Arrhenius Equation Calculator

How to use the Arrhenius equation calculator

What this calculator does

This calculator solves the Arrhenius equation for one unknown variable: the Arrhenius constant A, activation energy Eₐ, absolute temperature T, or rate constant k. It models the temperature dependence of a reaction's rate constant under the common assumption that A and Eₐ remain constant over the temperature range being considered. It does not predict a full reaction mechanism, concentration-time profile, equilibrium composition, or whether a proposed mechanism is chemically valid.

When to use it

Use it to check laboratory kinetics calculations, estimate how a rate constant changes with temperature, back-calculate a pre-exponential factor from measured data, or compare molar and per-molecule energy conventions. The underlying relationship and its linearized form are described in the IUPAC definition of the Arrhenius equation.

How to calculate

1. The calculator opens with a ready-to-use demonstration: per mole form, Eₐ = 115 kJ/mol, T = 593.15 K, and k = 0.5. It solves for A and immediately validates an Excel workbook for those values.
2. Choose Arrhenius equation form. Per mole uses the molar gas constant R; per molecule uses the Boltzmann constant k_B and expects activation energy in eV per molecule.
3. Choose the unknown in Solve for. The corresponding field is disabled, and the other three become required.
4. Replace the demonstration values. Use ordinary decimal or scientific notation, such as 6.72e9. Commas are accepted only as thousands separators, not as decimal commas.
5. Read the primary result, the exponent, Boltzmann factor, ln(k), and the constant used. When the plot is enabled, review the seven-point table and the straight-line graph of ln(k) versus 1/T.
6. Select Download Excel to export the current validated inputs, outputs, and plot data. Reset clears the demonstration and calculated state; Excel download remains disabled until a complete valid state is entered again.

Input guide

Arrhenius equation form is required. Choose Per mole for Eₐ in kJ/mol or Per molecule for Eₐ in eV/molecule. Switching form converts an existing activation-energy value. The common mistake is mixing molar energy with the molecular constant. Solve for is required and determines which field is the result. Arrhenius constant (A) is a positive number with the same units as k; an example is 6.72e9. Increasing A raises k proportionally. Activation energy (Eₐ) is nonnegative; 115 kJ/mol is a realistic demonstration value. A larger Eₐ lowers k at fixed A and T. Temperature (T) is required in kelvin and must exceed 0; 593.15 K equals 320 °C. Entering Celsius directly is a frequent error. Rate constant (k) must be positive; its units depend on reaction order, so the calculator preserves them generically as “rate units.” Show Arrhenius plot? controls whether the seven-point analytical visualization is displayed; it does not change the calculated result.

Output guide

The primary result is the selected unknown. The Dimensionless exponent is – Eₐ/(RT) or – Eₐ/(k_BT). The Boltzmann factor is e raised to that exponent and lies between 0 and 1 for nonnegative activation energy. ln(k) is the natural logarithm of the rate constant, which can be negative when 0 < k < 1. Constant used confirms whether the model used R or k_B. The plot table lists Temperature, inverse temperature 1/T, k, and ln(k). The line slope is – Eₐ/R for the molar form or – Eₐ/k_B for the molecular form; this is an exact identity within the model, not a fitted experimental recommendation.

Worked example

For the startup values, convert 115 kJ/mol to 115,000 J/mol. The exponent is – 115,000 ÷ (8.314462618 × 593.15) = approximately – 23.3211. Its exponential is about 7.44 × 10 ^{– 11}. Rearranging k = A e ^{– Eₐ/(RT)} gives A = k ÷ e ^{– Eₐ/(RT)}. Therefore A = 0.5 ÷ 7.44 × 10 ^{– 11} ≈ 6.72 × 10⁹, in the same units as k. For constants, see the NIST CODATA values for the molar gas constant and Boltzmann constant.