Calculator Tools
Wavelength Calculator
Convert frequency to wavelength, wavelength to frequency, or photon energy to either, with EM band lookup and antenna lengths. Runs in your browser.
Calculator mode
Accepts scientific notation like 1.5e9. Comma decimals also work.
n = 1 (exact). Used by default.
Worked examples
Tap any example to load it into the calculator. Mixes Wi-Fi, ham radio, optics, telecom fiber, and physics homework.
Which formula does this use?
- Frequency, wavelength: c = lambda x f, where c is the speed of light (299,792,458 m/s in a vacuum). In a medium with refractive index n, the wave travels at v = c / n, so lambda = v / f.
- Photon energy: E = h x f = h x c / lambda. The Planck constant h is 6.62607015 x 10^-34 J*s (exact, per the 2019 SI redefinition). Use 1 eV = 1.602176634 x 10^-19 J to convert to electronvolts.
- Antenna length: A free-space quarter wavelength is lambda / 4. On wire, end-effect capacitance shortens the resonant length to roughly 95 percent of the geometric value, which the calculator surfaces as a practical dipole row. Inside coaxial cable, multiply by the cable velocity factor (commonly 0.66, 0.78, or 0.85).
- Wavenumber: k = 1 / lambda. Spectroscopists usually express this in 1/cm.
Common pitfalls
- Use Hz, not kHz, when plugging frequency into c = lambda x f. Mixing units is the easiest way to be off by a factor of 1,000.
- In water (n = 1.333) and other media, the frequency is unchanged but the wavelength shrinks because v drops to c / n.
- The eye sees light from roughly 380 nm (violet) to 780 nm (red). Anything outside that range is invisible even though it is still electromagnetic radiation.
- For antennas, the velocity factor of the conductor or surrounding material matters. A quarter-wave whip on a steel ground plane in free space is close to lambda / 4, but a dipole made of wire should be cut to about 95 percent of lambda / 2.
- Photon energy and intensity are not the same thing. A single X-ray photon carries far more energy than a visible photon even though a flashlight emits many more photons per second than a medical X-ray tube.
How to use
- Pick a mode at the top: Frequency to wavelength, Wavelength to frequency, Photon energy, or Antenna length.
- Enter your value and choose the right unit (Hz through PHz for frequency, pm through km for wavelength, J through MeV for photon energy).
- Optional: pick a medium (vacuum by default, or air, water, glass, ice, diamond, or a custom refractive index) so the wavelength is reported inside that medium.
- Read the wavelength, frequency, period, photon energy, wavenumber, spectrum band, and (for visible light) the named color in the result panel.
- For antenna mode, set the velocity factor: 1.00 for free space, around 0.66 to 0.85 for common coax, around 0.95 for a thin-wire dipole.
- Tap a worked example to load a canonical Wi-Fi, ham radio, optics, or physics problem and inspect the result.
- Click Copy on any row, or Copy summary, to paste the values into a lab report, build sheet, or notes.
About this tool
Wavelength Calculator solves the basic electromagnetic-wave relationships used in physics homework, ham radio, Wi-Fi planning, optics, fiber-optic telecom, and spectroscopy. Four solver modes share the same constants and conversions so you can answer the four questions that show up most often: what wavelength corresponds to a given frequency, what frequency corresponds to a given wavelength, what frequency and wavelength match a given photon energy, and how long should an antenna be for a given frequency. Frequency mode accepts Hz, kHz, MHz, GHz, THz, and PHz. Wavelength mode accepts picometers, nanometers, micrometers, millimeters, centimeters, meters, and kilometers. Photon energy mode accepts joules, millielectronvolts, electronvolts, kiloelectronvolts, and megaelectronvolts. Every result reports the wavelength in an auto-selected human-readable unit and in scientific-notation meters, the matching frequency in Hz, the period (1 / f), the photon energy in both joules and electronvolts, and the wavenumber in 1/m and 1/cm for spectroscopy use. A spectrum-band lookup labels the answer with the standard ITU and IEEE band names from ELF through gamma rays, and a visible-color lookup maps optical wavelengths to a named color band such as violet, blue, cyan, green, yellow, orange, or red. Selecting a medium (vacuum, air, water, ice, window glass, diamond, or a custom refractive index) divides the speed of light by n so the wavelength inside the medium is reported correctly while the frequency stays the same, which is the standard textbook treatment for refractive index. Antenna mode includes a velocity-factor input for cable and wire shortening and surfaces the full wavelength, quarter wavelength, half wavelength, five-eighths wavelength, and a practical wire-dipole length at about 95 percent of the geometric half-wave. Constants come from CODATA and the 2019 SI redefinition: c = 299,792,458 m/s exact, h = 6.62607015 x 10^-34 J*s exact, and 1 eV = 1.602176634 x 10^-19 J exact, so the same formulas reproduce in any textbook. Worked examples cover Wi-Fi at 2.4 and 5 GHz, FM broadcast at 100 MHz, the ham 2 m band, green light at 550 nm, a 650 nm red laser pointer, fiber-optic telecom at 1550 nm, a 1.00 eV photon, and a 10 keV diagnostic X-ray. Everything runs locally in your browser. The numbers and frequencies you enter are not uploaded.
Free to use. Works in your browser. No signup, no login.
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