Kilohertz to Radians Per Second (kHz to rad/s)

1 kilohertz equals 6,283.185307 radians per second (rounded).

How to convert kilohertz to radians per second

To convert kilohertz to radians per second, multiply the number of kilohertz by 6,283.185307. The factor is rounded to 10 significant digits. To go the other way, multiply radians per second by 0.0001591549431 (rounded).

radians per second = kilohertz × 6,283.185307

Example: 10 kilohertz = 62,831.85307 radians per second.

About these units

Kilohertz (kHz)

Metric (SI)Current unit

1,000 hertz. AM radio stations are tuned in kilohertz and audio is sampled at 44.1 kHz.

Older radio operators called it the kilocycle. Before the CGPM adopted the hertz in 1960, thousands of cycles per second were written kc/s, and the popular press only switched to kilohertz in the late 1960s. The name changed, but the number on the dial did not.

A kilohertz is 1,000 hertz, a range that covers audible sound and medium-wave radio. Medium wave runs from 531 to 1602 kHz in Europe, Asia and Africa with 9 kHz channel spacing, and from 530 to 1700 kHz in the Americas with 10 kHz spacing. Audio engineers use it for sampling rates: 44.1 kHz comes from the Compact Disc, which Sony used from 1979, and the rate was originally chosen so digital audio could fit on video tape for both PAL and NTSC. Because sampling must exceed twice the highest frequency, 44.1 kHz comfortably covers hearing up to 20 kHz.

1 kilohertz = 1,000 hertz (exactly).

Sources: Wikipedia: Medium wave; Wikipedia: 44,100 Hz; Wikipedia: Kilohertz

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.