1 hertz equals approximately 6.2832 radians.
Since 1 hertz means one cycle per second, converting it to radians involves multiplying by 2π, because one cycle corresponds to 2π radians. Therefore, 1 Hz equals 2π radians, which is about 6.2832 radians.
Conversion Result for 1 Hertz to Radians
Conversion Tool
Result in rad:
Conversion Formula
The conversion from hertz to radians is based on the fact that one cycle equals 2π radians. To convert a frequency in hertz to radians per second, multiply the number of hertz by 2π. This works because hertz measures cycles per second, and radians measure angles.
Mathematically, the formula is: radians = hertz × 2π. For example, if you have 5 Hz, then the calculation is 5 × 2π = 10π, which equals approximately 31.4159 radians. This direct multiplication links frequency to angular displacement.
Conversion Example
- Convert 3 Hz to radians:
- Step 1: Write the formula: radians = 3 × 2π
- Step 2: Calculate: 3 × 6.2832
- Step 3: Result is approximately 18.8496 radians
- Convert 0.5 Hz to radians:
- Step 1: Write the formula: radians = 0.5 × 2π
- Step 2: Calculate: 0.5 × 6.2832
- Step 3: Result is approximately 3.1416 radians
- Convert 10 Hz to radians:
- Step 1: Write the formula: radians = 10 × 2π
- Step 2: Calculate: 10 × 6.2832
- Step 3: Result is approximately 62.8320 radians
Conversion Chart
The table below shows values from -24.0 to 26.0 Hz converted to radians. To read this chart, find the frequency in the first column, then read the corresponding radians value in the second column. Use this to quickly reference common conversions without recalculating.
| Frequency (Hz) | Radians |
|---|---|
| -24.0 | -150.7964 |
| -23.0 | -144.5134 |
| -22.0 | -138.2304 |
| -21.0 | -131.9474 |
| -20.0 | -125.6644 |
| -19.0 | -119.3814 |
| -18.0 | -113.0984 |
| -17.0 | -106.8154 |
| -16.0 | -100.5324 |
| -15.0 | -94.2494 |
| -14.0 | -87.9664 |
| -13.0 | -81.6834 |
| -12.0 | -75.4004 |
| -11.0 | -69.1174 |
| -10.0 | -62.8344 |
| -9.0 | -56.5514 |
| -8.0 | -50.2684 |
| -7.0 | -43.9854 |
| -6.0 | -37.7024 |
| -5.0 | -31.4194 |
| -4.0 | -25.1364 |
| -3.0 | -18.8534 |
| -2.0 | -12.5704 |
| -1.0 | -6.2874 |
| 0.0 | 0.0000 |
| 1.0 | 6.2832 |
| 2.0 | 12.5664 |
| 3.0 | 18.8496 |
| 4.0 | 25.1328 |
| 5.0 | 31.4160 |
| 6.0 | 37.6992 |
| 7.0 | 43.9824 |
| 8.0 | 50.2656 |
| 9.0 | 56.5488 |
| 10.0 | 62.8320 |
| 11.0 | 69.1152 |
| 12.0 | 75.3984 |
| 13.0 | 81.6816 |
| 14.0 | 87.9648 |
| 15.0 | 94.2480 |
| 16.0 | 100.5312 |
| 17.0 | 106.8144 |
| 18.0 | 113.0976 |
| 19.0 | 119.3808 |
| 20.0 | 125.6640 |
| 21.0 | 131.9472 |
| 22.0 | 138.2304 |
| 23.0 | 144.5136 |
| 24.0 | 150.7968 |
| 25.0 | 157.0800 |
| 26.0 | 163.3632 |
Related Conversion Questions
- How many radians are in 1.5 hertz?
- What is the radian equivalent of 0.2 Hz?
- Convert 10 hertz to radians per second?
- How do I convert 1 Hz to radians in physics?
- What is 1 Hz in radians per cycle?
- How to find radians from frequency in hertz?
- What is the formula to change hertz to radians?
Conversion Definitions
Hertz (Hz) is a unit of frequency that measures how many cycles or oscillations occur in one second. It indicates how often a repeating event happens per second, used in fields like physics and electronics to describe wave or signal rates.
Radians (rad) are units of angular measurement, representing the ratio of an arc length to its radius. One radian corresponds to the angle at the center of a circle where the arc length equals the radius, fundamental in geometry and trigonometry calculations.
Conversion FAQs
What does 1 hertz mean in terms of oscillations?
One hertz indicates that an event or wave completes one full cycle or oscillation every second, reflecting the frequency of periodic phenomena like sound waves, electromagnetic signals, or mechanical vibrations.
Can I use the same formula for converting other frequency units to radians?
No, the formula specifically relates to hertz because it measures cycles per second. For other units like revolutions per minute, you need to convert into hertz first before multiplying by 2π to get radians.
Why is 2π used in the conversion?
Because one cycle equals 2π radians, multiplying the frequency by 2π converts the number of cycles per second into the total angular displacement in radians, linking the two measurements directly.
Is the result of converting 1 Hz to radians per second always about 6.2832?
Yes, since 2π is approximately 6.2832, multiplying 1 Hz by 2π always results in about 6.2832 radians per second, representing the angular velocity of a wave with that frequency.
What is the significance of radians in wave analysis?
Radians are used to measure angular displacement, which is important in analyzing wave phase, oscillations, and angular velocities, providing a precise way to describe the motion or rotation involved in wave phenomena.