Photon Energy Calculator

Calculate the energy of photons using Planck's equation from wavelength or frequency.

Convert between wavelength, frequency, and photon energy using E = hν = hc/λ. Supports multiple energy units including Joules, electron volts (eV), and kilocalories per mole.

Examples

Click on any example to load it into the calculator.

Green Light (550 nm)

Visible Light

Typical green light wavelength, commonly used in lasers and displays.

Wavelength: 550 nm

Energy Unit: eV

Ultraviolet Light (254 nm)

Ultraviolet

UV-C wavelength used in germicidal lamps and sterilization.

Wavelength: 254 nm

Energy Unit: eV

Near Infrared (850 nm)

Near Infrared

Common wavelength for fiber optic communications and remote controls.

Wavelength: 850 nm

Energy Unit: J

Radio Frequency (100 THz)

Radio Frequency

High-frequency electromagnetic radiation in the terahertz range.

Frequency: 100 THz

Energy Unit: kcal/mol

Other Titles
Understanding Photon Energy Calculator: A Comprehensive Guide
Explore the fundamental relationship between light's wavelength, frequency, and energy. Learn how Planck's equation connects these properties and discover real-world applications in physics, chemistry, and technology.

What is Photon Energy?

  • Quantum Nature of Light
  • Planck's Equation
  • Energy-Wavelength Relationship
Photon energy is the fundamental concept that bridges classical and quantum physics. A photon, the quantum particle of light, carries energy that is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is governed by Planck's equation, one of the most important formulas in modern physics.
The Quantum Revolution
In 1900, Max Planck introduced the revolutionary idea that electromagnetic radiation is quantized - meaning it can only exist in discrete packets of energy called photons. This discovery laid the foundation for quantum mechanics and fundamentally changed our understanding of light and matter. Each photon carries a specific amount of energy determined by its frequency or wavelength.
Planck's Equation: E = hν = hc/λ
The core equation governing photon energy is E = hν = hc/λ, where E is the photon energy, h is Planck's constant (6.626 × 10^-34 J·s), ν (nu) is the frequency, c is the speed of light (3 × 10^8 m/s), and λ (lambda) is the wavelength. This equation shows that higher frequency (shorter wavelength) light carries more energy per photon.
Understanding the Units
Photon energy can be expressed in various units depending on the application. Joules (J) are the SI unit of energy, electron volts (eV) are commonly used in atomic and nuclear physics, and kilocalories per mole (kcal/mol) are useful in chemistry for understanding reaction energetics. The calculator automatically converts between these units for convenience.

Key Energy Ranges:

  • Radio waves: 10^-9 to 10^-6 eV (very low energy)
  • Microwaves: 10^-6 to 10^-3 eV (low energy)
  • Infrared: 10^-3 to 1.7 eV (thermal energy)
  • Visible light: 1.7 to 3.1 eV (moderate energy)
  • Ultraviolet: 3.1 to 124 eV (high energy)
  • X-rays: 124 to 124,000 eV (very high energy)
  • Gamma rays: >124,000 eV (extremely high energy)

Step-by-Step Guide to Using the Calculator

  • Input Methods
  • Unit Selection
  • Result Interpretation
The Photon Energy Calculator is designed to be intuitive and accurate. You can input either wavelength or frequency - the calculator will automatically compute the other value and the corresponding photon energy.
Method 1: Using Wavelength
Enter the wavelength in nanometers (nm). This is often the most convenient method since wavelength is easily measured with spectrometers and is commonly reported in scientific literature. The calculator will convert this to frequency and calculate the photon energy.
Method 2: Using Frequency
Enter the frequency in terahertz (THz). This method is useful when working with frequency-domain measurements or when frequency is the primary parameter of interest. The calculator will convert this to wavelength and calculate the photon energy.
Energy Unit Selection
Choose your preferred energy unit: Joules for general physics calculations, electron volts for atomic and particle physics, or kilocalories per mole for chemical applications. The calculator provides all three values regardless of your selection.
Understanding the Results
The calculator displays the photon energy in your selected unit, along with the corresponding wavelength and frequency values. This allows you to verify the calculations and understand the relationships between these fundamental properties of light.

Common Wavelengths and Their Energies:

  • Red light (650 nm): 1.91 eV, 2.45 × 10^-19 J
  • Green light (550 nm): 2.25 eV, 3.61 × 10^-19 J
  • Blue light (450 nm): 2.76 eV, 4.42 × 10^-19 J
  • UV-C (254 nm): 4.88 eV, 7.82 × 10^-19 J
  • X-ray (0.1 nm): 12,400 eV, 1.99 × 10^-15 J

Real-World Applications of Photon Energy Calculations

  • Spectroscopy
  • Photochemistry
  • Technology Applications
Understanding photon energy is crucial across numerous scientific and technological fields. From analyzing the composition of stars to designing efficient solar cells, photon energy calculations are fundamental to modern science and engineering.
Spectroscopy and Chemical Analysis
Spectroscopy relies on the fact that atoms and molecules absorb or emit light at specific wavelengths corresponding to their energy level transitions. By calculating photon energies, scientists can identify chemical compounds, determine molecular structures, and analyze the composition of materials. This is essential in chemistry, biology, astronomy, and environmental science.
Photochemistry and Light-Induced Reactions
Many chemical reactions are initiated or catalyzed by light. The energy of photons determines whether a reaction can occur - if the photon energy is less than the activation energy, the reaction won't proceed. This principle is used in photosynthesis, photovoltaics, phototherapy, and numerous industrial processes.
Technology and Engineering Applications
Modern technology heavily relies on precise photon energy calculations. LED lighting, laser systems, optical communications, medical imaging, and solar energy conversion all depend on understanding and controlling photon energies. Engineers use these calculations to optimize device performance and efficiency.

Practical Applications:

  • Solar cells: Optimizing bandgap energy for maximum efficiency
  • LED lighting: Matching photon energy to desired color output
  • Medical imaging: Using appropriate photon energies for different tissue types
  • Optical communications: Selecting wavelengths for minimal signal loss
  • Environmental monitoring: Detecting specific pollutants by their absorption spectra

Common Misconceptions and Correct Methods

  • Energy vs. Intensity
  • Wavelength vs. Color
  • Quantum vs. Classical
Several misconceptions surround photon energy and its relationship to other properties of light. Understanding these distinctions is crucial for accurate calculations and proper interpretation of results.
Misconception: Higher Intensity Means Higher Energy
This is a common confusion. The intensity of light refers to the number of photons per unit area per unit time, while photon energy refers to the energy carried by each individual photon. A dim blue light has higher energy photons than a bright red light, even though the red light might appear more intense to our eyes.
Misconception: Wavelength and Color Are Always Related
While wavelength and color are related in the visible spectrum, this relationship doesn't hold for all electromagnetic radiation. Infrared, ultraviolet, X-rays, and gamma rays don't have 'colors' in the traditional sense, but they still have specific photon energies that can be calculated using the same equations.
Quantum vs. Classical Understanding
Classical physics treats light as a continuous wave, while quantum physics treats it as discrete particles (photons). The photon energy calculator bridges these two descriptions by showing how the wave properties (wavelength, frequency) relate to the particle properties (energy). This dual nature is fundamental to understanding modern physics.

Important Distinctions:

  • Photon energy (E = hν): Energy per individual photon
  • Light intensity: Number of photons per unit area per unit time
  • Power: Total energy delivered per unit time (intensity × photon energy)
  • Spectral power density: Power per unit wavelength or frequency range

Mathematical Derivation and Advanced Concepts

  • Planck's Constant
  • Relativistic Effects
  • Energy Conservation
The relationship between photon energy, frequency, and wavelength is derived from fundamental principles of quantum mechanics and special relativity. Understanding these derivations provides deeper insight into the nature of light and energy.
The Significance of Planck's Constant
Planck's constant (h = 6.626 × 10^-34 J·s) is one of the most important constants in physics. It represents the fundamental quantum of action and sets the scale for quantum effects. The small value of h explains why quantum effects are not noticeable in everyday macroscopic objects but become crucial at atomic and molecular scales.
Relativistic Considerations
While the basic photon energy equation E = hν is valid for most practical purposes, relativistic effects become important for very high-energy photons (gamma rays). At these energies, the photon's momentum and energy must be considered together, and the full relativistic energy-momentum relationship applies.
Energy Conservation and Photon Interactions
When photons interact with matter, energy conservation requires that the total energy before and after the interaction remains constant. This principle underlies phenomena like the photoelectric effect, Compton scattering, and pair production. Understanding photon energy is essential for predicting and analyzing these interactions.

Advanced Calculations:

  • Compton scattering: Δλ = (h/mc)(1 - cos θ) - wavelength shift due to scattering
  • Photoelectric effect: KE = hν - φ - kinetic energy of ejected electrons
  • Pair production: E ≥ 2mₑc² - minimum energy for electron-positron pair creation
  • Doppler effect: ν' = ν√[(1 + v/c)/(1 - v/c)] - frequency shift due to relative motion