Conversion Result: 1 Hertz equals approximately 6.2832 Radians
Since 1 hertz equals 6.2832 radians, it means that one cycle per second corresponds to about 6.2832 radians, which is a full circle. This conversion shows how frequency in hertz relates to angular displacement in radians per second.
What does 1 hertz convert to in radians?
Converting 1 hertz to radians involves multiplying by 2π because one hertz, representing one cycle per second, corresponds to an angular displacement of 2π radians. This means every second, an object moving at 1 Hz completes a rotation of 2π radians, making the conversion straightforward and consistent with circular motion principles.
Conversion Tool
Result in rad:
Conversion Formula
To convert hertz to radians, multiply the frequency value by 2π, because one cycle in a second (1 Hz) equals 2π radians. This works because a complete rotation or cycle is 2π radians, and frequency indicates how many cycles occur per second. So, the formula is: radians = hertz × 2π.
For example, if you have 2 Hz, then the conversion is 2 × 2π = 4π, which equals approximately 12.5664 radians. The process involves basic multiplication, making it simple to switch between frequency and angular displacement.
Conversion Example
- Convert 3 Hz to radians:
- Multiply 3 by 2π
- 3 × 6.2832 = 18.8496 radians
- Convert 0.5 Hz to radians:
- 0.5 × 6.2832 = 3.1416 radians
- Convert 10 Hz to radians:
- 10 × 6.2832 = 62.832 radians
- Convert 7.5 Hz to radians:
- 7.5 × 6.2832 = 47.124 radians
- Convert 1.2 Hz to radians:
- 1.2 × 6.2832 = 7.5398 radians
Conversion Chart
This chart shows how different frequencies in hertz convert to radians, ranging from -24.0 to 26.0 Hz. Use it to quickly find the radians value for a given frequency, noting that negative values represent reverse directions in oscillations or rotations.
| Hz | Radians |
|---|---|
| -24.0 | -150.796 |
| -20.0 | -125.664 |
| -15.0 | -94.2478 |
| -10.0 | -62.832 |
| -5.0 | -31.416 |
| 0.0 | 0.0 |
| 5.0 | 31.416 |
| 10.0 | 62.832 |
| 15.0 | 94.2478 |
| 20.0 | 125.664 |
| 24.0 | 150.796 |
| 26.0 | 163.362 |
Related Conversion Questions
- How many radians are in 1 hertz of oscillation?
- What is the radian equivalent of 1 cycle per second?
- Convert 1 Hz to radians per second in angular displacement?
- How do I find radians for a frequency of 1 Hz?
- What is the angular measure in radians of a 1 Hz signal?
- How many radians correspond to 1 oscillation per second?
- What is the radians value for 1 Hz in wave motion?
Conversion Definitions
Hertz
The hertz (Hz) measures frequency, indicating how many complete cycles or oscillations happen each second in a periodic motion or wave.
Rad
Rad, short for radian, is a unit of angular measure representing the angle where the arc length equals the radius; 2π radians equal a full circle.
Conversion FAQs
Why does multiplying by 2π convert hertz to radians?
Because each cycle in a wave or rotation corresponds to 2π radians, multiplying the frequency in hertz by 2π gives the total radians covered per second, transforming cyclical frequency into angular displacement.
Can I convert any frequency in hertz to radians directly?
Yes, by using the formula radians = hertz × 2π, you can convert any frequency value to radians per second, which describes the angular speed of oscillation or rotation.
What does a negative hertz value imply in radians?
A negative value indicates reverse direction in oscillation or rotation, but the magnitude in radians remains positive, representing the size of the angle covered per second.
Is the conversion same for angular velocity in physics?
Yes, angular velocity in radians per second is directly calculated from frequency in hertz using this formula, making the conversion standard in physics and engineering.