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Hertz to Radians/second Converter

Convert hertz to radians per second and rad/s to hertz instantly. Bidirectional frequency converter with formula and common values.

Hz

Radians/second

314.1593

rad/s

50 Hz = 314.1593 rad/s

rad/s = Hz × 2π

Hertz to Radians/second: 1 Hz equals 6.283185 rad/s. To convert hertz to radians/second, multiply by 6.283185 (rad/s = Hz × 2π). For example, 10 Hz = 62.831853 rad/s.

How to Convert Hertz to Radians/second

To convert from hertz to radians/second, multiply the value by 6.283185. The conversion is linear, meaning doubling the input doubles the output.

Conversion Formula

  • Hertz to Radians/second: rad/s = Hz × 2π
  • Radians/second to Hertz: Hz = rad/s ÷ 2π

Hertz to Radians/second Conversion Chart

Hertz (Hz)Radians/second (rad/s)
0.10.628319
0.251.570796
0.53.141593
16.283185
212.566371
318.849556
531.415927
1062.831853
20125.663706
25157.079633
50314.159265
100628.318531
2501570.796327
10006283.185307

Understanding the Units

What is a Hertz?

The hertz is the SI derived unit of frequency, equal to one cycle per second (1 Hz = 1/s).

Named after Heinrich Hertz (1857–1894), German physicist who experimentally demonstrated electromagnetic waves.

Common contexts: audio, radio, computing clock speeds.

Real-World Reference Points

Item Hertz (Hz) Radians/second (rad/s)
US power-grid frequency60376.9911
Concert pitch (A4)4402764.6015

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FAQ

How do I convert hertz to radians per second?

Multiply the hertz value by 2π (approximately 6.2832). For example, 50 Hz = 314.16 rad/s.

What is angular frequency?

Angular frequency (omega, ω) measures how fast an object rotates in radians per second. It is the standard frequency unit in physics equations for oscillation, waves, and AC circuits.

Why use radians per second instead of hertz?

Radians per second simplifies many physics and engineering formulas. For example, in AC circuits, impedance calculations use ω directly: X_L = ωL and X_C = 1/(ωC).

How many radians/second are in 1 hertz?

1 Hz equals 6.283185 rad/s.

How do you convert hertz to radians/second?

Multiply the hertz value by 6.283185. Formula: rad/s = Hz × 2π.

How many radians/second are in 5 hertz?

5 Hz = 31.415927 rad/s.

How do you convert radians/second back to hertz?

Use the inverse formula: Hz = rad/s ÷ 2π. For example, 1 rad/s = 0.159155 Hz.