Free · Physics models
Equal-Degeneracy Thermal Population Ratio
Calculate the state-one to state-two equilibrium population ratio from energies and temperature.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
boltzmann factor = 1.0000. This worked example uses the displayed units and declared assumptions.
boltzmann_factor = one_way((temperature > 0 and abs((second_energy-first_energy)/(1.380649e-23*temperature)) <= 1000) ? exp((second_energy-first_energy)/(1.380649e-23*temperature)) : 0)
Worked example
Enter these known values and leave the other values blank.
- E==1==
- 0.1 eV
- E==2==
- 0.1 eV
- Temperature
- 300 K
- Boltzmann factor
- 1
Assumptions and limitations
- n1/n2=exp((E2−E1)/(kBT)) assumes equal degeneracies and thermal equilibrium. The supported numerical exponent magnitude is at most 1000. Direct high-precision arithmetic replaces captured floating-point overflow and large-value rounding; this is not a measured population prediction.
- Clear an unknown to solve a supported inverse; keep known values fixed with locks. Singular or underdetermined inverses may remain incomplete.
Common questions
What assumptions apply?
n1/n2=exp((E2−E1)/(kBT)) assumes equal degeneracies and thermal equilibrium. The supported numerical exponent magnitude is at most 1000. Direct high-precision arithmetic replaces captured floating-point overflow and large-value rounding; this is not a measured population prediction.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
Translate the captured binary-floating-point helper to direct high-precision population-ratio arithmetic exp((E2−E1)/(kBT)) for equal degeneracies, preserving its one output branch. Avoid its large-result four-significant-figure rounding; impose a finite numerical exponent range ±1000 and positive temperature. Thermodynamic temperature must be positive. The supported numerical exponent magnitude is at most 1000.