Kilohertz (kHz)	Radians per Second (rad/s)
1 kHz	6283.19 rad/s
2 kHz	12566.37 rad/s
5 kHz	31415.93 rad/s
10 kHz	62831.85 rad/s
25 kHz	157079.63 rad/s
50 kHz	314159.27 rad/s
100 kHz	628318.53 rad/s
250 kHz	1570796.33 rad/s
500 kHz	3141592.65 rad/s
1000 kHz	6283185.31 rad/s

Convert Kilohertz to Radians per Second

Convert kilohertz to radians per second (kHz to rad/s) with our instant calculator. 1 kHz = 6283.185307 rad/s. Includes exact formula and reference tables.

How to Convert Kilohertz to Radians per Second (kHz to rad/s)

1 Kilohertz (kHz) is equal to 6283.185307 Radians per Second (rad/s). Multiply the kilohertz value by 6283.185307

Quick Answer 1 kHz = 6283.185307 rad/s

Formula rad/s = kHz × 6283.185307

Inverse Factor 1 rad/s = 0.000159 kHz

Unit Definitions & Metrology Context

The standard SI unit of frequency is the hertz (Hz), defined as one complete cycle or oscillation per second (1 s⁻¹).

About Kilohertz (kHz): Kilohertz (kHz) is a unit in the Frequency measurement category. It is widely used in audio & am radio (1,000 hz). Relative to the frequency base unit, 1 kHz equals 1000 Hertz (Hz).

About Radians per Second (rad/s): Radians per Second (rad/s) is a unit in the Frequency measurement category. It is widely used in angular velocity (ω = 2πf). Relative to the frequency base unit, 1 rad/s equals 0.159155 Hertz (Hz).

Need to convert in the opposite direction? Visit our Convert Radians per Second to Kilohertz (rad/s to kHz) calculator (1 rad/s = 0.000159 kHz).

Step-by-Step Worked Examples (kHz to rad/s)

Convert 5 Kilohertz to Radians per Second: Applying the formula (rad/s = kHz × 6283.185307): starting with 5 kHz, multiply the kilohertz value by 6283.185307 to get 31415.9265 rad/s.
Convert 10 Kilohertz to Radians per Second: Applying the formula (rad/s = kHz × 6283.185307): starting with 10 kHz, multiply the kilohertz value by 6283.185307 to get 62831.8531 rad/s.
Convert 50 Kilohertz to Radians per Second: Applying the formula (rad/s = kHz × 6283.185307): starting with 50 kHz, multiply the kilohertz value by 6283.185307 to get 314159.2654 rad/s.

Popular Frequency Conversions

Hertz ⇄ Revolutions per Minute

Multiply Hertz by 60 to calculate Revolutions per Minute (RPM = Hz × 60).

Revolutions per Minute ⇄ Hertz

Divide RPM by 60 to find frequency in Hertz (Hz = RPM ÷ 60).

Gigahertz ⇄ Megahertz

1 gigahertz (GHz) contains exactly 1,000 megahertz (MHz).

Megahertz ⇄ Kilohertz

1 megahertz (MHz) contains exactly 1,000 kilohertz (kHz).

Radians per Second ⇄ Hertz

Divide radians per second by 2π (~6.283185) to calculate frequency in Hertz.

Frequently Asked Questions

Verified answers and formulas for converting kilohertz to radians per second.

How many radians per second are in 1 kilohertz?

There are 6283.185307 radians per second (rad/s) in 1 kilohertz (kHz). Conversely, 1 radians per second equals 0.000159 kilohertz.

How do you convert kilohertz to radians per second?

To convert kilohertz (kHz) to radians per second (rad/s), use the formula: rad/s = kHz × 6283.185307. Multiply the kilohertz value by 6283.185307. For example, 10 kHz equals 62831.8531 rad/s.

How do I convert back from radians per second to kilohertz?

To convert in the reverse direction from radians per second (rad/s) to kilohertz (kHz), use the inverse formula: kHz = rad/s × 0.0001591549431. Multiply the radians per second value by 0.0001591549431 (1 rad/s = 0.000159 kHz).

What is the difference between kilohertz (kHz) and radians per second (rad/s)?

Both kilohertz and radians per second measure frequency. Kilohertz (kHz) is a unit in the Frequency measurement category. It is widely used in audio & am radio (1,000 hz). Relative to the frequency base unit, 1 kHz equals 1000 Hertz (Hz). Radians per Second (rad/s) is a unit in the Frequency measurement category. It is widely used in angular velocity (ω = 2πf). Relative to the frequency base unit, 1 rad/s equals 0.159155 Hertz (Hz).

How do you convert RPM to Hertz (Hz)?

To convert RPM (revolutions per minute) to Hertz (cycles per second), divide by 60. For example, a car engine idling at 600 RPM is spinning at 10 Hz (600 ÷ 60 = 10 Hz).