Boltzmann Factor Calculator

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Choose what you want to calculate. Forward mode takes energy and temperature; reverse modes solve for energy or temperature given the factor.
Energy of the higher state minus the lower state, i.e. E2 - E1. Must be >= 0. Use the energy unit selector above.
eV
System temperature in the unit selected above.
K
Boltzmann factor
0.380206

exp(-deltaE / kT) - the relative thermal probability weight

Population ratio (N2 / N1)0.380206
Thermal energy kT0.025852
deltaE / kT0.967
Upper state occupancy0.28%
0.380206
Negligible<0.01Rare0.01-0.1Moderate0.1-0.5High0.5-0.9Near-equal0.9+

Boltzmann factor 0.3802: the upper state has appreciable thermal population.

  • The gap is 0.97 kT, meaning the upper state is moderately occupied relative to the lower state.
  • Thermal energy kT at this temperature is 2.585e-2 eV, the natural scale for comparing energy barriers.
  • In a simple two-level system, 27.55 % of the population sits in the upper state.

Next stepTo study temperature dependence, try increasing or decreasing the temperature and observe how quickly the factor changes.

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