Frequency Calculator

This frequency calculator works out frequency, period, and angular frequency from a single input. Frequency is the number of complete cycles that occur per second, measured in hertz (Hz), and it describes everything from the oscillation of a pendulum to the vibration of a guitar string, the alternation of electrical current, and the propagation of light and radio waves. The three quantities covered here are closely related. Period (T) is the time in seconds for one complete cycle; frequency (f) is its reciprocal, so f = 1/T and T = 1/f. Angular frequency (omega) measures the same oscillation but in radians per second, with omega = 2 x pi x f, which makes it the natural unit for trigonometric wave equations and AC circuits. You enter a period in seconds and the calculator instantly returns the frequency in hertz, the angular frequency in radians per second, and the period itself as a cross-check. New Zealand mains electricity oscillates at 50 Hz, which means a period of 0.02 seconds and an angular frequency of about 314.16 rad/s. These are the default values pre-filled in the calculator. The tool is useful for physics and engineering students working on oscillation problems, electronics technicians analysing AC signals, and anyone who needs to convert between the three common ways of expressing how fast something repeats. A separate section lets you derive frequency from a wave's speed and wavelength using f = v / lambda. Results are mathematical and assume a simple sinusoidal waveform with constant frequency.

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Enter the period in seconds. New Zealand mains is 50 Hz (T = 0.02 s). Angular frequency omega = 2 x pi x f.

Sound in air is about 343 m/s. Light in a vacuum is about 3 x 10^8 m/s. Frequency = speed / wavelength.