Angular Frequency Calculator
Calculate rotational speed and oscillation rates instantly
Angular Frequency (ω)
radians per second (rad/s)
What is Angular Frequency?
Angular frequency (denoted by the Greek letter omega ω) measures how quickly an object rotates or oscillates in terms of radians per unit of time. Unlike standard frequency (measured in Hertz or cycles per second), angular frequency focuses on the displacement of the angle over time.
The Physics Formula
This calculator uses the two primary mathematical relationships for angular frequency:
- From Frequency: ω = 2πf
- From Period: ω = 2π / T
Where π (Pi) is approximately 3.14159, f is the ordinary frequency in Hz, and T is the time it takes for one full cycle to complete.
Practical Examples
Example 1: Electricity
Standard household AC power in many regions has a frequency of 60 Hz.
Calculation: 60 × 2 × 3.14159 = 376.99 rad/s.
Standard household AC power in many regions has a frequency of 60 Hz.
Calculation: 60 × 2 × 3.14159 = 376.99 rad/s.
Example 2: Pendulums
If a pendulum takes 2 seconds to complete one full swing (Period T = 2s):
Calculation: (2 × 3.14159) / 2 = 3.14 rad/s.
If a pendulum takes 2 seconds to complete one full swing (Period T = 2s):
Calculation: (2 × 3.14159) / 2 = 3.14 rad/s.