Boltzmann Factor Calculator

Thermal Population of Energy States

At finite temperature, higher energy states are less populated. The Boltzmann factor gives the relative weight of a state separated by energy ΔE from a reference level at temperature T.

Boltzmann Factor Formula

$$ \text{factor} = e^{-\Delta E / k_B T} \qquad \frac{N_2}{N_1} = e^{-\Delta E / k_B T} $$

For two states with energy difference ΔE, the population ratio equals the Boltzmann factor. At room temperature (300 K), kT ≈ 0.026 eV. Related: Blackbody Radiation Calculator and Boyle's Law Calculator.

Frequently Asked Questions

What does the Boltzmann factor represent?

It is the exponential weight exp(-ΔE/kT) that tells how much less likely a state at energy ΔE above a reference is at temperature T.

What is kT at 300 K in eV?

About 0.0259 eV (26 meV). Energy gaps much larger than kT give very small Boltzmann factors.

Can I enter energy in joules?

Yes. Select joules as the energy unit, or use electronvolts for atomic-scale transitions.

When is the factor equal to 1?

When ΔE = 0 or T approaches infinity. At zero temperature, only the lowest state is populated.

How is population ratio related to the factor?

For two states separated by ΔE, N₂/N₁ = exp(-ΔE/kT), assuming the same degeneracy for each state.

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Thermal Population of Energy States

Boltzmann Factor Formula

Frequently Asked Questions

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