Photon Energy Calculator — Planck's Equation
Use this photon energy calculator to explore the relationship between wavelength, frequency, and energy of a photon. Based on Planck's equation, this tool supports both metric and imperial-style units and outputs energy in multiple unit systems used in physics and chemistry.
What Is Planck's Equation?
Planck's equation describes the energy of a single photon:
E = h × f = h × c / λ
- E — energy of the photon (Joules)
- h = 6.6261 × 10−34 J·s — Planck constant
- f — frequency of the photon (Hz)
- c = 2.998 × 108 m/s — speed of light in vacuum
- λ — wavelength of the photon (meters)
How to Calculate the Energy of a Photon
- Choose your input: wavelength or frequency
- Enter the value and select the unit (nm, μm, pm, Å for wavelength; THz, GHz, Hz for frequency)
- Click Calculate
- The calculator outputs energy in Joules, eV, erg, and kJ/mol, plus both wavelength and frequency in multiple units
Supported Unit Systems
Wavelength Units
- nm (nanometers) — most common in optics and visible light (400–700 nm)
- μm (micrometers) — used in infrared spectroscopy
- pm (picometers) — used for X-rays
- Å (Angstroms) — traditional unit in crystallography and X-ray diffraction (1 Å = 0.1 nm)
- m (meters) — SI base unit
Energy Output Units
- Joules (J) — SI unit, standard in physics
- Electron-volts (eV) — standard in atomic and particle physics (1 eV = 1.60218 × 10−19 J)
- Erg — CGS unit, used in astrophysics (1 J = 107 erg)
- kJ/mol — molar energy, used in chemistry and thermodynamics
Electromagnetic Spectrum Regions
| Region | Wavelength | Typical Energy (eV) |
|---|---|---|
| Gamma rays | < 0.01 nm | > 100 keV |
| X-rays | 0.01 – 10 nm | 0.1 – 100 keV |
| Ultraviolet (UV) | 10 – 400 nm | 3.1 – 124 eV |
| Visible light | 400 – 700 nm | 1.77 – 3.1 eV |
| Near infrared | 700 – 1000 nm | 1.24 – 1.77 eV |
| Infrared (IR) | 1 μm – 1 mm | 1.24 meV – 1.24 eV |
| Microwave | 1 mm – 1 m | 1.24 μeV – 1.24 meV |
| Radio waves | > 1 m | < 1.24 μeV |
Planck's Constant and Quantum Mechanics
The Planck constant h = 6.6261 × 10−34 J·s is one of the fundamental constants of nature. It appears in the uncertainty principle (ΔE × Δt ≥ ℏ/2), quantum harmonic oscillators, and countless other quantum mechanical formulas.
The concept that light energy is quantized — carried in discrete packets called photons — was revolutionary when Max Planck introduced it in 1900. Albert Einstein later used it to explain the photoelectric effect, earning him the Nobel Prize in Physics in 1921.
Example Calculations
- Green light (λ = 532 nm): E = 3.73 × 10−19 J = 2.33 eV
- UV light (λ = 254 nm): E = 7.82 × 10−19 J = 4.88 eV
- X-ray (λ = 0.1 nm): E = 1.99 × 10−15 J = 12.4 keV
- Visible red (λ = 700 nm): E = 2.84 × 10−19 J = 1.77 eV
Frequently Asked Questions
What is a photon?
A photon is the fundamental quantum of electromagnetic radiation. It is a massless particle that travels at the speed of light (c ≈ 3 × 108 m/s) and carries energy proportional to its frequency.
Can I use wavelength in Angstroms?
Yes! The Angstrom (Å) is a unit commonly used in X-ray crystallography and atomic physics. 1 Å = 0.1 nm = 10−10 m. The calculator accepts wavelength in Å.
What is the difference between Joules and electron-volts?
Both are units of energy. The electron-volt (eV) is defined as the energy gained by one electron accelerating through a 1-volt potential difference. 1 eV = 1.60218 × 10−19 J. Electron-volts are more convenient for atomic-scale energies.
What is an erg?
The erg is the CGS (centimeter-gram-second) unit of energy. 1 J = 107 erg. Ergs are still used in astrophysics and some older literature.
What does kJ/mol mean for photon energy?
kJ/mol represents the total energy of one mole (6.022 × 1023) of photons in kilojoules. This unit is widely used in photochemistry and thermodynamics to compare photon energies with chemical bond energies.