Frequency Calculator
Find frequency in hertz three ways: from a period (seconds, ms, or µs), from wave speed and wavelength, or from angular frequency in rad/s. Pick a mode and the calculator returns the frequency and the matching period.
Example: with Find frequency from Period (T) · Period 0.02 · Period unit s (seconds) · Wave speed (m/s) 343 · Wavelength (m) 0.686 → Frequency: 50.00 Hz.
- Matching period20.000 ms per cycle
- Where it landsWithin human hearing (20 Hz to 20 kHz); 50–60 Hz is mains power
Computed by the calculator below using its default values. Change any input to see your own numbers.
Frequency is cycles per second (hertz). From a period, f = 1/T. From a wave, f = v/λ. From angular frequency, f = ω/2π. Period and frequency are always reciprocals.
Frequency and period are reciprocals
Frequency counts how many complete cycles happen each second, measured in hertz. Its partner, the period, is how long one cycle takes. They are simple reciprocals: a signal that repeats every 0.02 seconds has a frequency of 1 / 0.02 = 50 Hz, and a 50 Hz signal has a period of 20 milliseconds. Knowing either one gives you the other instantly.
This reciprocal link shows up everywhere from a pendulum's swing to an engine's rpm to the pixels refreshing on a screen. Whenever something repeats at a steady rate, frequency and period are two ways of describing the same rhythm.
From waves and from angles
For a traveling wave, frequency also equals speed divided by wavelength, f = v/λ. A sound wave moving at 343 m/s with a 0.686 m wavelength cycles 500 times a second. This is how pitch, wavelength, and the speed of sound in a medium all connect.
Angular frequency ω, used in rotations and oscillations, measures radians per second instead of cycles. Since one cycle is 2π radians, f = ω/2π converts between them. An ω of about 314 rad/s corresponds to 50 Hz — the same mains-power rhythm seen from an angular point of view.
How it’s calculated
Frequency in hertz by mode: from a period f = 1/T (period converted to seconds, 1 ms = 1e-3 s, 1 µs = 1e-6 s); from a wave f = v/λ with speed in m/s and wavelength in m; from angular frequency f = ω/2π. The matching period is reported as 1/f.
Treats a single, steady periodic signal. Real signals can contain many frequencies at once; this returns one fundamental frequency from the inputs you give.
Frequencies and periods around us
| Source | Frequency | Period |
|---|---|---|
| Mains power (US) | 60 Hz | 16.7 ms |
| Middle C (music) | 262 Hz | 3.82 ms |
| Top of human hearing | 20 kHz | 50 µs |
| AM radio | ≈ 1 MHz | 1 µs |
| Wi-Fi (2.4 GHz) | 2.4 GHz | 0.42 ns |
Period = 1/frequency; representative published values for each source.
Common mistakes
- Forgetting to convert the period to seconds — a period in milliseconds gives a frequency 1,000 times too small if left unconverted.
- Confusing angular frequency (rad/s) with ordinary frequency (Hz); divide ω by 2π to convert.
- Dividing wavelength by speed instead of speed by wavelength when finding frequency.
- Assuming a signal has one frequency when it may be a mix of several.
Frequently asked questions
What is the frequency formula?
Frequency equals one divided by the period: f = 1/T. For waves it also equals speed divided by wavelength, f = v/λ, and from angular frequency it is f = ω/2π. The unit is hertz, or cycles per second.
How do I convert a period to a frequency?
Take the reciprocal. A period of 0.02 seconds gives 1 / 0.02 = 50 Hz. Convert any milliseconds or microseconds to seconds first so the answer comes out in hertz.
What is the difference between frequency and angular frequency?
Frequency counts full cycles per second in hertz; angular frequency counts radians per second. Since one cycle is 2π radians, angular frequency is 2π times the frequency.
How are frequency and wavelength related?
For a wave, frequency times wavelength equals speed, so frequency is speed divided by wavelength. Higher frequency means shorter wavelength for a fixed wave speed.
What is one hertz?
One hertz is one complete cycle per second. A 60 Hz power line alternates 60 times each second, and a 440 Hz musical note vibrates 440 times a second.