Wave Speed, Frequency and Wavelength Calculator

What this calculator does

Find a wave's length, frequency or speed when you know the other two. Every repeating wave, from ripples on a pond to radio signals, follows one rule. Its speed equals its frequency times its wavelength: v = f × λ.

Frequency (f) counts how many crests pass a point each second. Wavelength (λ, the Greek letter lambda) is the distance between neighboring crests. Multiply the two and you get how far the wave travels each second, its speed (v).

This calculator solves that equation for whichever one you're missing. Choose a preset speed for light in a vacuum or sound in air, or type in any wave speed. It also shows the period, the time one full cycle takes. And it gives the angular frequency, a version of frequency used in many physics formulas.

Where it's used

Why this math matters outside the classroom:

• FM radio. An FM station at 100 MHz sends out waves about 3 × 10⁸ ÷ 10⁸ = 3 m long.
• Musical notes. A tuning fork at 440 Hz in air at 343 m/s makes sound waves about 0.78 m long.
• Wi-Fi antennas. Network engineers note that 2.4 GHz Wi-Fi has a wavelength of about 12.5 cm, which shapes antenna sizes.
• Ocean waves. Surf forecasters find wave speed from the distance between crests and the time between them.
• Colors of light. Students convert green light's 530 nm wavelength into a frequency of about 5.7 × 10¹⁴ Hz.

Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics HSA.CED.A.4, 8.EE.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

1. Choose whether to solve for wavelength, frequency or wave speed.
2. Pick a wave speed preset. Or choose to enter your own speed, for sound in water, waves on a string, earthquake (seismic) waves and so on.
3. Enter the frequency or wavelength you know, with its unit.
4. Choose the unit for the answer. The period, angular frequency and the answer in other units are listed underneath.

What the inputs mean

Wave speed

The speed of light in a vacuum is exactly 299,792,458 m/s, because the meter is defined from it. The sound preset, 343 m/s, is a rounded value for dry air at 20 °C. Real air at other temperatures differs, and the speed of sound calculator can work that out.

Wave speed (v)

How fast the wave travels through its material. For example, sound in water moves at about 1,480 m/s.

Frequency (f)

Frequency is measured in hertz (Hz), meaning cycles per second. Radio and light are usually given in megahertz, gigahertz or terahertz.

Wavelength (λ)

Visible light spans roughly 380 to 750 nanometers. Sound you can hear in air ranges from about 17 meters (20 Hz) down to about 1.7 centimeters (20 kHz).

Formula and method

v = f × λ
λ = v ÷ f
f = v ÷ λ
T = 1 ÷ f
ω = 2π × f

Here v is the wave's speed, f is its frequency, λ is its wavelength, T is the period and ω (omega) is the angular frequency.

In one period T, the wave moves forward exactly one wavelength. Speed is distance over time, so v = λ ÷ T. And because T = 1 ÷ f, that's the same as v = f × λ.

The calculator first converts your inputs to meters, hertz and meters per second. Then it converts the answer to the unit you choose. Angular frequency ω, in radians per second, is 2π times the ordinary frequency. A radian is a unit of angle, and one full cycle is 2π radians.

Worked example

A tuning fork sounds the note A at 440 Hz in room-temperature air. How long is each sound wave?

1. Use the speed of sound in dry air at 20 °C: v = 343 m/s.
2. λ = v ÷ f = 343 ÷ 440 = 0.7795 m (to four decimal places).
3. The period is T = 1 ÷ 440 = 0.0022727 s, about 2.27 milliseconds.

Result: Each wave is about 0.78 m (78 cm) long, and one cycle lasts about 2.27 ms.

Understanding the result

At a fixed speed, frequency and wavelength move in opposite directions. Double the frequency and the wavelength halves. That's why high-pitched sounds and high-frequency radio bands have short waves.

When a wave passes from one material into another, its frequency stays the same but its speed changes. So its wavelength changes too. Light slows down in glass and its wavelength shrinks. The color you see is set by the frequency.

Assumptions and limitations

• The wave travels at a steady speed through a material that's the same all the way through.
• The wave repeats at a single frequency (a pure tone or a single color).
• The sound preset is a fixed 343 m/s. The true speed depends on air temperature and, slightly, on humidity.
• In some materials, the speed itself depends on frequency. Light in glass and deep-water ocean waves both work this way (it's called dispersion). There, you must enter the speed that applies to your frequency.
• Light in air travels about 0.03% slower than in a vacuum. This calculator only reflects that if you enter that speed yourself.

Frequently asked questions

How this calculator is checked

Method: Wave equation v = fλ and T = 1/f (standard kinematics of periodic waves); speed of light exact by the SI definition of the meter. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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