# Arrhenius Equation Calculator

k = A·e^(−Ea/RT) solved for k, A, or Ea (two-point form), with Ea in kJ/mol and kcal/mol.

> Canonical page: https://elysiatools.com/en/tools/arrhenius-equation-calculator

- **Category:** Science & Education

- **Keywords:** arrhenius equation, activation energy, rate constant, pre-exponential factor, two point arrhenius, temperature dependence

## Overview

The Arrhenius Equation Calculator evaluates chemical reaction kinetics using the Arrhenius relationship k = A·e^(−Ea/RT). It allows you to solve for the reaction rate constant (k), determine the pre-exponential frequency factor (A), or calculate the activation energy (Ea) from two experimental temperature-rate data points, supporting energy units in both kJ/mol and kcal/mol.

## Inputs

- **Solve for** (select)
- **Pre-exponential factor A** (number): e.g. 1e13 s⁻¹
- **Measured rate constant k** (number): e.g. 0.05 (for solving A)
- **Activation energy Ea** (number): e.g. 75
- **Activation energy unit** (select)
- **Temperature T** (number): e.g. 298.15
- **Temperature unit** (select)
- **k₁ (at T₁)** (number): e.g. 1
- **T₁** (number): e.g. 293.15
- **k₂ (at T₂)** (number): e.g. 2
- **T₂** (number): e.g. 303.15

## When to use

- Predicting reaction rate constants at elevated or reduced temperatures from known kinetic parameters.
- Determining experimental activation energy from two measured rate constants at different temperatures.
- Back-calculating the pre-exponential frequency factor from observed reaction rates and known activation barriers.

## How it works

- Choose your calculation mode to solve for rate constant (k), pre-exponential factor (A), or activation energy (Ea).
- Enter your reaction parameters, selecting appropriate units for activation energy (kJ/mol or kcal/mol) and temperature (K or °C).
- Input two distinct temperature and rate constant pairs if using the two-point activation energy solver.
- Review the calculated kinetic values alongside the intermediate exponent and converted energy units.

## Use cases

- Chemical reaction engineering and thermal process optimization under varying operating temperatures.
- Academic physical chemistry lab analysis for determining activation energy from kinetic data.
- Pharmaceutical and materials stability testing evaluating temperature-dependent degradation rates.

## Frequently asked questions

### What is the Arrhenius equation?

The Arrhenius equation, k = A·e^(−Ea/RT), mathematically describes how chemical reaction rate constants vary with absolute temperature and activation energy.

### What units are supported for activation energy?

You can input activation energy in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol), and outputs display both units simultaneously.

### Can I input temperatures in Celsius?

Yes, you can toggle between Kelvin (K) and Celsius (°C), and the calculator automatically converts values to absolute temperature.

### How does the two-point activation energy calculation work?

It applies the formula Ea = R·ln(k₂/k₁)·T₁T₂/(T₂−T₁) using two empirical rate constant and temperature pairs.

### What is the pre-exponential factor A?

The pre-exponential factor, or frequency factor, represents the total collision rate that possesses the proper spatial orientation for reaction.

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