Arrhenius equation calculator.
Find a reaction rate constant from the Arrhenius equation. Enter the pre-exponential factor, the activation energy and the temperature, and the calculator returns k.
Arrhenius inputs
LiveUses k = A e^(-Ea/RT) with R = 8.314 J/mol-K. Enter Ea in kJ/mol and temperature in kelvin (K = C + 273.15).
Rate constant k
0.708
in the same units as A
Assumes the Arrhenius model holds over the range. R = 8.314 J/mol-K. Calculations run in your browser; nothing you enter is stored.
How it works
Rate rises with temperature
The Arrhenius equation, k = A times e to the power of minus Ea over RT, describes how a reaction rate constant grows as temperature rises. A is the pre-exponential factor, Ea the activation energy, R the gas constant and T the absolute temperature in kelvin.
The exponential term is the fraction of collisions with enough energy to react. A higher temperature or a lower activation energy makes that fraction larger, so k increases. With A of 1e13, Ea of 75 kJ/mol at 298 K, k is about 0.71.
Reference
Temperature and rate.
Rate constant k for A = 1e13 and Ea = 75 kJ/mol, showing how rate climbs with temperature.
| Temperature | Rate constant k |
|---|---|
| 290 K | 0.309 |
| 300 K | 0.873 |
| 310 K | 2.3 |
| 320 K | 5.72 |
| 330 K | 13.4 |
The full guide
The complete guide to the Arrhenius equation.
What each term means, how to use the equation, and why rate is so sensitive to temperature.
The Arrhenius equation
The equation k = A e^(-Ea/RT) links a reaction’s rate constant to temperature. The pre-exponential factor A reflects how often molecules collide with the right orientation, and the exponential term is the fraction of those collisions energetic enough to clear the activation energy.
Together they explain why most reactions speed up sharply as you heat them.
What the terms mean
A, the pre-exponential or frequency factor, has the same units as k and represents the maximum possible rate if every collision worked. Ea is the energy barrier in joules or kilojoules per mole. R is 8.314 J/mol-K and T is the absolute temperature in kelvin.
Enter Ea in kJ/mol here and the calculator converts it to J/mol to match R.
Using the equation
Plug in A, Ea and T to get k. To go the other way and find Ea from rates at two temperatures, use the two-point form in the activation energy calculator. The exponent shown here, minus Ea over RT, is the key quantity inside the exponential.
Keep units consistent: Ea and R must both be in joules, and temperature in kelvin, or the result will be wrong.
Why temperature matters so much
Because temperature sits inside an exponential, small changes have large effects. A rough rule of thumb is that many reactions roughly double in rate for every 10 C rise, which the table above illustrates.
A higher activation energy makes the reaction even more temperature-sensitive, since the exponential term changes faster.
The formula
Energy over
temperature.
k = A e^(-Ea/RT). The exponential is the fraction of collisions with enough energy to react.
Find Ea instead ›# Arrhenius equation
k = A × e^(−Ea / (R·T))
R = 8.314 J/mol·K
# worked example
1e13 × e^(−30.27) ≈ 0.71Questions
Arrhenius questions.
What is the Arrhenius equation?
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It is k = A times e to the power of minus Ea over RT, linking a reaction rate constant to temperature. A is the pre-exponential factor, Ea the activation energy, R the gas constant and T the temperature in kelvin.
How do I calculate the rate constant k?
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Enter the pre-exponential factor A, the activation energy Ea and the temperature in kelvin. The calculator computes k = A e^(-Ea/RT) with R as 8.314 J/mol-K.
What units should I use?
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Enter Ea in kJ/mol and temperature in kelvin. A and k share the same units. The calculator converts Ea to J/mol internally to match R.
How do I find activation energy instead?
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Use the two-point form with rate constants at two temperatures, which the activation energy calculator does. This equation goes the other way, finding k from a known Ea.
Is this Arrhenius calculator free?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The Arrhenius equation calculator uses R = 8.314 J/mol-K and is for education and lab estimates.