Rate Constant Calculator — Arrhenius Equation
Calculate the rate constant k at any temperature using the Arrhenius equation: k = A × exp(−Ea / RT). Enter the pre-exponential factor A, activation energy Ea (kJ/mol), and temperature to get k and an Arrhenius plot.
kJ/mol
°C
Temperature unit
k = A × exp(−Ea / RT), R = 8.314 J mol⁻¹ K⁻¹
- 1
Temperature in Kelvin
25 + 273.15 = 298.15 K - 2
Activation energy in J/mol
60 × 1000 = 60,000 J/mol - 3
Exponent (−Ea ÷ RT)
−60,000 ÷ (8.314 × 298.15) = -24.205074The Boltzmann factor: fraction of collisions with enough energy to react - 4
Rate constant k = A × eˣ
10,000,000,000,000 × e^(-24.2051) = 307.517534
How does this calculator work?
k = A × exp(−Ea / RT), where R = 8.314 J mol⁻¹ K⁻¹ and T is in Kelvin. Enter Ea in kJ/mol (converted internally to J/mol), the pre-exponential factor A, and temperature to get k. The Arrhenius plot (ln(k) vs 1000/T) is linear with slope −Ea/R. Units of A and k depend on reaction order.
Formula
How this is calculated
The Arrhenius equation, k = A × exp(−Ea / RT), describes how the rate constant of a chemical reaction depends on temperature. A is the pre-exponential (frequency) factor — related to how often reactant molecules collide in the correct orientation — and Ea is the activation energy (J/mol), the minimum kinetic energy required for a collision to result in reaction. R is the universal gas constant (8.314 J mol⁻¹ K⁻¹) and T is absolute temperature in Kelvin.
As temperature rises, the exponential term exp(−Ea / RT) increases because more molecular collisions exceed the activation energy threshold, so k increases rapidly — roughly doubling for every 10 °C rise for many common reactions. The Arrhenius plot (shown as ln(k) vs 1000/T) is linear with slope = −Ea/R, providing a way to measure activation energy experimentally from rate constants measured at different temperatures.
The units of k depend on the reaction order (s⁻¹ for first-order, L mol⁻¹ s⁻¹ for second-order) and A must have the same units. The Arrhenius equation is empirical and works well for many gas-phase and solution reactions; it breaks down near phase transitions, for reactions in viscous media, or when tunnelling is significant.
Frequently asked questions
The Arrhenius equation k = A × exp(−Ea / RT) gives the rate constant k of a reaction as a function of temperature T (in Kelvin), activation energy Ea (J/mol), pre-exponential factor A, and the gas constant R = 8.314 J mol⁻¹ K⁻¹.
A and k have the same units, which depend on reaction order. For a first-order reaction: s⁻¹. For second-order: L mol⁻¹ s⁻¹. For third-order: L² mol⁻² s⁻¹. Always match A to the expected order of your reaction.
Use the two-temperature Arrhenius form: ln(k₂/k₁) = (Ea/R) × (1/T₁ − 1/T₂). Rearrange to Ea = R × ln(k₂/k₁) / (1/T₁ − 1/T₂). This is equivalent to measuring the slope of the ln(k) vs 1/T Arrhenius plot and multiplying by −R.
Also known as
TG we-Calculate Editorial Team. (2026). Rate Constant Calculator — Arrhenius Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rate-constant-calculator
TG we-Calculate Editorial Team. "Rate Constant Calculator — Arrhenius Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/rate-constant-calculator.
TG we-Calculate Editorial Team, "Rate Constant Calculator — Arrhenius Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rate-constant-calculator
@misc{wecalculate_rate_constant_calculator, title = {Rate Constant Calculator — Arrhenius Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rate-constant-calculator}}, year = {2026}, note = {TG we-Calculate} }
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