Gigahertz to Radians Per Second
Type a value in either box to convert between gigahertz and radians per second. The factor is 6.28319e+09.
| Gigahertz | Radians Per Second |
|---|---|
| 1 GHz | 6283185307.179586 rad/s |
| 2 GHz | 12566370614.359173 rad/s |
| 3 GHz | 18849555921.538757 rad/s |
| 5 GHz | 31415926535.897934 rad/s |
| 10 GHz | 62831853071.795868 rad/s |
| 25 GHz | 157079632679.489655 rad/s |
| 50 GHz | 314159265358.979309 rad/s |
| 100 GHz | 628318530717.958618 rad/s |
How to use
- Enter a value in the Gigahertz field.
- The Radians Per Second figure appears immediately — no button to press.
- Typing in the Radians Per Second field converts back to Gigahertz the same way.
- Use the reference table for the values that come up most often.
Gigahertz to Radians Per Second formula
Converting gigahertz to radians per second is a single multiplication by 6.28318531e+09.
rad/s = GHz × 6.28318531e+09
Why this factor: the gigahertz and the radian per second are both defined against the hertz, so dividing one definition by the other gives 6.28318531e+09 directly. Both definitions are set out in full below.
To go the other way, divide by 6.28318531e+09 — or use the Radians Per Second to Gigahertz converter, which is the same calculation reversed.
Worked example
Take 1000 GHz and multiply by the factor 6.28318531e+09: the result is 6.28319e+12 rad/s.
1000 GHz × 6.28318531e+09 = 6.28319e+12 rad/s
The converter above does this for any value you type, in either direction.
What is a gigahertz?
A gigahertz is one billion cycles per second — the scale of modern processors and wireless.
Definition: Exactly 1×10⁹ hertz.
Where it is used: CPU clock speeds, Wi-Fi bands (2.4 and 5 GHz), mobile networks, and radar.
What is a radian per second?
Radians per second is the SI measure of angular velocity — how fast an angle is swept out.
Definition: One full revolution is 2π radians, so 1 rad/s equals 1/(2π) hertz, about 0.159155 Hz.
Where it is used: Rotational dynamics, control systems, signal processing, and motor modeling.
Worth knowing: Angular velocity and frequency are related but not identical quantities; the 2π factor is exactly what separates them.
Gigahertz vs Radians Per Second
The gigahertz is a metric unit while the radian per second is an SI unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many radians per second are in a gigahertz?
One gigahertz equals 6.28318531e+09 radians per second.
What is the formula to convert gigahertz to radians per second?
Multiply the number of gigahertz by 6.28318531e+09. To reverse it, divide by 6.28318531e+09 instead.
How do I convert radians per second back to gigahertz?
Divide by 6.28318531e+09, which is the same as multiplying by 1.59154943e-10.
How many radians per second are in 10 gigahertz?
10 GHz works out to 62831853071.795868 rad/s.
Is there anything to watch out for with radians per second?
Angular velocity and frequency are related but not identical quantities; the 2π factor is exactly what separates them.
How is the gigahertz defined?
Exactly 1×10⁹ hertz.