Hertz (Hz)	Radians per Second (rad/s)
1 Hz	6.2832 rad/s
2 Hz	12.5664 rad/s
5 Hz	31.4159 rad/s
10 Hz	62.8319 rad/s
25 Hz	157.0796 rad/s
50 Hz	314.1593 rad/s
100 Hz	628.3185 rad/s
250 Hz	1570.8 rad/s
500 Hz	3141.59 rad/s
1000 Hz	6283.19 rad/s

Convert Hertz to Radians per Second

Convert hertz to radians per second (Hz to rad/s) with our instant calculator. 1 Hz = 6.283185 rad/s. Includes exact formula and reference tables.

How to Convert Hertz to Radians per Second (Hz to rad/s)

1 Hertz (Hz) is equal to 6.283185 Radians per Second (rad/s). Multiply the hertz value by 6.283185307

Quick Answer 1 Hz = 6.283185 rad/s

Formula rad/s = Hz × 6.283185307

Inverse Factor 1 rad/s = 0.159155 Hz

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 Hertz (Hz): Hertz (Hz) is a unit in the Frequency measurement category. It is widely used in base si unit (1 cycle/sec). The hertz (Hz) serves as the primary reference base unit for the frequency domain.

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 Hertz (rad/s to Hz) calculator (1 rad/s = 0.159155 Hz).

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

Convert 5 Hertz to Radians per Second: Applying the formula (rad/s = Hz × 6.283185307): starting with 5 Hz, multiply the hertz value by 6.283185307 to get 31.4159 rad/s.
Convert 10 Hertz to Radians per Second: Applying the formula (rad/s = Hz × 6.283185307): starting with 10 Hz, multiply the hertz value by 6.283185307 to get 62.8319 rad/s.
Convert 50 Hertz to Radians per Second: Applying the formula (rad/s = Hz × 6.283185307): starting with 50 Hz, multiply the hertz value by 6.283185307 to get 314.1593 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 hertz to radians per second.

How many radians per second are in 1 hertz?

There are 6.283185 radians per second (rad/s) in 1 hertz (Hz). Conversely, 1 radians per second equals 0.159155 hertz.

How do you convert hertz to radians per second?

To convert hertz (Hz) to radians per second (rad/s), use the formula: rad/s = Hz × 6.283185307. Multiply the hertz value by 6.283185307. For example, 10 Hz equals 62.8319 rad/s.

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

To convert in the reverse direction from radians per second (rad/s) to hertz (Hz), use the inverse formula: Hz = rad/s × 0.1591549431. Multiply the radians per second value by 0.1591549431 (1 rad/s = 0.159155 Hz).

What is the difference between hertz (Hz) and radians per second (rad/s)?

Both hertz and radians per second measure frequency. Hertz (Hz) is a unit in the Frequency measurement category. It is widely used in base si unit (1 cycle/sec). The hertz (Hz) serves as the primary reference base unit for the frequency domain. 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).