Frequency to Energy Converter

Calculate the photon energy at any frequency using Planck's relation E = hf. Output in electron-volts (auto-scaled µeV → GeV), joules, and kJ/mol. Includes EM-spectrum band classification and an ionizing-radiation indicator (above 13.6 eV).

Input

Photon Sources Across the EM Spectrum

Result

Photon Energy (E = h × f)
Energy (Joules)
Energy (per mole)
Wavelength (λ = c/f)
Visible Colour (if any)
Ionizing Radiation? (threshold = 13.6 eV)
Formulas & Constants
E = h × f   (Planck's relation)
h = 6.626 × 10⁻³⁴ J·s   (Planck constant, exact)
1 eV = 1.602 × 10⁻¹⁹ J   (electron volt)
E_kJ/mol = E_J × N_A / 1000   (N_A = 6.022 × 10²³)

Photon Energies Across the EM Spectrum

SourceFrequencyWavelengthPhoton EnergyBand
AM radio (mid)1 MHz~300 m4.14 neVRadio
FM radio (mid)100 MHz~3 m414 neVRadio
WiFi 2.4 GHz2.4 GHz~12.5 cm9.93 µeVMicrowave
Microwave oven2.45 GHz~12.2 cm10.1 µeVMicrowave
Far IR1 THz300 µm4.14 meVInfrared
Near IR300 THz1,000 nm1.24 eVInfrared
Red light430 THz697 nm1.78 eVVisible
Green light540 THz555 nm2.23 eVVisible
Violet light750 THz400 nm3.10 eVVisible
UV-A~900 THz~333 nm~3.72 eVUV (non-ionizing)
UV-C (germicidal)1 PHz300 nm4.14 eVUV
Hydrogen ionization3.29 PHz91.2 nm13.6 eVUV (threshold)
Soft X-ray100 PHz3 nm414 eVX-ray
Hard X-ray10 EHz30 pm41.4 keVX-ray / Gamma
Cobalt-60 gamma~283 EHz~1.06 pm1.17 MeVGamma

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About Photon Energy & Planck's Relation

This frequency to energy converter (also usable as a photon energy calculator) applies the Planck formula E = hf to calculate photon energy. Light comes in discrete packets called photons, each carrying energy proportional to its frequency (where h is Planck's constant, 6.626 × 10⁻³⁴ J·s). This quantization, first articulated by Max Planck in 1900 and confirmed by Einstein's explanation of the photoelectric effect in 1905, launched quantum mechanics. The same formula governs phenomena from radio-wave photon detection in sensitive receivers to gamma-ray energy deposition in medical imaging. The tool covers radio (~10⁻⁹ eV) to gamma (~10⁶ eV) — a span of 15 orders of magnitude.

Why three energy units (eV, J, kJ/mol)?

Electron-volts (eV) are the most intuitive unit for photons because they map directly to atomic phenomena: the Hz-to-eV conversion shows that visible light photons are ~1.5–3 eV (matches electronic transitions), UV-C is ~4–10 eV (breaks bonds), 13.6 eV ionizes hydrogen. Joules are SI energy. kJ/mol matters in chemistry — multiplying a single photon's energy by Avogadro's number gives the energy of one mole of those photons, the meaningful quantity for bulk reactions like photosynthesis (~180 kJ/mol per red photon × ~6 × 10²³ = ~600 kJ/mol absorbed).

The 13.6 eV ionizing threshold

Photons with energy ≥ 13.6 eV can ionize hydrogen atoms (knock the electron out). This corresponds to ~3.3 PHz (91 nm wavelength), deep in the UV. Below 13.6 eV is "non-ionizing" radiation (visible light, IR, microwaves, radio) — energetically incapable of breaking molecular bonds directly. Above is "ionizing" (UV-C, X-ray, gamma) — biologically damaging because individual photons carry enough energy to break DNA. Use this tool as an ionizing radiation calculator by entering any frequency to instantly see whether the resulting photon energy clears the ionization threshold. In medical imaging, diagnostic X-ray photons typically land in the keV range (20–150 keV), while PET-scan gamma photons from fluorine-18 decay carry 511 keV each. These values appear in the reference table above and can be verified with this converter by entering frequencies in the EHz range. To explore how wavelength relates to frequency at visible-light scales, see the frequency to wavelength converter.

Energy → photon count conversion

A 60-watt light bulb (60 J/s) emitting 600 nm green light (2 eV = 3.2 × 10⁻¹⁹ J per photon) emits about 60 / 3.2 × 10⁻¹⁹ = 1.9 × 10²⁰ photons per second. The discreteness only becomes practically observable at very low intensities or for highly energetic photons. Note that a light bulb's color temperature (measured in Kelvin) describes the peak of its blackbody radiation spectrum using Planck's law, which integrates E = hf over all frequencies — this tool computes energy for a single frequency rather than a thermal distribution. For audio-frequency calculations — where Planck-scale photon energies are negligible and wave behavior dominates — you can convert between Hz and wavelength using the wavelength calculator.

Frequently Asked Questions

How do I calculate photon energy from frequency?
Multiply the frequency in Hz by Planck's constant: E = h × f, where h = 6.626 × 10⁻³⁴ J·s. The result is in joules. To get electron-volts, divide by 1.602 × 10⁻¹⁹. For 500 THz (green light): E = 6.626e-34 × 5e14 = 3.31e-19 J = 2.07 eV.
What's the energy of a visible light photon?
Visible light spans 430–750 THz (700–400 nm), giving photon energies of 1.78–3.10 eV. Red is the lowest energy (~1.78 eV), violet is the highest (~3.10 eV). This range is "just below" the ionization threshold for most biological molecules — why visible light is energetically safe but UV is harmful.
Is microwave radiation ionizing?
No. A 2.45 GHz microwave photon carries about 10 µeV (10 millionths of an eV) — over a million times less than the ~10 eV needed to break molecular bonds. Microwave ovens cook food by exciting water molecule rotations (thermal effect), not by ionization. Same logic applies to WiFi, FM radio, and cell signals — all far below ionizing.
What's special about 13.6 eV?
13.6 eV is the ionization energy of hydrogen — the energy needed to knock the single electron out of a ground-state hydrogen atom. Many introductory physics texts use this as the convenient "ionization threshold" for biological radiation safety, though specific molecules have different thresholds. Wavelength corresponds to 91.2 nm, deep in the UV range.
How many photons does a 1-watt laser emit?
Depends on wavelength. A 1 W green laser (532 nm, 2.33 eV ≈ 3.74 × 10⁻¹⁹ J per photon) emits 1 / 3.74e-19 ≈ 2.7 × 10¹⁸ photons per second. A 1 W red laser (660 nm, 1.88 eV) emits ~3.3 × 10¹⁸ per second — more photons per second because each carries less energy.
Why use kJ/mol for photon energy?
Chemistry deals with moles (6.022 × 10²³ particles) rather than single particles. A photochemical reaction like photosynthesis absorbs many photons per mole of product. Expressing photon energy in kJ/mol lets chemists directly compare it to bond-dissociation energies (typically 150–500 kJ/mol). Red photons (~170 kJ/mol) can excite photosynthesis pigments but not break most chemical bonds; UV-C (~400 kJ/mol) can break C–C bonds.
How does E = hf relate to the photoelectric effect?
Einstein's 1905 explanation of the photoelectric effect was the first direct experimental proof of photon quantization: when light hits a metal, electrons are ejected only if the photon energy (E = hf) exceeds the metal's work function — regardless of light intensity. Brighter light ejects more electrons but cannot kick out an electron if the frequency is too low. This is why a UV lamp can discharge a zinc plate in physics demonstrations but a very bright red light cannot — the individual photon energies matter, not the total power.
Can I convert wavelength to energy instead of frequency?
Yes — since wavelength λ = c / f (where c = 3 × 10⁸ m/s), you can convert wavelength to frequency first and then apply E = hf. A convenient shortcut for photons is E (eV) ≈ 1240 / λ (nm). For example, a 620 nm red photon gives roughly 1240 / 620 = 2.0 eV. Enter your wavelength in the frequency to wavelength converter to get the frequency, then paste it here.
What photon energy do X-rays have, and why does that matter in medicine?
Diagnostic X-ray photons carry 20–150 keV depending on the tube voltage (kVp setting). At these energies, photons penetrate soft tissue but are absorbed by denser bone and metal, creating contrast. CT scanners use the same keV range; PET scanners detect 511 keV gamma photons from positron-electron annihilation. Because each X-ray photon carries roughly 10,000 times more energy than a UV photon, even a brief exposure involves billions of ionizing events — which is why medical X-ray dose is carefully minimized.