Arrhenius Equation Calculator
Find the activation energy and pre-exponential factor of a reaction from rate constants measured at two temperatures.
K
K
Energy barrier from the two-point Arrhenius equation
- 1
Rate constant ratio ln(k₂ ÷ k₁)
ln(0.05 ÷ 0.001) = 3.91202 - 2
Inverse temperature difference 1/T₂ − 1/T₁
1 ÷ 350 − 1 ÷ 300 = -0.00047619Units are K⁻¹; the sign determines whether Ea is positive (endothermic barrier). - 3
Activation energy Ea = −R × ln ratio ÷ inv. diff.
−8.314 × 3.91202 ÷ (-0.00047619) = 68,301.6 - 4
Ea in kJ/mol
68,301.6 ÷ 1000 = 68.302
How does this calculator work?
The Arrhenius equation links a reaction rate constant to temperature. Using two rate constants k1, k2 at temperatures T1, T2, this calculator solves ln(k2/k1) = -(Ea/R)(1/T2 - 1/T1) for the activation energy Ea, then derives the pre-exponential factor A and plots ln k versus 1/T, whose slope equals -Ea/R.
Formula
How this is calculated
Enter the rate constant k1 measured at absolute temperature T1 and k2 at T2. Temperatures must be in kelvin and rate constants must be positive; the two temperatures must differ so the term (1/T2 - 1/T1) is non-zero. The calculator uses the gas constant R = 8.314 J/mol·K.
The two-point form of the Arrhenius equation, ln(k2/k1) = -(Ea/R)·(1/T2 - 1/T1), is solved for the activation energy Ea = -R·ln(k2/k1) / (1/T2 - 1/T1), reported in both J/mol and kJ/mol. The pre-exponential (frequency) factor A is then recovered from the single-temperature form k = A·e^(-Ea/RT), giving A = k1·e^(Ea/(R·T1)).
Plotting ln k against 1/T yields a straight line whose slope is -Ea/R and whose intercept is ln A; the chart shows this line through your two data points. This assumes Ea and A are temperature-independent over the measured range and that both rate constants are expressed in the same units, so A inherits those units.
Frequently asked questions
Always use absolute temperature in kelvin. Convert from Celsius by adding 273.15 before entering values.
The method divides by (1/T2 - 1/T1). If T1 equals T2 this term is zero and Ea is undefined, so you need rate data at two distinct temperatures.
The pre-exponential factor A carries the same units as the rate constant k, which depend on the reaction order (e.g. 1/s for first order).
Also known as
TG we-Calculate Editorial Team. (2026). Arrhenius Equation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/arrhenius-equation-calculator
TG we-Calculate Editorial Team. "Arrhenius Equation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/arrhenius-equation-calculator.
TG we-Calculate Editorial Team, "Arrhenius Equation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/arrhenius-equation-calculator
@misc{wecalculate_arrhenius_equation_calculator, title = {Arrhenius Equation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/arrhenius-equation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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