Arrhenius Calculator

Calculate the rate constant k, the pre-exponential factor A, the activation energy Ea, or the temperature T using the Arrhenius equation $ k = A \cdot e^{-E_a / (R \cdot T)} $ – simply leave the variable you are looking for blank. The calculator automatically converts between units (kJ/mol, J/mol, K, °C) and demonstrates how strongly the reaction rate depends on the temperature.

Enter Values

Do you want to convert shelf life or half-life from one temperature to another? Use our Half-Life Calculator.

Rate constant (unit depends on reaction order, e.g., 1/s or L/(mol·s)) – enter k and A in the same units.
Pre-exponential factor (frequency factor), same unit as k.
Activation energy (always molar, e.g., 75 kJ/mol).
Absolute temperature at which the reaction occurs.

Explanation: The Arrhenius Equation

What Does the Arrhenius Equation Describe?

The Arrhenius equation describes how strongly the rate of a chemical reaction depends on the temperature. Even minor increases in temperature can significantly accelerate a reaction.

The reason for this is the activation energy Ea: only particles with sufficient energy can overcome the reaction barrier. The higher the temperature, the more particles reach this energy level.

Basic Formula

$$ k = A \cdot e^{-E_a / (R \cdot T)} $$

Overview of the Four Variables

Rate Constant (k)

k describes how fast a reaction occurs at a given temperature. The larger k is, the faster the reaction.

Pre-exponential Factor (A)

A (also called the frequency factor) relates to the collision frequency and the spatial orientation of the particles. It is approximately independent of temperature.

Activation Energy (Ea)

Ea is the energy barrier that must be overcome for a reaction to take place. The higher Ea is, the more sensitive k reacts to changes in temperature.

Temperature (T)

T is the absolute temperature in Kelvin at which the reaction occurs.

Pay Attention to the Units of k and A

k and A have different units depending on the reaction order (e.g., 1/s for 1st order, L/(mol·s) for 2nd order). The calculator does not perform any conversion here – the only important thing is to enter k and A in the same unit, as it cancels out in the term k/A anyway.

Solving the Formula for Each Variable

Depending on which variable is being solved for, the formula is rearranged as follows:

Solving for A

$ A = \dfrac{k}{e^{-E_a / (R \cdot T)}} $
Used when k, Ea, and T are known.

Solving for Ea

$ E_a = -R \cdot T \cdot \ln(k/A) $
Used when k, A, and T are known.

Solving for T

$ T = \dfrac{-E_a}{R \cdot \ln(k/A)} $
Used when k, A, and Ea are known. Note: if k = A, T cannot be determined (Ea = 0 for any temperature).

Example Problems

Two examples demonstrate how to calculate depending on the variable you are solving for.

Example 1: Calculating k

A reaction has A = 5·10¹³ 1/s and Ea = 75 kJ/mol at T = 298 K. What is k?

Given

A = 5·10¹³ 1/s, Ea = 75000 J/mol, T = 298 K

Solution

k = A · e^(−Ea / (R·T))

k = 5·10¹³ · e^(−75000 / (8.314 · 298)) = 5·10¹³ · e^(−30.28) ≈ 3.57 1/s

k ≈ 3.57 1/s

Example 2: Finding Ea

At T = 300 K, a rate constant of k = 2.0·10⁻⁴ 1/s was measured, with A = 1·10¹² 1/s. What is Ea?

Given

k = 2.0·10⁻⁴ 1/s, A = 1·10¹² 1/s, T = 300 K

Solution

Ea = −R·T·ln(k/A)

Ea = −8.314 · 300 · ln(2.0·10⁻¹⁶) ≈ −8.314 · 300 · (−36.15) ≈ 90170 J/mol

Ea ≈ 90.2 kJ/mol

Tips and Common Mistakes

Common Sources of Error

k and A in Different Units

Since k and A are not converted here, using different units (e.g., k in 1/s, A in 1/min) will lead to incorrect results. Always enter both in the same unit.

Temperature in °C instead of Kelvin

The formula always requires the absolute temperature in Kelvin, not in degrees Celsius. Do not forget to add 273.15.

Using Ea in kJ/mol instead of J/mol in the Formula

Since R is given in J/(mol·K), Ea must be entered in J/mol. The calculator handles this conversion automatically, but you must remember it when calculating by hand.

Where is This Used?

The Arrhenius equation is central to reaction kinetics:

  • Predicting how much a reaction rate increases with temperature
  • Determining the activation energy from measurements at different temperatures
  • Estimating shelf life and storage conditions (e.g., for food, pharmaceuticals)

Frequently Asked Questions about the Arrhenius Equation

The Arrhenius equation $ k = A \cdot e^{-E_a / (R \cdot T)} $ describes how the rate constant k of a chemical reaction depends exponentially on temperature T. The higher the temperature, the more particles possess enough energy to overcome the activation energy Ea – the reaction runs faster.

Ea is given as molar energy, usually in kJ/mol or J/mol. Since the universal gas constant R is expressed in J/(mol·K), Ea must be in J/mol when substituted into the formula – the calculator performs this conversion automatically.

The Arrhenius equation requires the absolute temperature because it appears in the exponent, and negative or zero values would make no physical sense. To convert from °C to Kelvin, add 273.15 (e.g., 25 °C = 298.15 K).

A (also called the frequency factor or pre-exponential factor) relates to the frequency and spatial orientation of particle collisions. It indicates how often a successful reaction could theoretically occur – provided sufficient energy – and is assumed to be approximately constant within the investigated temperature range.

The larger Ea is, the more k decreases at the same temperature, as the magnitude of the negative exponent $ -E_a / (R \cdot T) $ increases. Furthermore, reactions with high activation energy are particularly sensitive to temperature changes.

Yes. The calculator automatically solves the Arrhenius equation for whichever variable you leave blank – as long as the other three values (k, A, Ea, T) are known. One exception: If k = A, then Ea = 0 and T cannot be uniquely determined, as any temperature satisfies the equation.