Wavelength & Frequency Calculator

Background.

This wavelength calculator (and frequency calculator, depending on which way you run it) solves the universal wave equation v = λf for whichever quantity you do not know, and then returns the photon energy E = hf, the period T = 1/f, and the wavelength in nanometres as bonus outputs.

For electromagnetic waves in vacuum the wave speed is the speed of light c = 299,792,458 m/s — a value that has been exact by definition since the 2019 SI redefinition, in which the metre is now derived from c and the second rather than the other way around. For waves in any other medium (light in glass, microwaves in a waveguide, sound in air, water waves in a tank) you override the mediumSpeed input with the phase velocity of the wave in that medium, and the same c = λf relation becomes v = λf with no other change to the math.

Pick a 'solve for' mode, enter the one quantity you know in SI base units (metres for wavelength, hertz for frequency), and the tool returns the full set: wavelength in metres and nanometres, frequency in hertz, photon energy in joules, and period in seconds.

The reason this single triangle of equations matters so much, and the reason physicists and engineers reach for it dozens of times a day, is that it ties together the three different languages we use to describe waves: a spatial-period language (wavelength, in metres — what you measure with a ruler and a diffraction grating), a temporal-period language (frequency, in hertz — what you read off a spectrum analyser or a stopwatch on a pendulum), and an energy language (photon energy, in joules or electronvolts — what matters for photochemistry, atomic spectroscopy, and the photoelectric effect). The same green photon at 550 nm has frequency 5.45 × 10¹⁴ Hz and carries 2.25 eV of energy — three numbers that look unrelated until you go through c = λf and E = hf.

Below the widget you will find a tour of the electromagnetic spectrum from radio (kilometre wavelengths, kilohertz frequencies, sub-microelectronvolt photons) up through visible light, ultraviolet, X-ray, and gamma (sub-picometre wavelengths, exahertz frequencies, megaelectronvolt photons), the derivation of why c is now an exact integer rather than a measured quantity, the change of wavelength (but not frequency) when light enters a denser medium such as glass or water, the relationship to the Planck relation E = hf and how it underwrites Einstein's 1905 explanation of the photoelectric effect, and worked examples drawn from astronomy (redshift), telecommunications (Wi-Fi at 2.4 GHz), and medical imaging (X-ray at 0.1 nm). The calculator is a thin shell over a pure-function solver registered at wavelengthFrequency.solve in the Quanta engine; 30 unit tests cover the visible spectrum, radio, microwave, X-ray, and non-vacuum media so the number you read here is the same number used in our other physics tooling.

What is wavelength & frequency calculator?

Wavelength (λ, the Greek letter lambda) is the spatial period of a wave — the distance, measured along the direction of propagation, between two consecutive points that are in the same phase of oscillation (two adjacent crests, or two adjacent troughs, or two adjacent zero-crossings going in the same direction). It is measured in metres in SI, but in practice the unit is matched to the regime: kilometres for AM radio, metres for FM radio and HF, centimetres for microwaves, micrometres for infrared, nanometres for visible light and ultraviolet, ångströms or picometres for X-rays. Frequency (f, sometimes ν the Greek letter nu in physics texts) is the temporal period of the same wave — the number of complete cycles passing a fixed point per second. It is measured in hertz (Hz), where 1 Hz = 1 cycle per second, with multiplier prefixes scaling up through kHz, MHz, GHz, THz, PHz, and EHz. Wavelength and frequency are tied together by the wave equation v = λf, where v is the phase speed of the wave in whichever medium it is travelling through. For electromagnetic waves in vacuum, v is the speed of light c — a defined constant equal to 299,792,458 m/s exactly. Because v is fixed for a given medium, wavelength and frequency are inversely proportional: a wave with twice the frequency has half the wavelength. The full electromagnetic spectrum spans 24 orders of magnitude in frequency, from extremely low frequency radio at a few hertz (wavelengths of thousands of kilometres) at one end through the visible band (about 400–750 nm, 400–750 THz) to gamma rays beyond 10²⁰ Hz with sub-femtometre wavelengths at the other. The photon-energy language adds a third dimension: by the Planck relation E = hf, where h = 6.62607015 × 10⁻³⁴ J·s (also exact post-2019 SI), the same wave can be described as a stream of quanta each carrying energy proportional to the frequency. Radio photons carry nanoelectronvolts and so are imperceptible individually; visible photons carry a couple of electronvolts and trigger chemical changes in the retina; X-ray photons carry kiloelectronvolts and ionise atoms.

How to use this calculator.

1. 01Choose what to solve for: 'Frequency' if you know the wavelength, 'Wavelength' if you know the frequency, or 'Photon energy' if you want E = hf and have either λ or f.
2. 02Enter the known quantity in SI base units. Wavelength must be in metres — for nanometres divide by 1,000,000,000 (550 nm = 5.5e-7 m); for ångströms divide by 1e10 (1 Å = 1e-10 m). Frequency must be in hertz — for MHz multiply by 1,000,000; for GHz by 1,000,000,000; for THz by 1,000,000,000,000.
3. 03Leave the wave speed field at its default 299,792,458 m/s for any electromagnetic wave in vacuum or (to two decimal places) in air. Override it only for waves in a refractive medium (light in water ≈ 2.25 × 10⁸ m/s, light in glass ≈ 2.0 × 10⁸ m/s) or for non-EM waves (sound in air ≈ 343 m/s at 20 °C).
4. 04Leave the field for the unknown quantity blank — the calculator computes it from the input you supplied. If you set solveFor = 'energy' and provide both wavelength and frequency, frequency takes precedence.
5. 05Read the primary output (wavelength) plus the four derived outputs: frequency in Hz, photon energy in joules, wavelength in nanometres for spectroscopic convention, and period T in seconds.
6. 06To convert the photon energy from joules to electronvolts, divide by 1.602176634 × 10⁻¹⁹ (the elementary charge e, exact by SI definition). A red photon at 700 nm carries about 2.84 × 10⁻¹⁹ J = 1.77 eV.

The formula.

The three relationships baked into the calculator are:

v = λ × f (wave equation — any wave, any medium) c = λ × f (electromagnetic waves in vacuum, with c = 299,792,458 m/s exactly) E = h × f (Planck relation — photon energy) T = 1 / f (period, the temporal partner of wavelength)

Deriving λ = c / f and f = c / λ from the first line is a straightforward division — solve the equation for whichever variable is the unknown. The reason c is now an exact integer rather than a measured quantity with experimental uncertainty is that in 1983 the General Conference on Weights and Measures (CGPM) redefined the metre as 'the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second'. Before 1983 the metre was a physical artefact and then a wavelength of a krypton-86 transition, and c had to be measured by experiment with finite uncertainty. After 1983 the metre is derived from c and the second, so c is fixed by definition. The 2019 SI redefinition extended the same logic to four other base units, fixing exact numerical values for the Planck constant h, the elementary charge e, the Boltzmann constant k_B, and the Avogadro constant N_A — so the kilogram, the ampere, the kelvin, and the mole are now all defined in terms of these invariants of nature rather than physical artefacts. The Planck relation E = hf was introduced by Max Planck in 1900 to explain blackbody radiation, then promoted by Einstein in 1905 from a mathematical trick to a physical statement: each photon really does carry energy hf, which is why the photoelectric effect has a sharp frequency threshold. Two subtleties matter for the calculator. First, when light crosses from vacuum into a refractive medium with refractive index n, the frequency f is unchanged (the source is what determines f), but the phase speed drops to v = c/n and so the wavelength drops too: λ_medium = λ_vacuum / n. The calculator handles this if you override mediumSpeed to c/n. Second, for matter waves (electrons, neutrons) the relevant relation is the de Broglie wavelength λ = h/p, not λ = c/f — this calculator is for waves with a frequency, not for matter waves with a momentum.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST CODATA 2018 Recommended Values — speed of light in vacuum c = 299,792,458 m/s (exact). National Institute of Standards and Technology, Committee on Data for Science and Technology.
2. [2]NIST CODATA 2018 Recommended Values — Planck constant h = 6.62607015 × 10⁻³⁴ J·s (exact, post-2019 SI). National Institute of Standards and Technology.
3. [3]BIPM (2019). The International System of Units (SI), 9th edition. Bureau International des Poids et Mesures — the official document defining the 2019 SI redefinition in which c, h, e, k_B, and N_A are all fixed exactly and the metre, kilogram, ampere, kelvin, and mole are derived from them.
4. [4]Feynman, R. P., Leighton, R. B. & Sands, M. (1964). The Feynman Lectures on Physics, Volume I, Chapter 17 'Space-Time'. Caltech / Addison-Wesley. The wave equation v = λf and its derivation from the kinematics of a propagating disturbance.
5. [5]Halliday, D., Resnick, R. & Walker, J. (2014). Fundamentals of Physics, 10th edition. Wiley. Chapter 16 §16-2 (transverse waves, wavelength and frequency) and Chapter 33 §33-1 (Maxwell's prediction of electromagnetic waves and the constancy of c).
6. [6]Planck, M. (1901). Ueber das Gesetz der Energieverteilung im Normalspectrum. Annalen der Physik, 309(3), 553–563. The original derivation of E = hν (Planck relation) from the blackbody radiation law.
7. [7]Einstein, A. (1905). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik, 322(6), 132–148. Einstein's photoelectric-effect paper which promoted the Planck relation from a mathematical trick to a physical statement about photons.
8. [8]Hyperphysics — Wave Equation and Electromagnetic Spectrum reference pages, Georgia State University. Conceptual overview of the c = λf relation and tabulated benchmark frequencies for the full EM spectrum.