Activation energy calculator.
Find a reaction’s activation energy from two rate constants measured at two temperatures. The calculator uses the two-point Arrhenius equation and returns the energy in kJ/mol.
Rates and temperatures
LiveTemperatures must be in kelvin (K = degrees C + 273.15). The pre-exponential factor A cancels out, so only the two rate constants and temperatures are needed.
Activation energy
68.63 kJ/mol
from the two-point Arrhenius equation
Uses the gas constant R = 8.314 J/mol·K. For education and lab estimates. Calculations run in your browser; nothing you enter is stored.
How it works
Two rates, two temperatures
Activation energy is the minimum energy a reaction needs to proceed. The Arrhenius equation links a reaction rate constant to temperature, and its two-point form lets you find the activation energy from rate constants measured at two temperatures, without knowing the pre-exponential factor.
The calculator uses Ea = R times the natural log of k2 over k1, divided by (1/T1 minus 1/T2), with R as 8.314 J/mol-K. It returns the result in kilojoules per mole, the usual unit.
Reference
Celsius to kelvin.
The Arrhenius equation needs temperatures in kelvin. Add 273.15 to a Celsius temperature.
| Celsius | Kelvin |
|---|---|
| 0 C | 273.15 K |
| 25 C | 298.15 K |
| 37 C | 310.15 K |
| 50 C | 323.15 K |
| 100 C | 373.15 K |
The full guide
The complete guide to activation energy.
What activation energy is, how the Arrhenius equation finds it, and how to use the calculator.
What is activation energy?
Activation energy, written Ea, is the energy barrier a reaction must overcome for reactants to turn into products. A higher activation energy means a slower reaction at a given temperature, because fewer molecules have enough energy to react.
Catalysts speed reactions up by lowering the activation energy, giving more molecules a route over the barrier.
The Arrhenius equation
The Arrhenius equation, k = A times e to the power of minus Ea over RT, describes how a rate constant k rises with temperature. A is the pre-exponential factor, R is the gas constant and T is the absolute temperature in kelvin.
Taking the equation at two temperatures and dividing cancels A, which gives the two-point form used here and lets you solve for Ea directly.
Using the two-point form
Measure the rate constant at two temperatures, then apply Ea = R times ln(k2 over k1), divided by (1 over T1 minus 1 over T2). The calculator does the arithmetic and converts the answer to kilojoules per mole.
Make sure both temperatures are in kelvin and that each rate constant pairs with its own temperature, or the result will be wrong.
Reading the result
Most reactions have activation energies in the tens to low hundreds of kilojoules per mole. A larger Ea means the rate is more sensitive to temperature, so a small temperature rise speeds it up a lot.
Use the kcal/mol output if your course or text works in those units; 1 kcal is 4,184 joules.
The formula
Over the
barrier.
The two-point Arrhenius form gives Ea from two rate constants and temperatures, with R as 8.314.
More lab tools ›# Two-point Arrhenius
ln(k2/k1) = (Ea/R) × (1/T1 − 1/T2)
Ea = R × ln(k2/k1) / (1/T1 − 1/T2)
R = 8.314 J/mol·K
# worked example
→ about 68.6 kJ/molQuestions
Activation energy questions.
How do I calculate activation energy?
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Use the two-point Arrhenius equation: Ea equals R times the natural log of k2 over k1, divided by (1 over T1 minus 1 over T2), with R as 8.314 J/mol-K. Enter two rate constants and their kelvin temperatures above.
What units does it use?
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Rate constants can be in any consistent unit since only their ratio matters. Temperatures must be in kelvin. The result is given in kJ/mol, with J/mol and kcal/mol also shown.
Why do I need two temperatures?
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Measuring the rate at two temperatures lets the pre-exponential factor A cancel out, so you can solve for activation energy without knowing A.
How do I convert Celsius to kelvin?
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Add 273.15. So 25 degrees Celsius is 298.15 kelvin. The table on this page lists common conversions.
Is this activation energy 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 activation energy calculator uses the two-point Arrhenius equation and is for education and lab estimates.