Photon Energy Calculator: E = hν & E = hc/λ
This calculator computes the energy of a single photon using Planck's relation E = hν (given frequency) or E = hc/λ (given wavelength). It returns energy in both joules (J) and electron-volts (eV) and identifies the electromagnetic spectrum region. Enter either frequency (in Hz or THz) or wavelength (in nm or µm) and get the result instantly. Constants used (NIST CODATA 2018, exact since 2019 SI redefinition): - h = 6.62607015×10⁻³⁴ J·s - c = 2.99792458×10⁸ m/s - e = 1.602176634×10⁻¹⁹ C Used in quantum mechanics, photochemistry, spectroscopy, optics, semiconductor physics, and astrophysics to determine how much energy a single quantum of electromagnetic radiation carries.
Photon energy formula: **E = hν = hc/λ**, where h = 6.626×10⁻³⁴ J·s (Planck's constant) and c = 2.998×10⁸ m/s. Quick shortcut: **E(eV) ≈ 1240 / λ(nm)**. A 550 nm green photon carries 2.25 eV; a 300 nm UVB photon carries 4.13 eV; a 0.1 nm X-ray photon carries ~12,400 eV. Enter frequency (Hz or THz) or wavelength (nm or µm) above to get the exact result.
When to use this calculator
- Determining whether UV photons (E > 3.1 eV) carry enough energy to break chemical bonds and cause DNA damage or photodegradation of materials.
- Calculating the minimum photon energy needed to overcome the work function of a metal in photoelectric-effect experiments (e.g., gold: 5.1 eV threshold).
- Selecting the correct laser wavelength in photolithography or laser cutting so photons deposit exactly the energy required to ablate a specific material.
- Verifying that a semiconductor's band-gap energy (e.g., silicon: 1.12 eV) can be bridged by photons of a chosen wavelength for solar-cell design.
- Converting spectroscopic emission lines (e.g., hydrogen Lyman-alpha at 121.6 nm) to photon energies for astrophysical or lab plasma analysis.
- Estimating the number of photons per second in a laser beam of known power by dividing total beam power (W) by energy per photon (J).
Worked Example: Green Light at 550 nm
- Input: λ = 550 nm = 5.50×10⁻⁷ m
- E = hc/λ = (6.626×10⁻³⁴ × 2.998×10⁸) / 5.50×10⁻⁷
- E = 3.61×10⁻¹⁹ J
- In eV: 3.61×10⁻¹⁹ / 1.602×10⁻¹⁹ = 2.25 eV
- Quick check: 1240 / 550 nm = 2.25 eV ✓
How it works
3 min readHow Photon Energy Is Calculated
Photon energy follows Planck's relation, established by Max Planck in 1900 and confirmed by Einstein's 1905 photoelectric-effect paper:
E = h × ν (1) — given frequency ν in Hz
E = h × c / λ (2) — given wavelength λ in meters
Quick shortcut:
E(eV) ≈ 1240 / λ(nm) — accurate to 0.05%
Conversion:
1 eV = 1.602176634×10⁻¹⁹ J (exact)
E(eV) = E(J) / 1.602×10⁻¹⁹
NIST CODATA 2018 constants (exact since 2019 SI redefinition):
h = 6.62607015×10⁻³⁴ J·s
c = 2.99792458×10⁸ m/s
e = 1.602176634×10⁻¹⁹ C---
Reference Table — Photon Energy Across the Electromagnetic Spectrum
| Region | Wavelength | Frequency | Energy (eV) |
|---|---|---|---|
| Radio | > 1 m | < 300 MHz | < 1.2×10⁻⁶ |
| Microwave | 1 mm – 1 m | 300 MHz – 300 GHz | 1.2×10⁻⁶ – 1.2×10⁻³ |
| Infrared (IR) | 700 nm – 1 mm | 300 GHz – 430 THz | 1.2×10⁻³ – 1.77 |
| Visible (red) | 620 – 750 nm | 400 – 484 THz | 1.65 – 2.00 |
| Visible (green) | 495 – 570 nm | 526 – 606 THz | 2.18 – 2.50 |
| Visible (violet) | 380 – 450 nm | 666 – 789 THz | 2.76 – 3.26 |
| UVA | 315 – 380 nm | 789 – 952 THz | 3.26 – 3.94 |
| UVB | 280 – 315 nm | 952 THz – 1.07 PHz | 3.94 – 4.43 |
| UVC | 100 – 280 nm | 1.07 – 3.00 PHz | 4.43 – 12.4 |
| Soft X-ray | 0.1 – 10 nm | 30 – 3000 PHz | 0.12 – 12.4 keV |
| Hard X-ray / γ-ray | < 0.1 nm | > 3000 PHz | > 12.4 keV |
Source: NIST and standard electromagnetic spectrum definitions.
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Common Wavelengths → Energy (Quick-Reference Table)
| Wavelength (nm) | Color / Region | Energy (eV) | Energy (J) |
|---|---|---|---|
| 700 | Deep red | 1.77 | 2.84×10⁻¹⁹ |
| 620 | Red | 2.00 | 3.21×10⁻¹⁹ |
| 550 | Green | 2.25 | 3.61×10⁻¹⁹ |
| 450 | Blue | 2.76 | 4.42×10⁻¹⁹ |
| 380 | Violet | 3.26 | 5.23×10⁻¹⁹ |
| 300 | UVB | 4.13 | 6.62×10⁻¹⁹ |
| 200 | UVC | 6.20 | 9.93×10⁻¹⁹ |
| 100 | EUV | 12.4 | 1.99×10⁻¹⁸ |
| 10 | Soft X-ray | 124 | 1.99×10⁻¹⁷ |
| 0.1 | Hard X-ray | 12,400 | 1.99×10⁻¹⁵ |
All values computed with E(eV) = 1240 / λ(nm).
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Worked Examples
Example 1 — Green visible light (frequency given)
> Input: ν = 5.00×10¹⁴ Hz
> Formula: E = 6.626×10⁻³⁴ × 5.00×10¹⁴ = 3.31×10⁻¹⁹ J
> In eV: 3.31×10⁻¹⁹ / 1.602×10⁻¹⁹ = 2.07 eV
> Interpretation: Visible range; enough to trigger photochemical reactions in many organic dyes.
Example 2 — UVB photon (wavelength given)
> Input: λ = 300 nm = 3.00×10⁻⁷ m
> Formula: E = (6.626×10⁻³⁴ × 2.998×10⁸) / 3.00×10⁻⁷ = 6.62×10⁻¹⁹ J = 4.13 eV
> Interpretation: Above the C–C bond dissociation energy (~3.6 eV); at the threshold for DNA pyrimidine dimer formation — the primary mechanism of UV-induced skin damage.
Example 3 — Diagnostic X-ray photon
> Input: λ = 0.05 nm = 5.00×10⁻¹¹ m
> Formula: E = (6.626×10⁻³⁴ × 2.998×10⁸) / 5.00×10⁻¹¹ = 3.97×10⁻¹⁵ J ≈ 24.8 keV
> Interpretation: Typical of diagnostic chest X-rays (20–30 keV range); penetrates soft tissue but is attenuated by bone.
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Common Calculation Errors
1. Confusing nm vs. m: Plugging 550 (nm) into E = hc/λ without converting to meters overstates energy by a factor of 10⁹. Always convert to SI first.
2. Mixing ħ and h: Some texts use ħ (reduced Planck's constant = h/2π = 1.055×10⁻³⁴ J·s) with E = ħω, where ω = 2πν. Using ħ with ordinary frequency ν gives a result off by 2π ≈ 6.28.
3. Rounding the eV conversion factor: 1 eV = 1.602×10⁻¹⁹ J (not 1×10⁻¹⁹). Using the rounded value introduces ~0.6% systematic error.
4. Applying photon energy to laser power: E = hν is the energy of ONE photon. A 1 mW green (532 nm) laser emits ~2.68×10¹⁵ photons per second. Use N = P/E to find the count.
5. Wavelength in medium vs. vacuum: E = hν always uses the vacuum frequency (or vacuum wavelength). Photon energy is unchanged when light enters glass even though the wavelength shortens.
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Frequently asked questions
What is the photon energy formula?
Photon energy is given by Planck's relation: E = hν (if you know frequency ν in Hz) or E = hc/λ (if you know wavelength λ in meters). Constants: h = 6.626×10⁻³⁴ J·s, c = 2.998×10⁸ m/s. A practical shortcut when λ is in nanometers: E(eV) ≈ 1240 / λ(nm), accurate to better than 0.05%.
What is the photon energy of visible light in eV?
Visible light spans roughly 380–750 nm, corresponding to photon energies of about 1.65 eV (deep red, 750 nm) to 3.26 eV (violet, 380 nm). The center of the visible range — green at ~550 nm — carries about 2.25 eV per photon. Use the shortcut: E(eV) ≈ 1240 / λ(nm).
How do I convert wavelength in nm to photon energy in eV?
Use the shortcut E(eV) = 1240 / λ(nm). Examples: 700 nm (red) → 1.77 eV; 550 nm (green) → 2.25 eV; 450 nm (blue) → 2.76 eV; 300 nm (UVB) → 4.13 eV. This approximation (using hc ≈ 1240 eV·nm) is accurate to within 0.05%.
What is Planck's constant and why does it appear in the photon energy formula?
Planck's constant h = 6.62607015×10⁻³⁴ J·s is the fundamental quantum of action — it sets the scale at which energy is quantized. Since the 2019 SI redefinition, h has an exact fixed value (NIST CODATA 2018), so photon energy calculations are now exact within measurement precision of frequency or wavelength.
What is the energy of a UV photon compared to visible light?
UVA photons (315–380 nm) carry 3.26–3.94 eV; UVB photons (280–315 nm) carry 3.94–4.43 eV; UVC photons (100–280 nm) carry 4.43–12.4 eV. This is roughly 1.5× to 7× the energy of a typical visible photon (2.25 eV at 550 nm). Above ~3.1 eV (wavelengths shorter than ~400 nm) photons can break many chemical bonds, which is why UV causes sunburn and photodegradation of materials.
How does photon energy relate to ionizing radiation thresholds?
Ionizing radiation is generally defined as photons with enough energy to remove electrons from atoms or break chemical bonds — roughly 10–33 eV (soft UV / EUV boundary), corresponding to wavelengths shorter than ~124 nm. X-rays (>120 eV) and gamma rays are far above this threshold. The CDC and NIH classify UVC (4.4–12.4 eV) as biologically damaging but only at the lower boundary of ionization for biological molecules.
Can I use E = hν for electrons or neutrons (matter waves)?
No — E = hν applies specifically to photons (massless bosons). For particles with mass, energy and momentum follow the de Broglie relation λ = h/p and the relativistic energy–momentum relation E² = (pc)² + (m₀c²)². For a non-relativistic electron, kinetic energy is K = p²/2m = h²/(2mλ²) — an entirely different formula.
What is the photon energy of a 2.4 GHz Wi-Fi signal?
E = hν = 6.626×10⁻³⁴ × 2.4×10⁹ = 1.59×10⁻²⁴ J ≈ 9.93×10⁻⁶ eV (about 10 micro-eV). This is roughly 200 million times less energy than a visible photon — which is why microwave/radio photons cannot cause ionization or photochemical reactions; their individual quanta are far too weak.
Why do solar cells have a maximum efficiency tied to photon energy?
Silicon has a band gap of 1.12 eV. Photons with E < 1.12 eV (λ > 1107 nm, near-IR) pass through without being absorbed. Photons with E >> 1.12 eV are absorbed, but excess energy above the band gap is lost as heat (thermalization). This mismatch limits single-junction silicon solar cells to a theoretical Shockley–Queisser efficiency of ~33%.
How do I find the number of photons per second emitted by a laser?
Divide beam power P (watts) by energy per photon E (joules): N = P / E = Pλ / (hc). Example: a 5 mW red laser at 632.8 nm emits N = 0.005 × 632.8×10⁻⁹ / (6.626×10⁻³⁴ × 2.998×10⁸) ≈ 1.59×10¹⁶ photons per second.