 | 376.991 |
| Concert pitch (A4) | 440 | 2764.6006 |