# What is the wavelength?

Finds the wavelength from the frequency and the wave speed (λ = v ÷ f), or the frequency or the speed, for light, sound in air or any wave, with the period and the photon energy.

- Page: https://www.acalculator.org/physics/wavelength-calculator
- JSON spec: https://www.acalculator.org/physics/wavelength-calculator.json
- Version: bc2188c51789

## Default answer

Example with the default inputs (Find Wavelength, Wave Light or radio in a vacuum, Frequency 100, Frequency unit MHz): For this wave, λ = 2.99792458 m.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which of the three to work out from the other two. |
| wave | Wave | Light in a vacuum (299,792,458 m/s), sound in air at 20 °C (343 m/s), or a speed you type. |
| v | Wave speed (m/s) | The speed of the wave in metres per second. |
| f | Frequency | The number of waves per second, in the unit chosen below. |
| fu | Frequency unit | The unit of the frequency. |
| l | Wavelength | The distance from one crest to the next, in the unit chosen below. |
| lu | Wavelength unit | The unit of the wavelength. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The value found, in the unit that puts it from 1 to 1,000, to 10 significant figures. |
| wavelength | Wavelength λ (m) | The wavelength in metres. |
| frequency | Frequency f (Hz) | The frequency in hertz (waves per second). |
| speed | Wave speed v (m/s) | The speed of the wave in metres per second. |
| period | Period T (s) | The time for one full wave: 1 ÷ f. |
| energy | Photon energy (J) | For light: the energy of one photon, E = h × f, in joules. |
| ev | Photon energy (eV) | The photon energy in electronvolts: E ÷ 1.602176634 × 10⁻¹⁹. |

## Method

v = f × λ, so λ = v ÷ f and f = v ÷ λ; T = 1 ÷ f; for light E = h × f.

## Assumptions

- Light travels at exactly 299,792,458 m/s in a vacuum; in glass or water it is slower (type that speed instead).
- Sound travels at 343 m/s in dry air at 20 °C; it is faster in warmer air.
- Each value is read as the exact decimal you typed, so the results have no rounding error before they are shown.

## Worked examples

1. find = wavelength, wave = light, f = 100, fu = MHz gives result = λ = 2.99792458 m, wavelength = 2.997925, period = 0. Source: OpenStax, University Physics Volume 1, §16.1 Traveling Waves: v = λ ÷ T = λf (https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves, retrieved 2026-10-02); NIST CODATA: c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J/Hz, e = 1.602 176 634 × 10⁻¹⁹ C, all exact (https://physics.nist.gov/cgi-bin/cuu/Value?h, retrieved 2026-10-02).
2. find = frequency, wave = light, l = 500, lu = nm gives result = f = 599.584916 THz, frequency = 599,584,916,000,000, energy = 0, ev = 2.479684. Source: NIST CODATA: c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J/Hz, e = 1.602 176 634 × 10⁻¹⁹ C, all exact (https://physics.nist.gov/cgi-bin/cuu/Value?h, retrieved 2026-10-02).
3. find = wavelength, wave = sound, f = 440, fu = Hz gives result = λ = 779.5454545 mm, wavelength = 0.779545. Source: OpenStax, University Physics Volume 1, §17.2 Speed of Sound: 343 m/s in air at 20.0 °C (https://openstax.org/books/university-physics-volume-1/pages/17-2-speed-of-sound, retrieved 2026-10-02).
4. find = speed, f = 2, fu = Hz, l = 2.5, lu = m gives result = v = 5 m/s, speed = 5, period = 0.5. Source: OpenStax, University Physics Volume 1, §16.1 Traveling Waves: v = λ ÷ T = λf (https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves, retrieved 2026-10-02): waves at 2.00 Hz with λ = 2.50 m travel at 5.00 m/s.

## FAQ

### How do I calculate wavelength from frequency?

Divide the wave speed by the frequency: λ = v ÷ f. Radio at 100 MHz travels at the speed of light, 299,792,458 m/s, so λ = 299,792,458 ÷ 100,000,000 = 2.998 m.

### How do I find the frequency from the wavelength?

Divide the speed by the wavelength: f = v ÷ λ. Green light at 500 nm has f = 299,792,458 ÷ 0.0000005 = 5.996 × 10¹⁴ Hz, about 600 THz.

### What speed should I use for sound?

About 343 m/s in dry air at 20 °C. Sound is faster in warmer air and much faster in water and solids; pick "Another speed" and type it. Concert A, 440 Hz, has a wavelength of 343 ÷ 440 = 0.78 m in air.

### What is the energy of a photon?

E = h × f, with Planck’s constant h = 6.62607015 × 10⁻³⁴ J/Hz. A 500 nm photon carries 3.97 × 10⁻¹⁹ J, or 2.48 eV. The calculator shows it for light only.

### How are wavelength and period related?

The period T is the time for one full wave, 1 ÷ f. In one period the wave moves one wavelength, so v = λ ÷ T.

### Does light have the same wavelength in water?

No. Its frequency stays the same, but it slows down, so its wavelength gets shorter. Pick "Another speed" and type the speed in that material (the speed of light divided by the refractive index).

## Sources

- OpenStax, University Physics Volume 1, §16.1 Traveling Waves (v = λ ÷ T = λf; a 2.00 Hz wave with λ = 2.50 m moves at 5.00 m/s), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves
- OpenStax, University Physics Volume 1, §17.2 Speed of Sound (343 m/s in air at 20.0 °C), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/university-physics-volume-1/pages/17-2-speed-of-sound
- NIST CODATA 2022: Planck constant h = 6.626 070 15 × 10⁻³⁴ J Hz⁻¹ (exact), retrieved 2026-10-02. https://physics.nist.gov/cgi-bin/cuu/Value?h
- NIST CODATA 2022: speed of light in vacuum c = 299 792 458 m s⁻¹ (exact), retrieved 2026-10-02. https://physics.nist.gov/cgi-bin/cuu/Value?c
- NIST CODATA 2022: elementary charge e = 1.602 176 634 × 10⁻¹⁹ C (exact; 1 eV = e joules), retrieved 2026-10-02. https://physics.nist.gov/cgi-bin/cuu/Value?e