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Radian/sec to hertz Conversion

Enter an angular velocity in radians per second, press Convert, and the matching frequency in hertz appears below. One radian per second is about 0.159154943091895 hertz.

What this converter does

Radians per second describe an angular velocity or angular frequency, while hertz counts complete cycles each second. This tool takes the rad/s figure you type and expresses the same rate as a frequency in hertz.

Because one full cycle covers 2π radians, the two units differ only by that constant. Every result follows from a single division, so you can repeat it by hand with a calculator whenever you need to.

Rad/sec to hertz formula

The frequency f in hertz equals the angular velocity ω in radians per second divided by 2π, about 6.283185307179586:

Because 2π is irrational, it cannot be written out in full; this calculator works with it rounded to 16 significant digits, 6.283185307179586.

f (Hz) = ω (rad/s) / 6.283185307179586, and in turn 1 rad/s is about 0.159154943091895 Hz.

Worked example: an angular velocity of 300 rad/s gives f = 300 / 6.283185307179586, which is about 47.7464829275686 Hz.