Wavelength ↔ Frequency Calculator
Enter a wavelength λ or frequency f and the tool flips it via c = λf (with c = 299,792,458 m/s), reports the photon energy E = hf in eV and J, and labels which slice of the electromagnetic spectrum it falls in — radio, microwave, infrared, visible, ultraviolet, X-ray or gamma. Useful for quick physics-class checks, RF / radar engineering sanity numbers, or just answering "what wavelength is my 5 GHz Wi-Fi?".
Enter a positive wavelength or frequency.
Frequency f
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Photon energy E = hf
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Electromagnetic spectrum band
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Formula
c = λ · f | E = h · f ( c = 299,792,458 m/s, h = 6.626×10⁻³⁴ J·s )
Uses the exact 2019 SI constants for c, h and e (electronvolt). Visible-light range follows the NASA 400–700 nm convention used in introductory physics.
Formula
c = λ × f (speed of light c = 299,792,458 m/s — exact since 1983) f = c ÷ λ, λ = c ÷ f E = h × f (photon energy, h = 6.62607015 × 10⁻³⁴ J·s) E(eV) = E(J) ÷ 1.602176634 × 10⁻¹⁹
- · All physical constants use the exact CODATA 2018 / 2019 SI-redefinition values: c, h, e are defined constants with zero uncertainty.
- · Approximate band edges: radio < 1 m | microwave 1 mm – 1 m | infrared 700 nm – 1 mm | visible 400–700 nm | UV 10–400 nm | X-ray 0.01–10 nm | γ-ray < 0.01 nm.
- · The visible-light range follows the NASA "Tour of the EM Spectrum" 400–700 nm convention; some sources stretch it to 380–780 nm.
- · The radio / microwave boundary has two camps: 300 MHz (IEEE / Wikipedia "microwave") and 1–3 GHz. This tool uses 300 MHz, so 2.4 / 5 GHz Wi-Fi, 5G and radar all count as microwave.
- · The output describes the wave in vacuum. In a medium (glass, fibre, water), λ shrinks by the refractive index n — but frequency stays the same.
- · Inputs accept pm / nm / μm / mm / cm / m and Hz / kHz / MHz / GHz / THz / PHz, covering everything from long-wave radio to gamma rays.
Frequently asked
What is the wavelength of my 5 GHz Wi-Fi?
λ = c ÷ f = 299,792,458 ÷ 5 × 10⁹ ≈ 0.06 m, i.e. about 6 cm. That is also why 5 GHz Wi-Fi penetrates walls worse than 2.4 GHz (λ ≈ 12.5 cm) but suffers less congestion — shorter wavelengths permit smaller antennas yet attenuate faster. In the tool: pick "f → λ", enter 5, choose "GHz" — you will see ≈ 5.996 cm appear instantly.
Why is 550 nm light classified as "visible", and what colour is it?
Human-visible light is roughly 400 nm (violet) to 700 nm (red). 550 nm sits right in the middle as a yellowish green — and incidentally is near the peak of the CIE photopic luminosity function V(λ) at 555 nm, where the eye is most sensitive. LED streetlamps and night-vision systems exploit this band. Enter 550 with unit "nm" and the tool returns f ≈ 545 THz, E ≈ 2.25 eV, labelled "visible".
How do X-rays and γ-rays differ — both are very high frequencies?
Their frequency ranges overlap. Textbooks usually split by wavelength: λ ≳ 0.01 nm is "X-ray", λ ≲ 0.01 nm is "γ-ray" (the boundary lives near 3 × 10¹⁹ Hz). Another convention splits by origin: photons from atomic-electron transitions are X-rays, while photons from nuclear decay or particle annihilation are γ-rays — so a 100 keV line can be called either depending on the source. This tool only uses wavelength, so anything below 0.01 nm is tagged γ.
What is E = hf, and how does it relate to c = λf?
c = λf describes the wave geometry (wavelength × frequency). E = hf describes the quantum side — each photon carries that amount of energy, where h is Planck's constant. Combine them and you get E = hc / λ. Some useful anchors: visible red 700 nm ≈ 1.77 eV, blue 400 nm ≈ 3.10 eV; UV-C 254 nm ≈ 4.88 eV — strong enough to break some DNA bonds, hence its use in sterilisation; a 100 keV X-ray ≈ 0.0124 nm. Photon energy above roughly 10 eV is the threshold for "ionising radiation".
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