Photon Energy Calculator
Calculate photon energy from frequency (E=hf), wavelength (E=hc/λ), or wavenumber — converting between Joules, electron volts, and all common energy, wavelength, and frequency units — with full step-by-step working and real-time electromagnetic spectrum classification.
⚡ Golden Shortcut Formula
The most practical photon energy formula — avoids carrying h and c separately. For λ=550 nm: E = 1239.84/550 = 2.254 eV instantly.
Enter any one quantity — the calculator automatically detects the type from the unit and computes all other photon properties.
| Source | Wavelength | Energy (eV) | Energy (J) | Region |
|---|---|---|---|---|
| AM radio | 300 m | 4.1×10⁻⁹ | 6.6×10⁻²⁸ | Radio |
| Microwave oven | 12.2 cm | 1.0×10⁻⁵ | 1.6×10⁻²⁴ | Microwave |
| Far infrared | 100 μm | 0.0124 | 2.0×10⁻²¹ | Far-IR |
| Body heat | 10 μm | 0.124 | 2.0×10⁻²⁰ | Mid-IR |
| Near infrared | 1000 nm | 1.240 | 1.99×10⁻¹⁹ | Near-IR |
| Red light | 700 nm | 1.771 | 2.84×10⁻¹⁹ | Red |
| Green light | 550 nm | 2.255 | 3.61×10⁻¹⁹ | Green |
| Blue light | 450 nm | 2.755 | 4.41×10⁻¹⁹ | Blue |
| UV-A | 350 nm | 3.542 | 5.68×10⁻¹⁹ | UV-A |
| UV-C (germicidal) | 254 nm | 4.881 | 7.82×10⁻¹⁹ | UV-C |
| Vacuum UV | 100 nm | 12.40 | 1.99×10⁻¹⁸ | EUV |
| Soft X-ray | 10 nm | 124.0 | 1.99×10⁻¹⁷ | X-ray |
| Hard X-ray | 0.1 nm | 12,400 | 1.99×10⁻¹⁵ | Hard X-ray |
| Gamma ray | 0.001 nm | 1.24 MeV | 1.99×10⁻¹³ | γ-ray |
| Convert | Formula | Example |
|---|---|---|
| λ[nm] → E[eV] | E = 1239.84/λ | 500 nm → 2.480 eV |
| E[eV] → λ[nm] | λ = 1239.84/E | 2.0 eV → 619.9 nm |
| ν̃[cm⁻¹] → E[eV] | E = ν̃ × 1.23984×10⁻⁴ | 10000 cm⁻¹ → 1.240 eV |
| f[THz] → λ[μm] | λ = 299.79/f | 100 THz → 3.0 μm |
| f[Hz] → E[J] | E = 6.626×10⁻³⁴ × f | 5×10¹⁴ Hz → 3.31×10⁻¹⁹ J |
| λ[nm] → f[THz] | f = 299792/λ | 550 nm → 545.1 THz |
| E[eV] → ν̃[cm⁻¹] | ν̃ = E / 1.23984×10⁻⁴ | 1.240 eV → 10000 cm⁻¹ |
| Frequency | Energy (Joules) | Energy (eV) | Region |
|---|---|---|---|
| 1 Hz | 6.626×10⁻³⁴ J | 4.136×10⁻¹⁵ eV | Radio |
| 1 kHz | 6.626×10⁻³¹ J | 4.136×10⁻¹² eV | Radio |
| 100 MHz | 6.626×10⁻²⁶ J | 4.136×10⁻⁷ eV | Microwave |
| 2.45 GHz | 1.624×10⁻²⁴ J | 1.014×10⁻⁵ eV | Microwave |
| 1 THz | 6.626×10⁻²² J | 4.136×10⁻³ eV | Far-IR |
| 3×10¹³ Hz | 1.988×10⁻²⁰ J | 0.124 eV | Mid-IR |
| 5×10¹⁴ Hz | 3.313×10⁻¹⁹ J | 2.068 eV | Yellow |
| 7.5×10¹⁴ Hz | 4.970×10⁻¹⁹ J | 3.103 eV | UV |
| 3×10¹⁸ Hz | 1.988×10⁻¹⁵ J | 12,400 eV | X-ray |
Photon Energy Formula — E=hf and E=hc/λ
The photon energy formula comes in two equivalent forms. The first, E=hf, is the Planck-Einstein relation — the direct statement that photon energy is proportional to frequency. The second, E=hc/λ, uses the wave relation c=λf to express energy in terms of wavelength. Both are equally valid; the choice depends on which quantity you know.
Where: h = Planck's constant = 6.626×10⁻³⁴ J·s (exact since 2019 SI redefinition), f = frequency in Hz, c = speed of light = 2.998×10⁸ m/s (exact), λ = wavelength in meters. The two formulas are equivalent because c = λf, so hf = h(c/λ) = hc/λ.
The Golden Shortcut: E[eV] = 1239.84 / λ[nm]
Derived from: E[eV] = hc[eV·nm] / λ[nm] = 1239.84 / λ[nm]. This avoids carrying h and c separately and gives exact results. For green light at 550 nm: E = 1239.84/550 = 2.254 eV. Memorise this formula — it is the most practical photon energy formula in all of optics and photonics.
Derivation of E[eV] = 1239.84/λ[nm]
Starting from E = hc/λ in SI units: hc = (6.626×10⁻³⁴ J·s)(2.998×10⁸ m/s) = 1.986×10⁻²⁵ J·m. To get eV·nm: divide by eV = 1.602×10⁻¹⁹ J, multiply by 10⁹ nm/m. Result: hc = 1239.84 eV·nm. So E[eV] = 1239.84/λ[nm]. The number 1239.84 is exact to 6 significant figures.
How to Calculate Photon Energy — Step-by-Step
Two calculation paths — from frequency using E=hf, or from wavelength using E=hc/λ or the shortcut. Both paths always include unit conversion and verification.
Example 1 — Green Light: λ = 550 nm
- Convert to SI: λ = 550 nm = 550×10⁻⁹ m = 5.50×10⁻⁷ m
- Apply E=hc/λ: E = (6.626×10⁻³⁴ × 2.998×10⁸) / 5.50×10⁻⁷
- Calculate: E = 1.986×10⁻²⁵ / 5.50×10⁻⁷ = 3.610×10⁻¹⁹ J
- Shortcut check: E = 1239.84/550 = 2.254 eV ✓
- Frequency: f = c/λ = 2.998×10⁸/5.50×10⁻⁷ = 5.451×10¹⁴ Hz = 545.1 THz
- Classification: Green light (visible spectrum, 495-570 nm)
Example 2 — UV-C Germicidal: λ = 254 nm
- Convert: λ = 254×10⁻⁹ m
- Shortcut: E = 1239.84/254 = 4.881 eV
- In Joules: 4.881 × 1.602×10⁻¹⁹ = 7.820×10⁻¹⁹ J
- Frequency: f = 2.998×10⁸/254×10⁻⁹ = 1.180×10¹⁵ Hz = 1180 THz
- Classification: UV-C — germicidal radiation (dangerous to DNA)
Example 3 — Telecom Laser: λ = 1550 nm
- Shortcut: E = 1239.84/1550 = 0.800 eV
- In Joules: 0.800 × 1.602×10⁻¹⁹ = 1.282×10⁻¹⁹ J
- Classification: Near-infrared (fiber optic telecommunications band)
Example 4 — Hard X-ray: λ = 0.1 nm
- Shortcut: E = 1239.84/0.1 = 12,398 eV = 12.4 keV
- In Joules: 12,398 × 1.602×10⁻¹⁹ = 1.986×10⁻¹⁵ J
- Classification: Hard X-ray (medical imaging, crystallography)
Example 5 — Microwave Oven: f = 2.45 GHz
- Convert to Hz: f = 2.45 GHz = 2.45×10⁹ Hz
- Apply E=hf: E = 6.626×10⁻³⁴ × 2.45×10⁹ = 1.623×10⁻²⁴ J
- In eV: 1.623×10⁻²⁴ / 1.602×10⁻¹⁹ = 1.014×10⁻⁵ eV
- Wavelength: λ = c/f = 2.998×10⁸/2.45×10⁹ = 0.1224 m = 12.24 cm
- Classification: Microwave (resonates with water molecules)
Hz to Joules — Frequency to Energy Conversion
To convert Hz to Joules, use the photon energy formula E=hf where h = 6.626×10⁻³⁴ J·s (Planck's constant). The formula E=hf directly gives photon energy in Joules when frequency is in Hz. Multiply the frequency in Hz by Planck's constant: E[J] = 6.626×10⁻³⁴ × f[Hz].
Notice how incredibly small Planck's constant is: 1 Hz corresponds to only 6.626×10⁻³⁴ J — essentially unmeasurable for a single photon. This is why optical photons at ~5×10¹⁴ Hz still have energies of only ~10⁻¹⁹ J, and why we prefer electron volts for practical photon energy calculations.
Key insight: Energy is directly proportional to frequency (E=hf). Double the frequency → double the energy. A UV photon at 6×10¹⁴ Hz has exactly twice the photon energy of an infrared photon at 3×10¹⁴ Hz. This direct proportionality is the essence of quantum mechanics — photon energy is quantized in discrete packets of hf.
Photon Energy in Electron Volts (eV)
Electron volts are the preferred unit for photon energy in physics because the numbers are human-scale. Visible light photons carry roughly 2-3 eV — numbers you can reason with. The same photons in Joules give 10⁻¹⁹ J — requiring scientific notation and offering no intuition.
Conversion: 1 eV = 1.602176634×10⁻¹⁹ J (exact since 2019 SI redefinition). So 1 J = 6.242×10¹⁸ eV.
| EM Region | Wavelength Range | Photon Energy (eV) | Key Application |
|---|---|---|---|
| Radio | >1 mm | <1.24×10⁻³ eV | Broadcasting |
| Microwave | 1 mm–1 m | 1.24×10⁻⁶–1.24×10⁻³ eV | Radar, cooking |
| Infrared | 700 nm–1 mm | 1.24×10⁻³–1.77 eV | Thermal imaging |
| Visible light | 380–750 nm | 1.65–3.26 eV | Human vision |
| UV | 10–380 nm | 3.26–124 eV | Sterilisation, lithography |
| X-ray | 0.01–10 nm | 124 eV–124 keV | Medical imaging |
| Gamma ray | <0.01 nm | >124 keV | Nuclear medicine |
Key benchmark: Si semiconductor bandgap = 1.12 eV → photons with λ < 1107 nm can excite electrons (solar cells). GaAs bandgap = 1.42 eV → λ < 873 nm. Peak solar spectrum ≈ 2.0 eV = 620 nm — orange light. The 1239.84 eV·nm shortcut makes all these calculations instant.
Wavelength to Frequency — The c=λf Relationship
The speed of light c = λf connects wavelength and frequency. Rearranging: f = c/λ (frequency from wavelength) and λ = c/f (wavelength from frequency). Always convert wavelength to meters before using SI formulas.
Optical frequencies are enormous: 550 nm green light oscillates at 545 THz = 5.45×10¹⁴ Hz. Historically, wavelength was easier to measure than frequency (using diffraction gratings), which is why the optics community standardised on nanometers rather than terahertz. Modern frequency combs can now measure optical frequencies directly, but nm remains the dominant unit.
Wavenumber to Energy — Spectroscopy Units
Wavenumber ν̃ (cm⁻¹, pronounced "reciprocal centimeters" or "inverse centimeters") = 1/λ[cm] = the number of wavelengths per centimeter. It is directly proportional to energy — doubling the wavenumber doubles the photon energy. Used universally in IR and Raman spectroscopy.
The wavenumber shortcut: E[eV] = ν̃[cm⁻¹] × 1.23984×10⁻⁴. For IR spectroscopy, the standard range is 400–4000 cm⁻¹ (mid-IR). C-H stretches appear near 3000 cm⁻¹ (3.33 μm), C=O stretches near 1700 cm⁻¹ (5.88 μm).
Example: ν̃ = 3000 cm⁻¹ (C-H stretch)
- λ = 1/3000 cm = 3.333×10⁻⁴ cm = 3333 nm = 3.333 μm
- Shortcut: E = 1239.84/3333 = 0.3720 eV
- Wavenumber shortcut: E = 3000 × 1.23984×10⁻⁴ = 0.3720 eV ✓
- Frequency: f = c × ν̃[m⁻¹] = 2.998×10⁸ × 3×10⁴ = 8.994×10¹² Hz = 89.9 THz
Why spectroscopists prefer cm⁻¹: the same photon can be described as ν̃ = 3000 cm⁻¹, E = 0.372 eV, or f = 90 THz. The wavenumber 3000 is the most convenient number — not too large, not too small. Proportional to energy (unlike wavelength), which makes comparing spectral features intuitive.
Electromagnetic Spectrum — Energy Ranges by Region
The full electromagnetic spectrum spans over 20 orders of magnitude in frequency. All regions follow the same photon energy formula E=hf — the only difference is the frequency (and therefore wavelength) of the photon. Higher frequency = shorter wavelength = MORE energy per photon.
| EM Region | Wavelength | Frequency | Photon Energy (eV) | Photon Energy (J) |
|---|---|---|---|---|
| Gamma rays | <0.01 nm | >3×10¹⁹ Hz | >100 keV | >1.6×10⁻¹⁴ J |
| X-rays | 0.01–10 nm | 3×10¹⁶–3×10¹⁹ Hz | 100 eV–100 keV | 1.6×10⁻¹⁷–1.6×10⁻¹⁴ J |
| Ultraviolet | 10–380 nm | 7.9×10¹⁴–3×10¹⁶ Hz | 3.26–124 eV | 5.2×10⁻¹⁹–2×10⁻¹⁷ J |
| Visible | 380–750 nm | 4.0–7.9×10¹⁴ Hz | 1.65–3.26 eV | 2.6–5.2×10⁻¹⁹ J |
| Infrared | 750 nm–1 mm | 3×10¹¹–4×10¹⁴ Hz | 1.24 meV–1.65 eV | 2×10⁻²²–2.6×10⁻¹⁹ J |
| Microwave | 1 mm–1 m | 3×10⁸–3×10¹¹ Hz | 1.24 μeV–1.24 meV | 2×10⁻²⁵–2×10⁻²² J |
| Radio waves | >1 m | <3×10⁸ Hz | <1.24 μeV | <2×10⁻²⁵ J |
Gamma rays are dangerous because each photon carries MeV-scale energies — enough to ionize atoms, break chemical bonds, and damage DNA. Radio wave photons carry nanoelectron volt energies — billions of them pass through your body every second with no biological effect because no individual photon has enough energy to cause ionization.
Photon Momentum — p = h/λ
Photons carry momentum despite having zero mass. The de Broglie relation gives photon momentum as p = h/λ = E/c = hf/c. For green light at 550 nm:
Photon Momentum Calculation: λ = 550 nm (green)
- p = h/λ = 6.626×10⁻³⁴ / (550×10⁻⁹) = 1.205×10⁻²⁷ kg·m/s
- Verify via E/c: E = 3.610×10⁻¹⁹ J, p = 3.610×10⁻¹⁹ / 2.998×10⁸ = 1.204×10⁻²⁷ kg·m/s ✓
Applications of photon momentum: radiation pressure (light exerts force on surfaces — used in laser cooling), optical tweezers (momentum transfer traps microscopic particles — Nobel Prize 2018), solar sails (proposed spacecraft propulsion using sunlight pressure).
Common Mistakes in Photon Energy Calculations
Mistake 1 — Wavelength in nm instead of meters in E=hc/λ
- ❌ Wrong: E = hc/550 (using nm directly)
- ✅ Correct: E = hc/(550×10⁻⁹) — must use meters for SI formula
- Or: Use the shortcut E[eV] = 1239.84/550 = 2.254 eV — no unit conversion needed
Mistake 2 — Confusing f (frequency) with ω (angular frequency)
- ❌ Wrong: Using E = hω (where ω is in rad/s)
- ✅ Correct E=hf uses ordinary frequency f in Hz. For angular frequency: E = ℏω where ℏ = h/(2π) = 1.055×10⁻³⁴ J·s
- ω = 2πf, so ℏω = (h/2π)(2πf) = hf ✓ — both are equivalent but use different constants
Mistake 3 — Using ℏ instead of h in E=hf
- ❌ Wrong: E = ℏf (off by factor of 2π ≈ 6.28)
- ✅ Correct: E = hf with h = 6.626×10⁻³⁴ J·s (not ℏ = 1.055×10⁻³⁴ J·s)
- Use ℏ only with angular frequency: E = ℏω
Mistake 4 — Wrong wavenumber convention
- ❌ Wrong: ν̃ = 1/λ[m] giving ν̃ in m⁻¹
- ✅ Correct: Standard spectroscopy uses ν̃ = 1/λ[cm] in cm⁻¹ (3000 cm⁻¹, not 3×10⁵ m⁻¹)
- The shortcut E[eV] = ν̃[cm⁻¹] × 1.23984×10⁻⁴ only works with cm⁻¹
Mistake 5 — Confusing photon energy with beam intensity
- ❌ Wrong: "A 1 W green laser has E = 2.25 eV"
- ✅ Correct: Each photon has E = 2.25 eV, but the beam contains many photons/second
- Power [W] = photons/second × energy/photon: 1 W at 550 nm → 1/3.61×10⁻¹⁹ = 2.77×10¹⁸ photons/second