Radians Per Second to Hertz (rad/s to Hz)

1 radian per second equals 0.1591549431 hertz (rounded).

1 radian per second = 0.1591549431 hertz

How to convert radians per second to hertz

To convert radians per second to hertz, multiply the number of radians per second by 0.1591549431. The factor is rounded to 10 significant digits. To go the other way, multiply hertz by 6.283185307 (rounded).

hertz = radians per second × 0.1591549431

Example: 10 radians per second = 1.591549431 hertz.

About these units

Radian Per Second (rad/s)

ScientificCurrent unit

The SI unit of angular velocity. One full turn is 2π (about 6.283) radians, so 1 rad/s is about 0.159 Hz.

Physicists measure spin in radians per second because the angle then drops out of the equations neatly. Angular velocity is the rate of change of an angle, and its SI unit is the radian per second. Since the radian is dimensionless, the unit is dimensionally the same as 1 per second, so Wikipedia's article on angular velocity says rad/s is preferable, to avoid mixing it up with a rotation rate in hertz.

The link between the two is a factor of 2 pi. Angular velocity equals 2 pi times the frequency, so one rad/s is 1/(2 pi) hertz, about 0.159 Hz, and one hertz is about 6.283 rad/s. A disc turning at 60 revolutions per minute therefore spins at 1 Hz, which is 2 pi rad/s. The figure used on this site for the conversion is 0.15915494 hertz per radian per second, the same value to eight decimals.

1 radian per second = 0.1591549431 hertz (approximately).

Sources: Wikipedia: Angular velocity; Wikipedia: Hertz; Wikipedia: Revolutions per minute

Hertz (Hz)

Metric (SI)Current unit

The SI unit of frequency: one cycle per second. Named after Heinrich Hertz.

Heinrich Rudolf Hertz (1857 to 1894) was a German physicist who, in experiments between 1886 and 1889, produced and detected radio waves with a spark-gap transmitter and a loop receiver. He showed that they travel at the speed of light and can be polarised, reflected and refracted, confirming Maxwell's theory. Asked about uses for them, he is said to have replied, Nothing, I guess. The International Electrotechnical Commission established the name hertz in 1935, and the CGPM adopted it in 1960, replacing cycles per second.

One hertz is one cycle per second, equal to s to the minus one. A clock ticking once a second runs at 1 Hz, a human heart at rest beats at around 1.2 Hz, and young ears hear roughly 20 Hz to 20,000 Hz. The SI treats cycle itself as not a unit, and the hertz applies only to periodic events, whereas the becquerel counts random radioactive decays, even though both are one per second. The second is now defined by fixing the caesium frequency at exactly 9,192,631,770 hertz.

The hertz is the reference unit for frequency on this site.

Sources: Wikipedia: Hertz; Wikipedia: Heinrich Hertz; BIPM: SI Brochure, 9th edition

Related conversions

See all frequency units.