Skip to content
UtilLab

hertz [Hz] to radian per second [rad/s] Converter

Quick Reference

1 hertz (Hz) = 6.283185307 radian per second (rad/s)

1 radian per second (rad/s) = 0.1591549431 hertz (Hz)

How to Convert hertz to radian per second

1 Hz = 6.283185307 rad/s
1 rad/s = 0.1591549431 Hz

To convert hertz to radian per second, multiply the value by 6.283185307. To convert radian per second back to hertz, divide by 6.283185307.

Example: convert 10 Hz to rad/s:
10 Hz = 10 x 6.283185307 = 62.83185307 rad/s

↔ Convert radian per second to hertz

hertz

Definition: Hertz (symbol: Hz) is the SI unit of frequency, defined as the number of cycles per second of a periodic phenomenon. One hertz is equivalent to one cycle or event per second.

History/origin: The hertz is named after Heinrich Hertz, a German physicist who proved the existence of electromagnetic waves in the late 19th century. The unit was adopted as a standard unit for frequency in the 20th century.

Current use: Hertz is widely used across various fields to measure frequency, including radio waves, audio signals, computer processing speeds, alternating current (AC) electricity, and any oscillating or repeating phenomenon. It's a fundamental unit in physics, engineering, and technology.

radian per second

Definition: Radians per second (rad/s) is the SI unit of angular speed or angular velocity. It represents the rate of change of an angle in radians over time, specifically the number of radians rotated in one second.

History/origin: The radian as a unit of angle measurement is fundamental in mathematics and physics. Defining angular speed in radians per second is essential for consistency with other SI units and simplifies many equations in rotational dynamics.

Current use: Radians per second is widely used in physics, engineering, and mathematics for describing rotational motion. It's essential in calculations involving torque, angular momentum, and rotational kinetic energy. It appears in fields such as mechanics, electrical engineering (e.g., analyzing AC circuits), and signal processing (e.g., representing signal frequencies).

hertz to radian per second Conversion Table

hertz [Hz]radian per second [rad/s]
1 Hz6.283185307 rad/s
2 Hz12.56637061 rad/s
5 Hz31.41592654 rad/s
10 Hz62.83185307 rad/s
20 Hz125.6637061 rad/s
50 Hz314.1592654 rad/s
100 Hz628.3185307 rad/s
200 Hz1256.637061 rad/s
500 Hz3141.592654 rad/s
1000 Hz6283.185307 rad/s

Common hertz to radian per second conversions

  • 1 Hz = 6.283185 rad/s
  • 2 Hz = 12.566371 rad/s
  • 3 Hz = 18.849556 rad/s
  • 4 Hz = 25.132741 rad/s
  • 5 Hz = 31.415927 rad/s
  • 6 Hz = 37.699112 rad/s
  • 7 Hz = 43.982297 rad/s
  • 8 Hz = 50.265482 rad/s
  • 9 Hz = 56.548668 rad/s
  • 10 Hz = 62.831853 rad/s
  • 12 Hz = 75.398224 rad/s
  • 15 Hz = 94.24778 rad/s
  • 20 Hz = 125.663706 rad/s
  • 25 Hz = 157.079633 rad/s
  • 30 Hz = 188.495559 rad/s
  • 40 Hz = 251.327412 rad/s
  • 50 Hz = 314.159265 rad/s
  • 60 Hz = 376.991118 rad/s
  • 75 Hz = 471.238898 rad/s
  • 100 Hz = 628.318531 rad/s
  • 150 Hz = 942.477796 rad/s
  • 200 Hz = 1,256.637061 rad/s
  • 250 Hz = 1,570.796327 rad/s
  • 300 Hz = 1,884.955592 rad/s
  • 500 Hz = 3,141.592654 rad/s
  • 750 Hz = 4,712.38898 rad/s
  • 1,000 Hz = 6,283.185307 rad/s

Common pairs of Frequency

hertz [Hz] to radian per second [rad/s] Converter

What is 1 Hz in rad/s?
1 hertz (Hz) equals 6.283185 rad/s, and 1 rad/s equals 0.1591549431 Hz.
How do I convert hertz to radian per second?
Multiply by 6.283185: 10 Hz × 6.283185 = 62.831853 rad/s. The converter above does it for any value, with the precision you choose.
What is 100 Hz in rad/s?
100 Hz = 628.318531 rad/s. Common amounts are listed on this page, each with its own step-by-step page.
Is a hertz bigger than a radian per second?
Yes. 1 Hz = 6.283185 rad/s, so the same quantity becomes a larger number when written in rad/s.
hertz to radian per second Converter | UtilLab