Hertz to Radians per Second Converter
Hertz to Radians per Second Conversion Table
| Hertz (Hz) | Radians per Second (rad/s) |
|---|---|
| 1 Hz | 6.2832 rad/s |
| 5 Hz | 31.4159 rad/s |
| 10 Hz | 62.8319 rad/s |
| 20 Hz | 125.6637 rad/s |
| 50 Hz | 314.1593 rad/s |
| 60 Hz | 376.9911 rad/s |
| 100 Hz | 628.3185 rad/s |
| 500 Hz | 3141.5927 rad/s |
| 1000 Hz | 6283.1853 rad/s |
| 5000 Hz | 31415.9265 rad/s |
| 10000 Hz | 62831.8531 rad/s |
Understanding the Conversion
The relationship between frequency in Hertz (Hz) and angular frequency in radians per second (rad/s) is fundamental in physics, engineering, and signal processing.
Conversion Formula
To convert from Hertz to radians per second, use the following formula:
ω (rad/s) = 2π × f (Hz)
Where:
- ω (omega) is the angular frequency in radians per second
- f is the frequency in Hertz
- π (pi) is approximately 3.14159
Example Calculation
To convert 50 Hz to radians per second:
ω = 2π × 50 Hz
ω = 6.28319 × 50
ω = 314.159 rad/s
Reverse Conversion (rad/s to Hz)
To convert from radians per second back to Hertz, use:
f (Hz) = ω (rad/s) ÷ 2π
For example, to convert 314.159 rad/s to Hz:
f = 314.159 ÷ 2π
f = 314.159 ÷ 6.28319
f = 50 Hz
Physical Meaning
The angular frequency (ω) represents how many radians an object rotates through per second. One complete rotation equals 2π radians, which is why the conversion factor between Hz and rad/s is 2π.
In wave motion and oscillations, if a wave completes f cycles per second (Hz), then the angular displacement of a point on the wave changes at a rate of 2πf radians per second.
Applications
This conversion is commonly used in:
- Electrical engineering when analyzing AC circuits
- Mechanical engineering for rotational systems
- Physics when studying waves and oscillations
- Signal processing and communications
- Audio engineering and acoustics