Conversion of 1 Hertz to Radians
The value of 1 hertz is equal to 6.2832 radians.
Since 1 hertz corresponds to one cycle per second, and each cycle is 2π radians, multiplying the frequency by 2π gives the measure in radians per second. Therefore, 1 Hz equals 2π radians, which is approximately 6.2832 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. Since 1 Hz means one cycle per second, multiplying by 2π converts cycles to radians per second. The formula is: radians = hertz * 2π. For example, 2 Hz equals 2 * 2π = 12.5664 radians.
Conversion Example
- Convert 2 Hz to radians:
- Multiply 2 by 2π: 2 * 6.2832 = 12.5664 radians.
- Convert 0.5 Hz to radians:
- Multiply 0.5 by 2π: 0.5 * 6.2832 = 3.1416 radians.
- Convert 10 Hz to radians:
- Multiply 10 by 2π: 10 * 6.2832 = 62.832 radians.
- Convert 5.5 Hz to radians:
- Multiply 5.5 by 2π: 5.5 * 6.2832 = 34.5576 radians.
- Convert 7 Hz to radians:
- Multiply 7 by 2π: 7 * 6.2832 = 43.9824 radians.
Conversion Chart
| Hz | Radians |
|---|---|
| -24.0 | -150.7960 |
| -23.0 | -144.4616 |
| -22.0 | -138.1272 |
| -21.0 | -131.7928 |
| -20.0 | -125.4584 |
| -19.0 | -119.1240 |
| -18.0 | -112.7896 |
| -17.0 | -106.4552 |
| -16.0 | -100.1208 |
| -15.0 | -93.7864 |
| -14.0 | -87.4520 |
| -13.0 | -81.1176 |
| -12.0 | -74.7832 |
| -11.0 | -68.4488 |
| -10.0 | -62.1144 |
| -9.0 | -55.7800 |
| -8.0 | -49.4456 |
| -7.0 | -43.1112 |
| -6.0 | -36.7768 |
| -5.0 | -30.4424 |
| -4.0 | -24.1080 |
| -3.0 | -17.7736 |
| -2.0 | -11.4392 |
| -1.0 | -5.1048 |
| 0.0 | 0.0 |
| 1.0 | 6.2832 |
| 2.0 | 12.5664 |
| 3.0 | 18.8496 |
| 4.0 | 25.1328 |
| 5.0 | 31.4159 |
| 6.0 | 37.6991 |
| 7.0 | 43.9823 |
| 8.0 | 50.2655 |
| 9.0 | 56.5487 |
| 10.0 | 62.8320 |
| 20.0 | 125.6640 |
| 26.0 | 163.3629 |
Use this chart to quickly find the rad value for specific hertz values within this range. Read the row for the frequency in hertz and see the corresponding radian measure.
Related Conversion Questions
- How many radians are in 1.5 hertz?
- What is the radian equivalent of 0.25 Hz?
- Convert 10 Hz to radians per second?
- How do I convert 0.1 Hz to radians?
- What is the radian value for 5.5 Hz?
- How many radians does 100 Hz equal?
- Is 1 hertz equal to 2π radians?
Conversion Definitions
Hertz
Hertz (Hz) measures the number of complete cycles or oscillations that occur in one second in a periodic phenomenon, representing frequency. It is a fundamental unit in physics and engineering to quantify how often a repeating event happens per second.
Rad
Rad (radian) is a unit of angular measure, representing the angle where the arc length equals the radius of a circle. One radian equals approximately 57.2958 degrees, and it’s used to describe angles and rotational measurements in mathematics and physics.
Conversion FAQs
Why is 1 Hz equal to 2π radians?
This is because one cycle corresponds to 2π radians, which is the angle of a full circle. Since frequency in hertz describes how many cycles occur per second, multiplying by 2π converts cycles to radians, giving radians per second.
Can I convert any frequency from Hz to radians directly?
Yes, multiplying the frequency in Hz by 2π gives the angular velocity in radians per second. This applies to any frequency measurement, allowing for straightforward conversion between the two units of angular measurement.
What does the radian measure in practical terms?
The radian describes how far around a circle an angle extends, based on the length of the arc it subtends relative to the circle’s radius. It’s a natural measure for rotational and oscillatory phenomena, simplifying many mathematical formulas.
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.