Physics & Mechanics

Planck's Equation Calculator

Calculate the energy of a photon based on its frequency or wavelength using Planck's constant. Essential for quantum mechanics.

Photon Energy (E)
3.313 × 10⁻¹⁹
Energy in eV2.068 eV

Calculated locally in your browser. Fast, secure, and private.

Quantizing the Universe

In 1900, Max Planck was trying to solve a problem with glowing hot objects (blackbody radiation). To make his math work, he had to make a bizarre assumption: electromagnetic energy (like light) is not a continuous wave. Instead, it is emitted and absorbed in tiny, discrete packets called "quanta" (or photons).

This single equation marks the birth of Quantum Mechanics. It states that the energy of a photon is directly proportional to its frequency.

The Planck Constant

The proportionality constant ($h$) is known as Planck's constant. It is an incredibly small number ($6.626 \times 10^{-34} , \text{J} \cdot \text{s}$), which is why we don't notice the "chunkiness" of light in our everyday macroscopic lives. However, at the atomic level, this quantization dictates everything.

The Formula

E=hf=hcλ\begin{aligned} E = h \cdot f = \frac{h \cdot c}{\lambda} \end{aligned}

Where:
E=
Photon Energy (Joules or eV)
h=
Planck's Constant (6.626 × 10⁻³⁴ J·s)
f=
Frequency of the wave (Hz)
c=
Speed of Light (m/s)
λ\lambda=
Wavelength (meters)

Example Calculation

Calculate the energy of a single photon of green light with a frequency of $5.5 \times 10^{14} , \text{Hz}$.

  1. Planck's Constant: $6.626 \times 10^{-34}$.
  2. Multiply by Frequency: $(6.626 \times 10^{-34}) \times (5.5 \times 10^{14}) \approx 3.64 \times 10^{-19} , \text{Joules}$.

To make these tiny numbers easier, physicists use Electron-Volts (eV). Divide by $1.602 \times 10^{-19}$: $3.64 \times 10^{-19} / 1.602 \times 10^{-19} \approx 2.27 , \text{eV}$.

Frequently Asked Questions

Radio waves have very low frequencies, so their individual photons have almost zero energy. X-rays have incredibly high frequencies, meaning each X-ray photon carries enough energy to knock electrons out of your DNA, causing mutations.

It is both. This is called 'Wave-Particle Duality'. Light travels through space like a continuous wave (showing interference and diffraction), but it interacts with matter like a stream of bullet-like particles (photons).

An electron-volt is a tiny unit of energy used in quantum physics. It is the amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt.