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Arrhenius Equation Calculator

Arrhenius solver: find k, A, activation energy Ea or T at one point, or get Ea from two rate constants at two temperatures.

About this tool

The Arrhenius Equation Calculator is a free, in-browser chemical-kinetics tool built on k = A · exp(−Ea ⁄ (R·T)), which describes how a reaction's rate constant depends on temperature. In single-point mode you enter three of the four quantities — rate constant k, pre-exponential factor A, activation energy Ea, and temperature T — and it solves for the fourth. In two-point mode you supply two rate constants at two temperatures and it returns the activation energy.

Activation energy can be entered and displayed in kJ/mol or J/mol; internally it is always converted to J/mol to match the gas constant R = 8.314 J/mol·K. Single-point rearrangements are k = A·exp(−Ea ⁄ (R·T)), A = k·exp(Ea ⁄ (R·T)), Ea = −R·T·ln(k ⁄ A), and T = −Ea ⁄ (R·ln(k ⁄ A)). The two-point method uses ln(k₂ ⁄ k₁) = −(Ea ⁄ R)(1 ⁄ T₂ − 1 ⁄ T₁), which rearranges to Ea = R·ln(k₂ ⁄ k₁) ⁄ (1 ⁄ T₁ − 1 ⁄ T₂); the pre-exponential factor is then recovered from A = k₁·exp(Ea ⁄ (R·T₁)).

Everything runs locally in your browser with nothing uploaded. Temperatures must be in kelvin and above absolute zero, and k and A must be positive when a logarithm of their ratio is taken. A and k share the same units, which depend on the reaction order, so they are reported as plain numbers.

Frequently asked questions

What is the activation energy Ea and its unit?
Ea is the minimum energy barrier a reaction must overcome; a higher Ea means a stronger temperature sensitivity. You may enter it in kJ/mol or J/mol — the tool converts to J/mol internally to match R = 8.314 J/mol·K — and it reports Ea in the unit you select.
How does the two-point method find Ea?
From ln(k₂ ⁄ k₁) = −(Ea ⁄ R)(1 ⁄ T₂ − 1 ⁄ T₁), rearranged to Ea = R·ln(k₂ ⁄ k₁) ⁄ (1 ⁄ T₁ − 1 ⁄ T₂). Give two rate constants at two kelvin temperatures and it returns Ea, then back-solves the pre-exponential factor A from the first point.
Why must temperature be in kelvin?
The exponential term Ea ⁄ (R·T) needs an absolute temperature, and R = 8.314 J/mol·K is defined per kelvin. Celsius would give wrong, even negative, denominators, so enter T in kelvin; the two temperatures in two-point mode must differ.
What is the pre-exponential factor A?
A, also called the frequency factor, is the rate constant's ceiling as Ea ⁄ (R·T) approaches zero — roughly how often correctly-oriented collisions occur. It shares the same units as k, which depend on the reaction order, so both are shown as plain numbers.

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