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Radians/second to Hertz Converter

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

rad/s

Hertz

50.0001

Hz

314.16 rad/s = 50.0001 Hz

Hz = rad/s ÷ 2π

Radians/second to Hertz: 1 rad/s equals 0.159155 Hz. To convert radians/second to hertz, multiply by 0.159155 (Hz = rad/s ÷ 2π). For example, 10 rad/s = 1.591549 Hz.

How to Convert Radians/second to Hertz

To convert from radians/second to hertz, multiply the value by 0.159155. The conversion is linear, meaning doubling the input doubles the output.

Conversion Formula

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

Radians/second to Hertz Conversion Chart

Radians/second (rad/s)Hertz (Hz)
0.10.015915
0.250.039789
0.50.079577
10.159155
20.31831
30.477465
50.795775
101.591549
203.183099
253.978874
507.957747
10015.915494
25039.788736
1000159.154943

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 Radians/second (rad/s) Hertz (Hz)
US power-grid frequency376.991160
Concert pitch (A4)2764.6015440

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FAQ

How do I convert radians per second to hertz?

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

What is 314.16 rad/s in everyday terms?

314.16 rad/s equals 50 Hz, which is the mains electricity frequency in Europe, Asia, and most of the world outside North America.

How is angular frequency used in physics?

Angular frequency appears in simple harmonic motion (x = A sin(ωt)), wave equations, LC circuits, and quantum mechanics. It connects oscillation period T to angular displacement: ω = 2π/T.

How many hertz are in 1 radians/second?

1 rad/s equals 0.159155 Hz.

How do you convert radians/second to hertz?

Multiply the radians/second value by 0.159155. Formula: Hz = rad/s ÷ 2π.

How many hertz are in 5 radians/second?

5 rad/s = 0.795775 Hz.

How do you convert hertz back to radians/second?

Use the inverse formula: rad/s = Hz × 2π. For example, 1 Hz = 6.283185 rad/s.