How to calculate wavelength and frequency
Every travelling wave obeys one simple relationship between its speed, frequency and wavelength: v = f × λ. Here v is the wave's speed through its medium, f is the frequency — how many cycles pass a point each second, measured in hertz (Hz) — and λ (the Greek letter lambda) is the wavelength, the distance between two successive crests. Because the three quantities are tied together by one equation, knowing any two of them lets you rearrange the formula and find the third.
To solve for a single quantity, rearrange the equation: λ = v / f for wavelength, f = v / λ for frequency, and v = f × λ for speed. This calculator detects which field you leave blank and applies the matching form automatically.
The speed you use depends on the wave. Electromagnetic waves — radio, microwaves, infrared, visible light, X-rays — travel at the speed of light in a vacuum, c = 299,792,458 m/s. Sound waves travel far more slowly; in air at room temperature the speed is roughly 343 m/s. The tool offers both as presets and lets you enter a custom speed for other media. Units do not have to match the SI base units: frequency may be in Hz, kHz, MHz or GHz, and wavelength in m, cm, mm or nm. The calculator converts every input to hertz and metres, computes the answer, then converts it back into the unit you selected.
Common units and SI conversions
| Quantity | Unit | SI conversion |
|---|---|---|
| Frequency (f) | kHz | 1 kHz = 1,000 Hz |
| Frequency (f) | MHz | 1 MHz = 1,000,000 Hz |
| Frequency (f) | GHz | 1 GHz = 1,000,000,000 Hz |
| Wavelength (λ) | cm | 1 cm = 0.01 m |
| Wavelength (λ) | mm | 1 mm = 0.001 m |
| Wavelength (λ) | nm | 1 nm = 0.000000001 m |
| Wave speed (v) | m/s | SI base unit (light c = 299,792,458 m/s) |
Reference note: this is a neutral physics math tool. The simple relation v = f × λ assumes a single wave speed in a uniform, non-dispersive medium; in dispersive media the speed varies with frequency, and inside a material light travels slower than c by the refractive index. Visible light spans roughly 380–700 nm; band boundaries used here are approximate.
Frequently asked questions
- What is the wavelength formula?
- Wavelength is the wave speed divided by the frequency: λ = v / f. It comes from v = f × λ, where v is the wave's speed, f is the frequency in hertz and λ is the wavelength. Rearranged, frequency is f = v / λ and speed is v = f × λ, so any two of the three quantities give the third.
- How do I convert frequency to wavelength?
- Divide the wave speed by the frequency: λ = v / f. For electromagnetic waves use the speed of light, c = 299,792,458 m/s, so a 100 MHz radio wave has λ ≈ 3 m. For sound in air use v ≈ 343 m/s. This tool converts your units to SI, divides, then shows the result in your chosen wavelength unit.
- What speed do I use — light or sound?
- Use the speed at which the wave actually travels. For electromagnetic waves in a vacuum (radio, microwaves, light, X-rays) use the speed of light, 299,792,458 m/s. For sound in air at about 20 °C use roughly 343 m/s. For other media, such as light in glass or sound in water, enter a custom speed.
- What is the speed of light?
- The speed of light in a vacuum is exactly 299,792,458 metres per second, the defined constant c. All electromagnetic waves travel at this speed in a vacuum regardless of frequency. In a medium such as water or glass light is slower by a factor equal to the refractive index, so use a custom speed there.
- How do I find frequency from wavelength?
- Divide the wave speed by the wavelength: f = v / λ. For example, green light at 500 nm has f = 299,792,458 / 0.0000005 ≈ 6.0 × 10¹⁴ Hz. Enter the wavelength and the wave speed, leave the frequency blank, and the calculator solves for it in your chosen unit.
- What units are used?
- Frequency can be Hz, kHz, MHz or GHz; wavelength m, cm, mm or nm; and wave speed m/s. The tool converts every input to SI base units — hertz, metres and metres per second — computes with v = f × λ, then converts the answer back into the unit you selected.