The frequency of 2 Hz equals approximately 12.57 radians.
This conversion is based on the fact that 1 Hz corresponds to 2π radians per second, so multiplying by 2 gives the radians equivalent for 2 Hz, resulting in 2 × 2π = 4π radians, which is about 12.57 radians.
What is the conversion from Hz to Radians?
Converting from Hz to radians involves multiplying the frequency in hertz by 2π because 1 Hz equals 2π radians per second. This is because Hz measures cycles per second, and radians measure the angle in a circle’s arc. So, when you convert, you’re translating cycles into angles.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert Hz to radians is: radians = Hz × 2π. It works because a full cycle of a wave (1 Hz) is equivalent to 2π radians, which is one complete rotation around a circle. Multiplying the frequency by 2π calculates how many radians correspond to that many cycles per second.
For example, with 2 Hz: 2 × 2π = 4π radians, which mathematically is 4 × 3.1416 = 12.5664 radians. This shows that 2 Hz is equal to roughly 12.57 radians, representing the total angle covered in two cycles.
Conversion Example
- Convert 3 Hz to radians:
- Step 1: Write the formula: radians = Hz × 2π
- Step 2: Substitute 3 for Hz: 3 × 2π
- Step 3: Calculate: 3 × 6.2832 = 18.8496 radians
- Result: 3 Hz equals approximately 18.85 radians
- Convert 5 Hz to radians:
- Step 1: Use the formula: Hz × 2π
- Step 2: Plug in 5: 5 × 6.2832
- Step 3: Calculate: 31.416 radians
- Result: 5 Hz equals about 31.42 radians
- Convert 10 Hz to radians:
- Step 1: Apply formula: 10 × 2π
- Step 2: Calculate: 10 × 6.2832 = 62.832 radians
- Result: 10 Hz is roughly 62.83 radians
Conversion Chart
| Hz | Radians |
|---|---|
| -23.0 | -144.51 |
| -22.0 | -138.23 |
| -21.0 | -131.96 |
| -20.0 | -125.66 |
| -19.0 | -119.38 |
| -18.0 | -113.10 |
| -17.0 | -106.83 |
| -16.0 | -100.55 |
| -15.0 | -94.27 |
| -14.0 | -87.99 |
| -13.0 | -81.71 |
| -12.0 | -75.42 |
| -11.0 | -69.14 |
| -10.0 | -62.83 |
| -9.0 | -56.55 |
| -8.0 | -50.27 |
| -7.0 | -43.99 |
| -6.0 | -37.70 |
| -5.0 | -31.42 |
| -4.0 | -25.14 |
| -3.0 | -18.85 |
| -2.0 | -12.57 |
| -1.0 | -6.28 |
| 0.0 | 0.00 |
| 1.0 | 6.28 |
| 2.0 | 12.57 |
| 3.0 | 18.85 |
| 4.0 | 25.13 |
| 5.0 | 31.42 |
| 6.0 | 37.70 |
| 7.0 | 43.98 |
| 8.0 | 50.27 |
| 9.0 | 56.55 |
| 10.0 | 62.83 |
| 20.0 | 125.66 |
| 27.0 | 169.65 |
The chart shows Hz values in the first column and their equivalent radians in the second. Use it to quickly see how many radians correspond to given Hz values, whether positive or negative, by reading across the row.
Related Conversion Questions
- How many radians are in 2 Hz?
- What is 2 Hz in terms of angular displacement?
- Convert 2 Hz to radians per second?
- How do I convert 2 Hz to an angle in radians?
- What is the radian equivalent of a 2 Hz frequency?
- Is 2 Hz equal to a certain number of radians in circular motion?
- How many radians does 2 Hz cover in one cycle?
Conversion Definitions
Hz
Hz, or hertz, represents the number of cycles or oscillations completed per second in a wave or periodic event, measuring frequency. It indicates how many times a repeating pattern occurs each second, used in sound, radio, and signal processing.
Rad
Rad, or radians, is a unit of angle measurement based on the radius of a circle, where one radian equals the angle at the center of a circle subtending an arc equal to the radius length. It provides a natural measure for angles in mathematics and physics.
Conversion FAQs
Why does multiplying Hz by 2π give radians?
This is because one cycle of a wave corresponds to 2π radians, representing a full rotation around a circle. Therefore, each Hz (cycle per second) equates to 2π radians, and multiplying Hz by 2π converts the frequency into an angular measure.
Can I convert any frequency in Hz to radians manually?
Yes, by applying the formula radians = Hz × 2π, you can convert any frequency from Hz to radians. Just multiply the frequency by approximately 6.2832, which is the value of 2π, to get the radians per second.
What is the significance of radians in wave calculations?
Radians are crucial because they relate directly to the geometric representation of angles, simplifying calculations involving oscillations, rotations, and wave behaviors. Using radians makes mathematical formulas in physics and engineering more straightforward and consistent.
Last Updated : 31 May, 2025
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Sandeep Bhandari holds a Bachelor of Engineering in Computers from Thapar University (2006). He has 20 years of experience in the technology field. He has a keen interest in various technical fields, including database systems, computer networks, and programming. You can read more about him on his bio page.