Gigahertz to Radians Per Second (GHz to rad/s)

1 gigahertz equals 6,283,185,307 radians per second (rounded).

How to convert gigahertz to radians per second

To convert gigahertz to radians per second, multiply the number of gigahertz by 6,283,185,307. The factor is rounded to 10 significant digits. To go the other way, multiply radians per second by 1.591549431×10⁻¹⁰ (rounded).

radians per second = gigahertz × 6,283,185,307

Example: 10 gigahertz = 62,831,853,072 radians per second.

About these units

Gigahertz (GHz)

Metric (SI)Current unit

One billion hertz. Modern processor clocks and Wi-Fi run at gigahertz frequencies.

On 6 March 2000, AMD demonstrated a processor passing the 1 GHz mark, a few days before Intel shipped 1 GHz systems, according to Wikipedia. After that, clock rates rose more slowly: Intel's 3 GHz Pentium 4 arrived in 2002, and later performance came more from design changes than raw speed, since higher clock rates produce more heat. The highest boost clock on a production processor is listed as 6.2 GHz for the Intel i9-14900KS in 2024.

A gigahertz is a billion hertz, the range known as microwaves. The most familiar example may be the kitchen: consumer microwave ovens typically run at 2.45 GHz, a band that is available for industrial, scientific and medical use worldwide. Percy Spencer of Raytheon discovered the heating effect in 1945 when a radar set melted a candy bar in his pocket, and Raytheon sold the first commercial oven, the Radarange, in 1947.

1 gigahertz = 1,000,000,000 hertz (exactly).

Sources: Wikipedia: Clock rate; Wikipedia: Microwave oven; Wikipedia: Gigahertz

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.