Activation Energy Calculator — Arrhenius Two-Point Method
Find the activation energy of a reaction from two rate constants measured at different temperatures, using the linearised Arrhenius equation. Enter k₁, T₁, k₂, T₂ (temperatures in Kelvin) and get Ea in kJ/mol plus the characteristic ln(k) vs 1/T plot.
K
K
Energy barrier the reaction must overcome — two-point Arrhenius method
- 1
Rate constant ratio ln(k₂ ÷ k₁)
ln(0.0346 ÷ 0.0115) = 1.1015Natural log of the ratio — the A factor cancels out. - 2
Inverse temperature difference 1/T₁ − 1/T₂
1 ÷ 298 − 1 ÷ 318 = 0.000211 K⁻¹ - 3
Activation energy Ea = R × ln(k₂/k₁) ÷ (1/T₁ − 1/T₂)
8.314 × 1.1015 ÷ 0.000211 = 43,392.1 J/mol - 4
Activation energy in kJ/mol
43,392.1 ÷ 1 000 = 43.39 kJ/mol
How does this calculator work?
From two rate-constant measurements (k₁ at T₁, k₂ at T₂, both in Kelvin), activation energy is Ea = R × ln(k₂/k₁) / (1/T₁ − 1/T₂) with R = 8.314 J mol⁻¹ K⁻¹. Assumes constant Ea and simple Arrhenius behaviour across the temperature range.
Formula
How this is calculated
The Arrhenius equation k = A·e^(−Ea/RT) describes how a reaction rate constant k depends on temperature T (in Kelvin). Taking the ratio of two measurements and applying the natural log cancels the pre-exponential factor A, yielding the two-point form: ln(k₂/k₁) = −Ea/R × (1/T₂ − 1/T₁). Rearranging gives Ea directly from four observable quantities. The rate constants k₁ and k₂ can be in any consistent units (s⁻¹, M⁻¹s⁻¹, etc.) as they appear as a ratio.
The Arrhenius plot (ln k vs 1/T) is linear with slope −Ea/R when the Arrhenius assumptions hold. The two measured points are plotted alongside the straight line they define — if additional data points scatter away from this line, the reaction may have a non-Arrhenius temperature dependence (e.g. quantum tunnelling, competing pathways, or a change in mechanism).
This method assumes the activation energy is constant over the temperature range used and that the reaction follows simple Arrhenius behaviour. For broad temperature ranges or high-precision work, measure at several temperatures and fit a regression to the full Arrhenius plot.
Frequently asked questions
No — k₁ and k₂ must be in the same units, but those units cancel in the ratio k₂/k₁. Use whatever units your experiment gives (s⁻¹ for first-order, M⁻¹s⁻¹ for second-order, etc.).
The Arrhenius equation uses absolute temperature. Convert °C → K by adding 273.15. Using Celsius gives a nonsensical (and completely wrong) result because 0 °C is not "no temperature".
A negative Ea means the rate constant decreases with increasing temperature — unusual but physically possible for some radical recombinations or enzyme-catalysed reactions. Check your k values are not swapped, and verify units and temperatures are consistent.
Also known as
TG we-Calculate Editorial Team. (2026). Activation Energy Calculator — Arrhenius Two-Point Method [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/activation-energy-calculator
TG we-Calculate Editorial Team. "Activation Energy Calculator — Arrhenius Two-Point Method." TG we-Calculate. 2026. https://we-calculate.com/calculator/activation-energy-calculator.
TG we-Calculate Editorial Team, "Activation Energy Calculator — Arrhenius Two-Point Method," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/activation-energy-calculator
@misc{wecalculate_activation_energy_calculator, title = {Activation Energy Calculator — Arrhenius Two-Point Method}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/activation-energy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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