20 Hz to Rad – Answer and Calculator Tool

The conversion of 20 Hz to radians per second results in approximately 125.66 rad.

Since 1 Hz equals 2π radians per second, multiplying 20 Hz by 2π gives the value in radians. This conversion is based on the relationship between frequency and angular measure, where Hertz measures cycles per second, and radians measure angles. The calculation involves multiplying 20 by 2 times pi, which equals roughly 125.66 radians.

Conversion Tool

Conversion Formula

The formula to convert Hz to radians per second is: radians = Hz × 2π. This works because frequency in Hz measures how many cycles occur each second, while radians measure the angle covered in those cycles. Multiplying Hz by 2π converts cycles to radians, since each cycle equals 2π radians.

For example, if you have 10 Hz, the calculation is: 10 × 2π = 10 × 6.2832 ≈ 62.832 radians. This step-by-step process shows that multiplying the frequency by 2π translates cycles per second into angular displacement per second in radians.

Conversion Example

• Convert 5 Hz:
  • Multiply 5 by 2π: 5 × 6.2832
  • Result: 31.416 radians
• Convert 15 Hz:
  • 15 × 6.2832
  • Result: 94.248 radians
• Convert 30 Hz:
  • 30 × 6.2832
  • Result: 188.496 radians
• Convert 50 Hz:
  • 50 × 6.2832
  • Result: 314.16 radians
• Convert 100 Hz:
  • 100 × 6.2832
  • Result: 628.32 radians

Conversion Chart

This chart helps you quickly see how different Hz values convert into radians. Simply find the Hz value in the first column and read across to see its equivalent in radians in the second column.

Related Conversion Questions

• How many radians are in 20 Hz?
• What is the radian equivalent of 20 Hz frequency?
• Convert 20 Hz to radians per second, what is the value?
• How do I change 20 Hz into radians?
• What is the angular measure in radians for 20 Hz?
• Is 20 Hz equal to a certain number of radians?
• How many radians do 20 cycles per second cover?

Conversion Definitions

Hz (Hertz) measures how many complete cycles or oscillations occur in one second, representing frequency. Radians measure the angle of rotation or oscillation in a circle, with 2π radians equal to one complete cycle in periodic motion or waveforms.

Conversion FAQs

Why is 2π used in the conversion from Hz to radians?

The factor 2π is used because in a circle, one complete rotation equals 2π radians. Since Hz measures cycles per second, multiplying by 2π converts the number of cycles into angular displacement in radians per second, which is the standard measure of angular velocity.

Can I convert any frequency in Hz to radians per second directly?

Yes, for any frequency in Hz, multiplying by 2π gives you the value in radians per second. This direct conversion works because the relationship between frequency and angular velocity is linear and based on the circle’s circumference in radians.

What is the significance of radians in wave analysis?

Radians are used in wave analysis to measure phase and angular displacement. They provide a way to describe oscillations and rotations in a continuous and mathematically convenient form, especially useful in sinusoidal functions and Fourier analysis.

How does frequency affect the angular velocity in radians?

As frequency in Hz increases, the angular velocity in radians per second also increases proportionally. This means higher Hz values correspond to faster oscillations or rotations, measured in radians per second, which indicate how quickly the phase changes over time.

Is the conversion factor the same for all frequencies?

Yes, the conversion factor 2π remains constant for all frequencies. To convert any Hz value to radians per second, simply multiply the Hz value by 2π. This consistency makes it straightforward to switch between these two measurements.

Last Updated : 31 May, 2025

Sandeep Bhandari

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.