The frequency 20 Hz equals approximately 125.66 radians per second.
Since 1 Hz means one cycle per second, and each cycle corresponds to 2π radians, converting Hz to radians involves multiplying the frequency by 2π. Therefore, 20 Hz is 20 times 2π, which results in approximately 125.66 radians per second.
What does 20 Hz equal in radians?
The value of 20 Hz in radians per second is calculated by multiplying 20 by 2π, because a single cycle of frequency involves 2π radians. So, 20 Hz translates to 20 × 2π radians, which is about 125.66 radians. This helps understand the angular velocity for a wave or rotation at that frequency.
Conversion Tool
Result in rad:
Conversion Formula
The conversion from hz to rad involves multiplying the frequency value by 2π, because one cycle equals 2π radians. This works because hz measures cycles per second, and radians measure angular displacement. So, the formula is: radians = hz × 2π.
For example, converting 10 Hz: 10 × 2π = 20π ≈ 62.83 radians. It means a wave vibrating at 10 Hz completes 10 cycles every second, each cycle covering 2π radians, totaling approximately 62.83 radians per second.
Conversion Example
- Convert 5 Hz to radians:
- Step 1: Write down the formula: radians = hz × 2π
- Step 2: Plug in 5 Hz: 5 × 2π
- Step 3: Calculate 2π ≈ 6.2832
- Step 4: Multiply: 5 × 6.2832 = 31.416 radians
- Convert 15 Hz to radians:
- Step 1: Use the same formula: radians = 15 × 2π
- Step 2: 2π ≈ 6.2832
- Step 3: Multiply: 15 × 6.2832 = 94.248 radians
- Convert 25 Hz to radians:
- Step 1: Apply the formula: radians = 25 × 2π
- Step 2: 2π ≈ 6.2832
- Step 3: 25 × 6.2832 = 157.08 radians
Conversion Chart
| 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 |
| 5.0 | 31.416 |
| 10.0 | 62.832 |
| 15.0 | 94.248 |
| 20.0 | 125.664 |
| 25.0 | 157.08 |
| 30.0 | 188.496 |
| 35.0 | 219.912 |
| 40.0 | 251.328 |
| 45.0 | 282.744 |
This chart shows how to read the frequency in Hz and find its equivalent in radians. Use it to quickly estimate the angular displacement per second for different frequencies.
Related Conversion Questions
- How many radians are in 20 Hz frequency?
- What is the radian equivalent of 20 Hz?
- How do I convert 20 Hz to radians per second?
- What is the angular speed in radians for a 20 Hz wave?
- Convert 20 Hz to radians, what is the value?
- At 20 Hz, how many radians does the wave cover per second?
- How can I find radians from a frequency of 20 Hz?
Conversion Definitions
Hz
Hertz (Hz) measures the number of complete cycles or oscillations of a wave that occur in one second, making it a frequency unit used in physics and engineering to describe how often a repeating event happens per second.
Rad
Radian (rad) is a measure of angular displacement, defined as the angle created when an arc length equals the radius of a circle. It provides a way to quantify rotation or oscillations in terms of the radius, with 2π radians corresponding to one full circle.
Conversion FAQs
Why multiply Hz by 2π for radians?
This multiplication is necessary because one cycle of a wave corresponds to 2π radians, representing a complete rotation or oscillation. When converting, multiplying Hz by 2π gives the total radians covered in one second for that frequency.
Can I convert any Hz to radians directly?
Yes, as long as you know the frequency in Hz, multiplying by 2π will give you the angular displacement in radians per second. This formula applies universally for converting linear frequency to angular velocity.
What does it mean if a wave has 125.66 radians per second?
This indicates that the wave completes about 125.66 radians of angular displacement every second, meaning it oscillates at 20 Hz, covering full rotations multiple times within a second.
Is the radian measure relevant for frequency?
Yes, radians are relevant when analyzing oscillations or rotations, especially in physics and engineering, where angular velocity or phase calculations require angular measures like radians, not just cycles per second.