Boltzmann Factor Calculator
Calculate exp(−ΔE/(k_B T)) for statistical mechanics and thermodynamics problems.
How to Use This Calculator
1
Enter energy gap ΔE
Provide the energy difference between states in joules.
2
Enter temperature T
Use absolute temperature in kelvin.
3
Calculate and interpret
Smaller factors indicate lower probability of occupying the higher energy state.
Formula
factor = exp(−ΔE / (k_B T))
k_B = 1.380649×10⁻²³ J/K (Boltzmann constant).
Example: ΔE = 3e−21 J, T = 300 K → factor ≈ 4.847e-1
About Boltzmann Factor
The Boltzmann factor relates the probability of a system occupying a higher energy state to temperature.
Applications
- Population of molecular energy levels
- Arrhenius-type processes and reaction rates
- Thermodynamic partition functions
Frequently Asked Questions
Can I use eV for ΔE?
Convert eV to joules first (1 eV = 1.60218×10⁻¹⁹ J).
What happens as T → ∞?
The factor approaches 1; states become equally populated.
What if ΔE = 0?
The factor is 1; both states have equal probability.