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Arrhenius Equation Calculator

Calculate the rate constant of a reaction at a given temperature from the activation energy and pre-exponential factor.

Reviewed by Christopher FloiedPublished Updated

This free online arrhenius equation calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Frequency/collision factor.

Results

Rate Constant k

1.7198e+1

How to Use This Calculator

1

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Fill in all required input fields for the Arrhenius Equation Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

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Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

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4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Arrhenius Equation Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

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About Arrhenius Equation Calculator

The Arrhenius equation calculator computes the rate constant k for a chemical reaction at a specified temperature, given the activation energy (Ea) and the pre-exponential factor (A). Proposed by Svante Arrhenius in 1889, this equation is one of the most important relationships in chemical kinetics, providing a quantitative link between temperature and reaction rate. It explains the everyday observation that reactions speed up when heated and is used in fields ranging from chemical engineering (reactor design) to food science (shelf life prediction) to pharmacology (drug stability testing).

The Math Behind It

The Arrhenius equation k = A · e^(−Ea/RT) consists of two parts: the pre-exponential factor A represents the maximum possible rate constant if every molecular collision had sufficient energy and proper orientation, and the exponential term e^(−Ea/RT) represents the fraction of collisions that actually have enough energy to surmount the activation barrier. As temperature increases, the fraction of sufficiently energetic molecules grows exponentially, causing k to increase dramatically. A useful rule of thumb is that reaction rates roughly double for every 10 K increase in temperature, though this depends on the magnitude of Ea. The pre-exponential factor A has units that match k and is typically in the range of 10⁸–10¹³ s⁻¹ for first-order gas-phase reactions. For more complex reactions, A may include steric factors that account for the requirement that molecules collide in a specific orientation.

Formula Reference

Arrhenius Equation

k = A × e^(−Ea/RT)

Variables: k = rate constant; A = pre-exponential factor; Ea = activation energy (J/mol); R = 8.314 J/(mol·K); T = temperature (K)

Worked Examples

Example 1: First-order decomposition

A = 1 × 10¹⁰ s⁻¹, Ea = 50 kJ/mol, T = 298 K.

Step 1:Ea in J = 50 000 J/mol.
Step 2:Ea/(RT) = 50000 / (8.314 × 298) = 20.18.
Step 3:k = 1e10 × e^(−20.18) = 1e10 × 1.71 × 10⁻⁹ = 17.1 s⁻¹.

The rate constant is approximately 17.1 s⁻¹ at 298 K.

Common Mistakes & Tips

  • !Using Ea in kJ/mol without converting to J/mol (multiply by 1000).
  • !Using Celsius instead of Kelvin for temperature.
  • !Treating A as dimensionless — it has the same units as k.

Related Concepts

Activation Energy

Calculate Ea from rate constants at two temperatures.

Half-Life

Once you know k, calculate the half-life of the reaction.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Activation Energy Calculator

Half-Life Calculator

Frequently Asked Questions

What determines the pre-exponential factor A?

A is determined by the collision frequency and the steric factor (probability that colliding molecules have the correct orientation). It can be estimated from collision theory or transition state theory.

Does the Arrhenius equation work for all reactions?

It works well for most elementary reactions over moderate temperature ranges. Some reactions show non-Arrhenius behavior (curved Arrhenius plots), which may indicate a change in mechanism, tunneling, or complex multi-step pathways.

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