1 Hz equals approximately 6.2832 radians.
Since 1 Hertz (Hz) means one cycle per second, and one cycle corresponds to 2π radians, converting Hz to radians involves multiplying the frequency by 2π. Therefore, 1 Hz equals 2π radians, which is roughly 6.2832 radians.
Conversion Result
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert Hz to radians per second is multiplying the frequency by 2π because one cycle in radians is 2π. This works because Hz measures cycles per second, and each cycle equals 2π radians. The calculation: radians = Hz × 2π. For example, 2 Hz equals 2×2π = 12.5664 radians.
Conversion Example
- Convert 3 Hz:
- Start with 3 Hz.
- Multiply 3 by 2π: 3 × 6.2832 = 18.8496 radians.
- Result: 3 Hz equals approximately 18.8496 radians.
- Convert 0.5 Hz:
- Start with 0.5 Hz.
- Multiply 0.5 by 2π: 0.5 × 6.2832 = 3.1416 radians.
- Result: 0.5 Hz equals approximately 3.1416 radians.
- Convert 10 Hz:
- Start with 10 Hz.
- Multiply 10 by 2π: 10 × 6.2832 = 62.832 radians.
- Result: 10 Hz equals approximately 62.832 radians.
- Convert 0.1 Hz:
- Start with 0.1 Hz.
- Multiply 0.1 by 2π: 0.1 × 6.2832 = 0.6283 radians.
- Result: 0.1 Hz equals approximately 0.6283 radians.
Conversion Chart
| Hz | Radians |
|---|---|
| -24.0 | -150.7965 |
| -23.0 | -144.4610 |
| -22.0 | -138.1255 |
| -21.0 | -131.7900 |
| -20.0 | -125.4545 |
| -19.0 | -119.1190 |
| -18.0 | -112.7835 |
| -17.0 | -106.4480 |
| -16.0 | -100.1125 |
| -15.0 | -93.7770 |
| -14.0 | -87.4415 |
| -13.0 | -81.1060 |
| -12.0 | -74.7705 |
| -11.0 | -68.4350 |
| -10.0 | -62.0995 |
| -9.0 | -55.7640 |
| -8.0 | -49.4285 |
| -7.0 | -43.0930 |
| -6.0 | -36.7575 |
| -5.0 | -30.4220 |
| -4.0 | -24.0865 |
| -3.0 | -17.7510 |
| -2.0 | -11.4155 |
| -1.0 | -5.0800 |
| 0.0 | 0.0 |
| 1.0 | 6.2832 |
| 2.0 | 12.5664 |
| 3.0 | 18.8496 |
| 4.0 | 25.1328 |
| 5.0 | 31.4159 |
| 6.0 | 37.6991 |
| 7.0 | 43.9823 |
| 8.0 | 50.2655 |
| 9.0 | 56.5487 |
| 10.0 | 62.8320 |
| 26.0 | 163.3620 |
Use this chart to quickly find the radian equivalent for the Hz values shown. The columns display the Hz and its corresponding radian measure.
Related Conversion Questions
- What is the radian equivalent of 1.5 hz?
- How many radians are in 0.25 hz?
- Can I convert 2 Hz to radians per second?
- What is 10 Hz in terms of radians?
- How do I convert a frequency of 0.1 Hz into radians?
- What is the radians value for 5 Hz?
- How many radians is 100 Hz?
Conversion Definitions
Hz
Hz, or Hertz, measures the number of complete cycles or oscillations that occur in one second. It is a unit of frequency used in waves, signals, and oscillatory systems, indicating how often a repeating event happens per second.
Rad
Rad, short for radians, is a unit of angular measurement representing the angle where the arc length equals the radius. One full circle equals 2π radians, making it a natural measure for angles in mathematics and physics.
Conversion FAQs
Why does multiplying Hz by 2π give radians?
This is because one cycle in angular terms equals 2π radians. Since Hz counts cycles per second, multiplying by 2π converts cycles into radians, giving the angular measure per second.
Is the conversion from Hz to radians linear?
Yes, the conversion is linear because each Hz corresponds to a fixed multiple of 2π radians. Doubling the Hz doubles the radians, and so on, maintaining a straightforward proportional relationship.
Can I use this conversion for signals with fractional Hz?
Absolutely, the same formula applies regardless of whether the frequency is whole or fractional. Just multiply the Hz value by 2π to find radians per second.