The conversion of 20 Hz to radians per second results in approximately 125.66 rad/sec.
Since 1 Hz equals 2π radians per second, multiplying 20 Hz by 2π gives us the radians value, showing how frequency relates to angular velocity in radians per second.
What is the conversion from Hz to Radians
Result in rad:
Conversion Formula
The formula to convert Hz to radians per second is: radians = Hz × 2π. This works because Hz measures cycles per second, and each cycle corresponds to 2π radians. Multiplying Hz by 2π directly converts cycles into radians, which are units of angular measure. For example, 1 Hz equals 2π radians/sec, so for 20 Hz, the math is 20 × 2π = 125.66 radians/sec.
Conversion Example
- Convert 10 Hz:
- Multiply 10 by 2π
- 10 × 6.2832 = 62.832 radians/sec
- Convert 5 Hz:
- Multiply 5 by 2π
- 5 × 6.2832 = 31.416 radians/sec
- Convert 50 Hz:
- Multiply 50 by 2π
- 50 × 6.2832 = 314.16 radians/sec
- Convert 0.5 Hz:
- Multiply 0.5 by 2π
- 0.5 × 6.2832 = 3.1416 radians/sec
- Convert 100 Hz:
- Multiply 100 by 2π
- 100 × 6.2832 = 628.32 radians/sec
Conversion Chart
| Hz | Radians/sec |
|---|---|
| -5.0 | -31.416 |
| -4.0 | -25.132 |
| -3.0 | -18.849 |
| -2.0 | -12.566 |
| -1.0 | -6.283 |
| 0.0 | 0.000 |
| 1.0 | 6.283 |
| 2.0 | 12.566 |
| 3.0 | 18.849 |
| 4.0 | 25.132 |
| 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 |
The chart shows Hz values in the first column and their corresponding rad/sec values in the second. Simply locate the Hz value you’re interested in, and read across to see the rad/sec equivalent.
Related Conversion Questions
- What is 20 Hz in radians per second?
- How many radians per second are in 20 Hz?
- Convert 20 Hz to radians, what is the result?
- What is the angular velocity in radians/sec for 20 Hz?
- How do I convert 20 Hz into radians per second?
- If I have 20 Hz, how many radians does that correspond to?
- What is the rad/sec value for a frequency of 20 Hz?
Conversion Definitions
Hz, or hertz, measures frequency, indicating how many cycles occur per second, used in waves, signals, and oscillations, representing repetition rate in various systems. One Hz equals one cycle per second, crucial in physics and engineering for understanding wave behavior.
Rad, or radians, is a unit of angular measure representing the angle subtended at the center of a circle by an arc equal in length to the radius. One radian equals approximately 57.2958 degrees, and it’s used in mathematics, physics, and engineering to express angles and rotational quantities.
Conversion FAQs
Why is 20 Hz equivalent to 125.66 radians per second?
This is because 1 Hz equals 2π radians/sec, so multiplying 20 Hz by 2π gives the angular velocity in radians/sec. Specifically, 20 × 6.2832 = 125.664 radians/sec, which converts frequency into an angular measure.
Can I convert any Hz value to radians per second with this formula?
Yes, the formula radians = Hz × 2π works for any frequency in Hz to find its equivalent in radians/sec, as it directly relates cycles per second to radians per second, based on the circle’s geometry.
Is there a difference between frequency and angular velocity?
Yes, frequency (Hz) measures how many cycles happen per second, while angular velocity (radians/sec) measures how fast an object rotates or oscillates in radians per second. They are related but describe different aspects of motion.
What is the significance of using radians in angular calculations?
Radians provide a natural, unitless way to measure angles based on the radius of a circle, simplifying calculations involving rotations and oscillations by directly relating linear and angular measures.
How accurate is the conversion for high frequencies?
The conversion remains precise for high frequencies because it relies on the mathematical relationship between Hz and radians/sec, which is exact. Only rounding in calculations may introduce minor errors.