Frequency Wavelength Converter
Convert frequency to wavelength, or wavelength to frequency, using wave speed = frequency × wavelength. Choose the wave medium so the right propagation speed is used, or enter your own.
Frequency Wavelength Formula
For any wave, speed = frequency × wavelength (v = f × λ). Given the frequency you divide the speed by it to get the wavelength, and given the wavelength you divide the speed by it to get the frequency. The speed must match the wave and its medium. Light and radio waves travel at c = 299,792,458 m/s in vacuum and slightly slower in air, water or glass, where the speed is c ÷ n (n is the refractive index). Sound is far slower, about 343 m/s in air at 20 °C, so using the speed of light for sound would be wrong by a factor of more than 800,000. This tool never assumes light speed by default for other waves: it shows the speed it uses, and you can pick a medium or enter a custom speed in m/s.
What Are Frequency and Wavelength?
Frequency is the number of wave cycles that pass a point each second, measured in hertz (Hz). Wavelength is the distance between two matching points of a wave, such as crest to crest, and it is measured in meters or related units. The two are linked by the speed of the wave: the faster a wave travels, the longer its wavelength for the same frequency.
Why the Medium Matters
When a wave moves from one medium to another, its frequency stays the same, but its speed and wavelength change. Visible light of 500 nm in vacuum has a wavelength of about 375.1 nm in water (n ≈ 1.333) with the same frequency. For sound the speed depends strongly on the medium and also on temperature: in air it is roughly 331.3 + 0.606 × T m/s (T in °C), which gives about 343 m/s at 20 °C.
The speed list in this converter comes from established values. Light and radio waves in vacuum use the exact SI value of c. Air, water and glass use c ÷ n with typical refractive indices, and sound speeds are typical room-temperature values. Real values vary slightly with temperature, pressure, wavelength and material, so use the custom speed option when you have a precise figure.
Supported Frequency Wavelength Units
Frequency units are converted through hertz, wavelength units through meters, and the wave medium sets the speed v.
| Category | Unit | Symbol | Equivalent |
|---|---|---|---|
| Frequency | Hertz | Hz | 1 Hz |
| Frequency | Kilohertz | kHz | 1,000 Hz |
| Frequency | Megahertz | MHz | 1,000,000 Hz |
| Frequency | Gigahertz | GHz | 1,000,000,000 Hz |
| Frequency | Terahertz | THz | 1,000,000,000,000 Hz |
| Frequency | Petahertz | PHz | 1 × 10¹⁵ Hz |
| Wavelength | Kilometers | km | 1,000 m |
| Wavelength | Meters | m | 1 m |
| Wavelength | Centimeters | cm | 0.01 m |
| Wavelength | Millimeters | mm | 0.001 m |
| Wavelength | Micrometers | µm | 0.000001 m |
| Wavelength | Nanometers | nm | 1 × 10⁻⁹ m |
| Wavelength | Picometers | pm | 1 × 10⁻¹² m |
| Wavelength | Angstroms | Å | 1 × 10⁻¹⁰ m |
| Wavelength | Feet | ft | 0.3048 m |
| Wavelength | Inches | in | 0.0254 m |
| Wave medium | Light / radio waves in vacuum (exact c) | — | v = 299,792,458 m/s |
| Wave medium | Light / radio waves in air (n ≈ 1.000293) | — | v = 299,704,644.539 m/s |
| Wave medium | Light in water (n ≈ 1.333) | — | v = 224,900,568.642 m/s |
| Wave medium | Light in typical glass (n ≈ 1.5) | — | v = 199,861,638.667 m/s |
| Wave medium | Sound in air at 20 °C (≈ 343 m/s) | — | v = 343 m/s |
| Wave medium | Sound in fresh water at 20 °C (≈ 1,482 m/s) | — | v = 1,482 m/s |
| Wave medium | Sound in steel (≈ 5,960 m/s) | — | v = 5,960 m/s |
How to Use the Frequency Wavelength Converter
- Choose a direction with the tabs: Frequency to Wavelength or Wavelength to Frequency.
- Enter the value, then choose its unit and the unit you want the answer in.
- Select the wave medium. The wave speed in use is always shown below the buttons. Choose Custom wave speed to enter your own value in m/s.
- The result updates instantly, with the value in all other units of that quantity. Use Swap Direction to flip the conversion, Scientific notation for extreme values, Copy Result to copy, or Reset to clear.
Frequency, wavelength and wave speed must all be greater than zero. For radio and light in vacuum or air, the default selection works for most cases.
Practical Examples
- FM radio, 100 MHz in vacuum: λ = 299,792,458 ÷ 100,000,000 = 2.99792458 m.
- Wi-Fi, 2.4 GHz: λ = 12.4913524167 cm, and 5 GHz gives 5.99584916 cm.
- Green light, 532 nm: f = 563.519657895 THz.
- Sound, 440 Hz in air at 20 °C: λ = 343 ÷ 440 = 0.779545454545 m.
- Ultrasound, 40 kHz in air: λ = 343 ÷ 40,000 = 8.575 mm.
Frequency Wavelength – Common Values
Quick reference for frequently used conversions
| Wave / Band | Frequency | Wavelength | Medium |
|---|---|---|---|
| AM radio | 1 MHz | 299.792458 m | Vacuum |
| FM radio | 100 MHz | 2.99792458 m | Vacuum |
| Mobile (GSM 900) | 900 MHz | 33.3102731111 cm | Vacuum |
| Wi-Fi 2.4 GHz | 2.4 GHz | 12.4913524167 cm | Vacuum |
| Wi-Fi 5 GHz | 5 GHz | 5.99584916 cm | Vacuum |
| Microwave | 10 GHz | 2.99792458 cm | Vacuum |
| Red light | 428.27494 THz | 700 nm | Vacuum |
| Green light | 563.519657895 THz | 532 nm | Vacuum |
| Violet light | 749.481145 THz | 400 nm | Vacuum |
| Concert pitch A4 | 440 Hz | 0.779545454545 m | Sound in air, 20 °C |
| Ultrasonic sensor | 40 kHz | 8.575 mm | Sound in air, 20 °C |
Real-Life Applications of Frequency and Wavelength Conversion
- Radio and telecommunications: antenna length is often a fraction of the wavelength, so engineers convert between MHz or GHz and meters or centimeters.
- Wi-Fi, Bluetooth and mobile networks: each band has a wavelength that affects range and how well signals pass through walls.
- Optics and photonics: lasers, LEDs and filters are specified by wavelength in nanometers, while some physics work uses frequency in terahertz.
- Spectroscopy and astronomy: spectra are recorded in wavelength or frequency depending on the instrument.
- Acoustics and audio: room design, speakers and ultrasonic sensors use sound wavelength in air, where the speed is about 343 m/s.
- Education: the relation v = f × λ is basic wave physics taught at school and university.
For related unit conversions see the Luminance Converter and the Illumination Converter.