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

1 radian per second equals 9.549296586 revolutions per minute (rounded).

How to convert radians per second to revolutions per minute

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

revolutions per minute = radians per second × 9.549296586

Example: 10 radians per second = 95.49296586 revolutions per minute.

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

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

Related conversions

See all frequency units.