Revolutions Per Minute to Radians Per Second (rpm to rad/s)

1 revolution per minute equals 0.1047197551 radians per second (rounded).

1 revolution per minute = 0.1047197551 radians per second

How to convert revolutions per minute to radians per second

To convert revolutions per minute to radians per second, multiply the number of revolutions per minute by 0.1047197551. The factor is rounded to 10 significant digits. To go the other way, multiply radians per second by 9.549296586 (rounded).

radians per second = revolutions per minute × 0.1047197551

Example: 10 revolutions per minute = 1.047197551 radians per second.

About these units

Revolution Per Minute (rpm)

Metric (SI)Current unit

One 60th of a hertz. The unit for engine, motor and turntable speeds.

Records gave rpm its fame. The 78 rpm speed was not chosen for a clear engineering reason; Wikipedia says it apparently happened to be the speed of one of the early machines, and the Gramophone Company formally set it as a recording standard in 1912. Columbia unveiled the 33 and a third rpm LP on 21 June 1948, and RCA Victor released the 45 rpm single in February 1949, starting a period called the War of the Speeds.

One rpm equals one sixtieth of a hertz, so a disc at 60 rpm turns at 1 Hz. The SI does not recognise rpm as a unit, preferring hertz or radians per second, and r/min is the usual symbol in standards. Typical examples are a modern car engine idling at about 750 to 900 rpm, consumer hard drives at 7,500 to 10,000 rpm, power-generation turbines at 3,000 or 3,600 rpm, and uranium centrifuges of the Zippe type at 100,000 rpm or more.

1 revolution per minute = 0.01666666667 hertz (approximately).

Sources: Wikipedia: Revolutions per minute; Wikipedia: Phonograph record

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

Related conversions

See all frequency units.