Unit Converters · Browser · Free

Hertz to Radian per Second Conversion

This tool turns a frequency given in hertz into angular velocity in radians per second. Enter the hertz value and press Convert; the result follows the relation 1 Hz ≈ 6.283185307179586 rad/s, that figure being 2π rounded to 16 significant digits.

About the Hertz to rad/s conversion

Hertz counts how many cycles happen each second, while radians per second describes the resulting angular velocity or angular frequency. Since one complete cycle sweeps an angle of 2π radians, a frequency of 1 hertz corresponds to 2π rad/s, which the tool prints as 6.283185307179586 rad/s.

The reverse relation works the same way: 1 rad/s equals 1/(2π) Hz, about 0.1591549 Hz. Because the link between the two units is a constant multiplier, the conversion stays perfectly linear across any size of input.

Hertz to rad/s formula

The angular frequency ω in radians per second equals 2π times the frequency f in hertz: ω (rad/s) = 2π × f (Hz), which is the same as multiplying the hertz value by 2π rounded to 16 significant digits, 6.283185307179586. Because that multiplier is a rounded stand-in for 2π, the printed result inherits the same 16-digit rounding, so digits past the 16th are not part of 2π.

For example, a frequency of 300 Hz gives ω = 2π × 300 Hz, about 1884.956 rad/s. The converter applies this multiplication for you: type the value, press Convert, read the result, then use Copy or Clear.