# Frequency to Angular Frequency Conversion Calculator

This tool converts Frequency (in Hz) to the Angular Frequency in radians per second (rad/s)

## Formula

The relationship between frequency (f) and angular frequency (ω) is straightforward and governed by the formula:

ω = 2πf

Where:

• ω is the angular frequency in radians per second.
• f is the frequency in hertz.
• π is approximately 3.14159.

This formula indicates that one complete oscillation cycle in hertz is equivalent to a 2π radian rotation in a circular motion.

## Example

If you have a wave with a frequency of 50 Hz, its angular frequency would be:

ω = 2π×50 Hz = 314.16 rad/s

## What is Angular Frequency?

Angular frequency, often denoted by the Greek letter omega (ω), is a scalar measure of rotation rate. It represents the rate of change of the phase of a waveform, or in a more physical sense, it indicates how rapidly a sinusoidal wave, like sound or light, oscillates as it propagates.

Angular frequency is expressed in radians per second (rad/s), contrasting with ordinary frequency, which is expressed in cycles per second, or hertz (Hz). The difference primarily lies in the unit used to express a complete cycle; angular frequency uses radians, while standard frequency uses cycles.

## Practical Applications of Angular Frequency

Angular frequency is useful in various scientific and engineering disciplines:

• Electrical Engineering: Angular frequency is used in the analysis of alternating current (AC) circuits, where the sinusoidal variation of voltage and current is best described in terms of radians.
• Mechanics: In systems involving rotational motion, such as gears and turbines, angular frequency provides a clear measure of how fast these components rotate.
• Optics and Wave Mechanics: Angular frequency helps describe the propagation characteristics of waves, including light waves, sound waves, and other forms of electromagnetic radiation.