Table of Contents
The value of 20 Hz converts to approximately 125.66 radians per second.
Since 1 Hz equals 2π radians per second, multiplying 20 Hz by 2π gives the radian measure. So, 20 Hz * 2π = 125.66 rad/sec, showing how frequency in Hz relates directly to angular measure in radians, which is used in rotational and oscillatory calculations.
Conversion Result for 20 Hz to Rad
20 Hz equals about 125.66 radians because the conversion involves multiplying the frequency in Hz by 2π (approximately 6.2832), which converts cycles per second into radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert hertz to radians is: radians = hertz * 2π. This works because one cycle (hertz) equals 2π radians, which is the measure of one full rotation in radians. For example, if you have 5 Hz, multiply 5 by 2π to get 31.4159 rad.
Mathematically, it’s based on the fact that a complete rotation or cycle equates to 2π radians. So, converting frequency involves scaling the number of cycles per second by 2π, aligning cycles with radians, which are angular measurements.
Conversion Example
- Convert 10 Hz to radians:
- Step 1: Write the formula: radians = 10 * 2π
- Step 2: Calculate 2π ≈ 6.2832
- Step 3: Multiply 10 by 6.2832, resulting in 62.832 rad
- Convert 50 Hz to radians:
- Step 1: Use the formula: radians = 50 * 2π
- Step 2: Calculate 2π ≈ 6.2832
- Step 3: 50 * 6.2832 = 314.16 rad
- Convert 0.5 Hz to radians:
- Step 1: Use the formula: radians = 0.5 * 2π
- Step 2: Calculate 2π ≈ 6.2832
- Step 3: 0.5 * 6.2832 = 3.1416 rad
Conversion Chart
This table shows how different Hz values convert into radians, providing quick reference for common frequencies.
| Hz | Radians |
|---|---|
| -5.0 | -31.416 |
| -4.0 | -25.1327 |
| -3.0 | -18.8496 |
| -2.0 | -12.5664 |
| -1.0 | -6.2832 |
| 0.0 | 0.0 |
| 5.0 | 31.416 |
| 10.0 | 62.832 |
| 15.0 | 94.248 |
| 20.0 | 125.66 |
| 25.0 | 157.08 |
| 30.0 | 188.50 |
| 35.0 | 219.91 |
| 40.0 | 251.33 |
| 45.0 | 282.74 |
Use this chart to quickly find the radian equivalent for any Hz value listed, by matching the frequency with its radian measure.
Related Conversion Questions
- How do I convert 20 Hz into radians per second?
- What is the radian equivalent of 20 Hz?
- How many radians does 20 Hz correspond to?
- Can you show me the formula to convert 20 Hz to radians?
- What is the angular measure in radians for 20 cycles per second?
- How do I calculate radians from a frequency of 20 Hz?
- Is 20 Hz equal to about 125 radians?
Conversion Definitions
Hz
Hertz (hz) is a unit that measures the number of cycles, vibrations, or oscillations occurring per second in a periodic phenomenon, used in sound, radio waves, and other wave-related fields.
Rad
Rad, short for radians, is a unit of angular measurement representing the angle formed when the arc length equals the radius, with one full circle being 2π radians, used in geometry, physics, and engineering calculations involving rotation.
Conversion FAQs
Why multiply Hz by 2π to get radians?
Because one cycle in Hz equals 2π radians, multiplying the frequency by 2π converts cycles per second into an angular measure in radians per second, aligning cyclic frequency with rotational angle.
Can I convert any frequency in Hz to radians this way?
Yes, for rotational or oscillatory systems, multiplying the frequency in Hz by 2π always yields the radians per second, which is the standard conversion method for such contexts.
What does the radian measure indicate in physics?
The radian indicates the angle of rotation or oscillation in terms of the ratio of the arc length to the radius, providing a direct measure of angular displacement or frequency in rotational motions.