What is the wavelength?
Pick what to find, the kind of wave, and type the other values. The wavelength calculator uses v = f × λ, with the exact speed of light.
- Answer
- λ = 2.99792458 m
For this wave, λ = 2.99792458 m.
- Wavelength λ (m)
- 2.99792458
- Frequency f (Hz)
- 100,000,000
- Wave speed v (m/s)
- 299,792,458
- Period T (s)
- 0.00000001
- Photon energy (J)
- 0.0000000000000000000000000662607015
- Photon energy (eV)
- 0.0000004135667697
Answer: λ = 2.99792458 m. For this wave, λ = 2.99792458 m.
How to calculate
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.
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.
Method: v = f × λ, so λ = v ÷ f and f = v ÷ λ; T = 1 ÷ f; for light E = h × f.
- 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
Each example is checked against the calculator on every build.
- Find Wavelength, Wave Light or radio in a vacuum, Frequency 100, Frequency unit MHz gives Answer λ = 2.99792458 m, Wavelength λ (m) 2.997925, Period T (s) 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)
- Find Frequency, Wave Light or radio in a vacuum, Wavelength 500, Wavelength unit nm gives Answer f = 599.584916 THz, Frequency f (Hz) 599,584,916,000,000, Photon energy (J) 0, Photon energy (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)
- Find Wavelength, Wave Sound in air at 20 °C, Frequency 440, Frequency unit Hz gives Answer λ = 779.5454545 mm, Wavelength λ (m) 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)
- Find Speed, Frequency 2, Frequency unit Hz, Wavelength 2.5, Wavelength unit m gives Answer v = 5 m/s, Wave speed v (m/s) 5, Period T (s) 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
How it works
A wave’s speed v, frequency f and wavelength λ are linked by v = f × λ. Pick which one to find:
- Wavelength: λ = v ÷ f.
- Frequency: f = v ÷ λ.
- Speed: v = f × λ.
For the wavelength and the frequency, pick the wave: light or radio in a vacuum (v = 299,792,458 m/s exactly), sound in air at 20 °C (v = 343 m/s), or another speed you type in m/s. Frequencies are in Hz, kHz, MHz, GHz, THz or PHz (powers of 1,000), wavelengths in pm, nm, µm, mm, cm, m or km. Each value must be from 10⁻¹⁵ to 10²¹ in its unit.
Every typed number is read as the exact decimal you typed and multiplied by its exact unit size, so the results are exact fractions. Each one is then rounded half up (away from zero at a half) to 10 significant figures:
- Answer: the value found. The unit is chosen after rounding to 10 significant figures. A wavelength is shown in the largest of pm, nm, µm, mm, m and km (cm is not used) that leaves at least 1, and a frequency in the largest of Hz, kHz, MHz, GHz, THz and PHz that leaves at least 1; values below 1 pm or 1 Hz use pm or Hz. For example, 999.99999999999 m rounds to 1000 m, so it is shown as 1 km. A speed is in m/s.
- Wavelength (m), frequency (Hz), wave speed (m/s) and period T = 1 ÷ f (s).
- Photon energy E = h × f in joules, with h = 6.62607015 × 10⁻³⁴ J/Hz, and in electronvolts, E ÷ 1.602176634 × 10⁻¹⁹. Shown only for light (not for sound, another speed, or when finding the speed).
Worked examples by hand
FM radio at 100 MHz. f = 100 × 10⁶ = 10⁸ Hz. λ = 299,792,458 ÷ 10⁸ = 2.99792458 m. T = 1 ÷ 10⁸ = 10⁻⁸ s.
Green light, λ = 500 nm. λ = 5 × 10⁻⁷ m. f = 299,792,458 ÷ (5 × 10⁻⁷) = 5.99584916 × 10¹⁴ Hz = 599.584916 THz. E = 6.62607015 × 10⁻³⁴ × 5.99584916 × 10¹⁴ = 3.972891714 × 10⁻¹⁹ J, which is ÷ 1.602176634 × 10⁻¹⁹ = 2.479683969 eV.
Concert A, 440 Hz in air. λ = 343 ÷ 440 = 0.77954545… m = 779.5454545 mm.
A wave on a string: 2 Hz, λ = 2.5 m. v = 2 × 2.5 = 5 m/s; T = 1 ÷ 2 = 0.5 s.
Other questions people ask
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).