Last updated: June 2026
Use this Arrhenius equation calculator to connect the rate constant, activation energy, temperature and pre-exponential factor. The same tool can also calculate activation energy from two rate constants measured at two different temperatures.
- Choose whether you want to find k, find A, or calculate Ea from two rate constants.
- Enter all temperatures in kelvin. The calculator accepts Ea in kJ mol−1 and converts it internally to J mol−1.
- For the two-temperature method, enter k1 and k2 in the same units so that their ratio is unitless.
- Select Calculate to see the formula, conversion, substitution and final answer step by step.
What is the Arrhenius equation?
The Arrhenius equation explains how the rate constant changes with temperature:
In this equation, k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant and T is the absolute temperature. As temperature rises, the negative exponent becomes less negative, so the value of k normally increases.
Meaning of k, A, Ea, R and T
The rate constant k appears in the experimentally determined rate equation. The pre-exponential factor A is related to the frequency and orientation of potentially successful collisions. Ea is the minimum energy barrier associated with the reaction pathway.
The units of A are the same as the units of k for the chosen rate law. They are not always s−1. For example, an overall second-order reaction commonly has units of dm3 mol−1 s−1 for both A and k.
The linear Arrhenius equation
Taking natural logarithms gives:
This can be written in straight-line form as:
Therefore, a graph of ln k against 1/T has gradient −Ea/R and y-intercept ln A. A steeper negative gradient corresponds to a larger activation energy.
Calculating activation energy from two temperatures
When rate constants are known at two temperatures, the two-point form of the Arrhenius equation is:
A convenient rearrangement is:
The units of the two rate constants cancel in the ratio, but the two values must be expressed using the same unit system. The calculated Ea is first obtained in J mol−1 and can then be divided by 1000 to give kJ mol−1.
Worked examples
Example 1: Calculating k
A reaction has A = 1.00 × 1012 s−1, Ea = 75.0 kJ mol−1 and T = 298 K.
Example 2: Calculating activation energy
A reaction has k1 = 2.00 × 10−3 s−1 at 300 K and k2 = 1.20 × 10−2 s−1 at 320 K.
Example 3: Finding Ea from an Arrhenius plot
If the gradient of a graph of ln k against 1/T is −8400 K, then:
Common exam traps
Frequently asked questions
Why does a higher temperature increase k?
At a higher temperature, a larger fraction of particles have enough energy to reach the activated state. This raises the rate constant and normally makes the reaction faster at the same concentrations.
Can A and k have different units?
No. The exponential term is unitless, so A and k must have the same units for a given rate law.
Why is an Arrhenius plot negatively sloped?
The gradient is −Ea/R. Since activation energy and R are positive, the gradient is normally negative.
Does a catalyst lower the activation energy?
A catalyst provides an alternative reaction pathway with a lower activation energy. At the same temperature, this generally increases the rate constant.