What is the Arrhenius equation?

The Arrhenius equation k = A·e^(−Ea/RT) relates the rate constant k to temperature T. A is the pre-exponential (frequency) factor, Ea is the activation energy (J/mol), R is the gas constant (8.314472 J·mol⁻¹·K⁻¹), and T is temperature in Kelvin. The exponent −Ea/RT represents the fraction of molecules with enough energy to react.

What units does k have?

The units of k depend on the reaction order and match the units of A. For a first-order reaction k has units of s⁻¹; for a second-order reaction, L·mol⁻¹·s⁻¹. This tool computes the numeric value of k — make sure A carries the correct units for your reaction order.

What is the pre-exponential factor A?

A (also called the frequency factor or attempt frequency) represents the maximum possible rate if every collision were effective. It encodes collision frequency and the geometric/steric probability that a collision leads to reaction. A is typically determined experimentally from an Arrhenius plot.

Why must temperature be in Kelvin?

The Arrhenius equation uses absolute (thermodynamic) temperature because T appears in the denominator of the exponent. Using Celsius would give nonsensical results near 0 °C or below. This tool automatically converts °C to K by adding 273.15.

What is ln(k) used for?

Taking the natural log of the Arrhenius equation gives ln(k) = ln(A) − Ea/(R·T). Plotting ln(k) vs. 1/T yields a straight line with slope −Ea/R and intercept ln(A). This linearized form is the standard way to extract Ea and A from experimental rate constant measurements.

How does k change with temperature?

k increases exponentially with temperature. As a rough rule (the Arrhenius approximation of the Q₁₀ rule), many reactions roughly double in rate for every 10 °C rise near room temperature. The exact factor depends on Ea — higher activation energies produce larger k ratios for the same temperature increase.

Arrhenius Rate Constant Calculator

Enter the pre-exponential factor A, activation energy Ea, and temperature T to compute the rate constant k from k = A·e^(−Ea/RT).

Arrhenius Inputs

Pre-exponential factor A

Frequency factor (same units as k, e.g. s⁻¹ or L·mol⁻¹·s⁻¹)

Activation energy E_a

Temperature T

Optional — Compare at a second temperature

Enter A, E_a, and T on the left, then click Calculate k.

Temperature Comparison

Variable	T₁	T₂

k₂ / k₁ ratio

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Summary

The Arrhenius Rate Constant Calculator computes k directly from the three input variables of the Arrhenius equation: k = A·e^(−Ea/RT), where A is the pre-exponential (frequency) factor, Ea is the activation energy, R is the universal gas constant (8.314472 J·mol⁻¹·K⁻¹), and T is the absolute temperature in Kelvin. Unlike a full equation solver, this tool focuses on the forward calculation of k, shows the full substituted equation, and lets you sweep temperature to see how k changes across a range. All computation runs in your browser with no data sent to any server.

How it works

Enter the pre-exponential factor A (in s⁻¹ for first-order or L·mol⁻¹·s⁻¹ for second-order reactions).
Enter the activation energy Ea and choose units: J/mol or kJ/mol.
Enter the temperature and choose units: Kelvin (K) or Celsius (°C).
Click Calculate — the tool evaluates k = A·e^(−Ea/RT) and displays the result with scientific notation.
Review the step-by-step substitution and the ln(k) value for linearized Arrhenius analysis.
Optionally enter a second temperature to compare k values and see the k₂/k₁ ratio.

Use cases

Predict how fast a reaction runs at a specific temperature using known kinetics parameters.
Compare k at two temperatures to quantify the effect of heating on reaction speed.
Verify rate constant calculations for physical chemistry homework or lab reports.
Estimate shelf-life changes from temperature shifts using rate constant ratios.
Teach or demonstrate exponential temperature dependence in kinetics courses.
Cross-check k values extracted from Arrhenius plots (ln k vs. 1/T).
Evaluate whether a reaction is feasible at a given temperature based on its k.
Screen candidate catalysts by comparing pre-exponential factors and activation energies.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu