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
Result
Photon Energies Across the EM Spectrum
| Source | Frequency | Wavelength | Photon Energy | Band |
|---|---|---|---|---|
| AM radio (mid) | 1 MHz | ~300 m | 4.14 neV | Radio |
| FM radio (mid) | 100 MHz | ~3 m | 414 neV | Radio |
| WiFi 2.4 GHz | 2.4 GHz | ~12.5 cm | 9.93 µeV | Microwave |
| Microwave oven | 2.45 GHz | ~12.2 cm | 10.1 µeV | Microwave |
| Far IR | 1 THz | 300 µm | 4.14 meV | Infrared |
| Near IR | 300 THz | 1,000 nm | 1.24 eV | Infrared |
| Red light | 430 THz | 697 nm | 1.78 eV | Visible |
| Green light | 540 THz | 555 nm | 2.23 eV | Visible |
| Violet light | 750 THz | 400 nm | 3.10 eV | Visible |
| UV-A | ~900 THz | ~333 nm | ~3.72 eV | UV (non-ionizing) |
| UV-C (germicidal) | 1 PHz | 300 nm | 4.14 eV | UV |
| Hydrogen ionization | 3.29 PHz | 91.2 nm | 13.6 eV | UV (threshold) |
| Soft X-ray | 100 PHz | 3 nm | 414 eV | X-ray |
| Hard X-ray | 10 EHz | 30 pm | 41.4 keV | X-ray / Gamma |
| Cobalt-60 gamma | ~283 EHz | ~1.06 pm | 1.17 MeV | Gamma |
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.