Arrhenius Equation Calculator
Enter the pre-exponential factor A, activation energy Ea, and absolute temperature T to compute the reaction rate constant k = A·e^(−Ea/RT).
Input Data
Results
At a glance:Enter the pre-exponential factor A, activation energy Ea, and absolute temperature T to compute the reaction rate constant k = A·e^(−Ea/RT).
Formula
k = A · e^(−Ea / (R·T)), R = 8.314 J/(mol·K).
$$k = A\,e^{-E_a/(RT)}$$$$\ln k = \ln A - \dfrac{E_a}{R T}$$How to Use
- Enter the pre-exponential factor A and activation energy Ea (J/mol).
- Enter the absolute temperature T in kelvin.
- The calculator returns the rate constant k.
FAQ
Must temperature be in kelvin (K)?
Yes, you must use the absolute temperature in kelvin. The Arrhenius exponent is −Ea/(RT), where T is the thermodynamic absolute temperature. Using °C gives wrong results; convert first: T(K) = T(°C) + 273.15, e.g. 25°C = 298.15 K.
Should activation energy be J/mol or kJ/mol?
It must match the unit of the gas constant R. This calculator uses R = 8.314 J/(mol·K), so enter Ea in J/mol. If your source gives kJ/mol, multiply by 1000 first (e.g. 75 kJ/mol = 75000 J/mol); otherwise the exponent is 1000× too small and the result is severely wrong.
Why does a small temperature rise speed up the reaction a lot?
Because k depends on temperature exponentially as e^(−Ea/RT). A slight rise sharply increases the fraction of molecules whose energy exceeds the activation barrier (the tail of the Boltzmann distribution). Empirically, a ~10°C rise roughly doubles to triples many reaction rates.
How do I find activation energy Ea from experiments?
Take logs: ln k = ln A − Ea/(R·T). Measure k at several temperatures and plot ln k against 1/T; you get a straight line whose slope = −Ea/R, so Ea = −slope × R, and the intercept = ln A gives the pre-exponential factor. This is the standard use of an Arrhenius plot.
What does the pre-exponential factor A represent?
A (pre-exponential factor) summarizes the total collision frequency and whether the collision orientation is correct; think of it as the 'rate ceiling if there were no energy barrier'. When Ea = 0 or T is extremely high so the exponent approaches 1, k approaches A. Its unit is the same as k and depends on the reaction order.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.