Arrhenius Equation formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| k | Rate constant | — | Rate constant at temperature T |
| A | Pre-exponential factor | — | Pre-exponential (frequency) factor |
| Eₐ | Activation energy | J/mol | Activation energy |
| T | Temperature | K | Absolute temperature |
What is Arrhenius Equation?
Arrhenius Equation: The rate constant of a chemical reaction increases exponentially with temperature, governed by the activation energy. — Svante Arrhenius, 1889
The Arrhenius equation describes how reaction rates depend on temperature. Only collisions with energy above the activation energy Ea lead to reaction, and the fraction of such collisions is the Boltzmann factor e−Ea/RT. The pre-exponential factor A reflects collision frequency and orientation.
The same mathematics governs solid-state diffusion (see the Arrhenius diffusion calculator), the viscosity of liquids, and the ageing of materials in accelerated life testing.
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
A reaction has A = 1 × 10¹³ s⁻¹ and Ea = 75 kJ/mol. Find k at 25 °C.
- Eₐ/RT = 75 000 / (8.314 × 298.15) = 30.26.
- k = 10¹³ × e−30.26 = 0.725 s⁻¹.
Raising the temperature by 10 K multiplies the rate by about 2.7, which is the origin of the "rate doubles every 10 °C" rule of thumb.
Frequently asked questions
How do I find Eₐ from rate constants at two temperatures?
Use the two-point form: ln(k₂/k₁) = −(Eₐ/R)(1/T₂ − 1/T₁). Or plot ln k against 1/T: the slope is −Eₐ/R.
What units does k have?
k and A share the same units, which depend on reaction order: s⁻¹ for first order, L/(mol·s) for second order, and so on.