Angular Frequency Calculator

Calculate ω, f, T, and RPM

Input Parameters

Cycles per second (Hz)

Key Formulas:
ω = 2πf
f = 1/T
T = 1/f
RPM = f × 60

What is Angular Frequency?

Angular frequency (ω) is the rate of change of angular position, measured in radians per second.

Formula:

ω = 2πf

where f is frequency in Hz

Relationships:

• ω = 2πf = 2π/T

• f = ω/(2π) = 1/T

• T = 2π/ω = 1/f

Features

  • Calculate from frequency
  • Calculate from period
  • Calculate from RPM
  • Angular frequency (ω)
  • Frequency (f)
  • Period (T)
  • RPM conversion
  • Step-by-step solutions
  • Copy results

Units

Angular Frequency (ω):

Radians per second (rad/s)

Frequency (f):

Hertz (Hz) = cycles per second

Period (T):

Seconds (s)

RPM:

Revolutions per minute

Common Values

AC Power (US):

60 Hz = 377 rad/s

AC Power (EU):

50 Hz = 314 rad/s

Earth Rotation:

7.27 × 10⁻⁵ rad/s

Typical Motor:

3000 rpm = 314 rad/s

Use Cases

  • Physics and engineering
  • Electrical engineering (AC circuits)
  • Mechanical engineering (rotating systems)
  • Signal processing
  • Oscillations and waves
  • Motor speed calculations
  • Vibration analysis
  • Telecommunications

Applications

Real-World Applications:

Electrical:

AC power systems, generators, transformers

Mechanical:

Motors, turbines, rotating machinery

Physics:

Simple harmonic motion, pendulums, springs

Communications:

Radio waves, carrier frequencies, modulation

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