Arrhenius Equation Calculator

The Arrhenius Equation Calculator solves for key variables in the Arrhenius equation — the formula chemists use to predict how a chemical reaction's rate constant changes with temperature and activation energy. Select a calculation mode: find the rate constant k from the pre-exponential factor A, activation energy Eₐ, and temperature T; find the activation energy Eₐ from two rate constants and temperatures; or find a new rate constant k₂ at a second temperature. Results include the primary value, its natural log, and the Boltzmann exponent −Eₐ/(RT).

Select what you want to calculate.

Frequency factor A in the same units as k (s⁻¹ for first-order reactions).

kJ/mol

Activation energy in kilojoules per mole.

K

Temperature in Kelvin. (°C + 273.15 = K)

Rate constant at temperature T₁.

K

First temperature in Kelvin.

Rate constant at temperature T₂ (used when finding Eₐ).

K

Second temperature in Kelvin.

kJ/mol

Activation energy used when finding k₂ from k₁.

Results

Result

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ln(k) or ln(result)

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Exponent −Eₐ/(RT)

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Calculated Quantity

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Results Table

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Frequently Asked Questions

What is the Arrhenius equation?

The Arrhenius equation is k = A · e^(−Eₐ/RT), where k is the rate constant, A is the pre-exponential (frequency) factor, Eₐ is the activation energy, R is the universal gas constant (8.314 J/mol·K), and T is the absolute temperature in Kelvin. It quantifies how reaction rate depends on temperature.

What is activation energy (Eₐ) and why does it matter?

Activation energy is the minimum energy that reacting molecules must possess for a collision to result in a reaction. A higher Eₐ means the reaction is more sensitive to temperature changes — a small rise in T produces a large increase in k. It is typically expressed in kJ/mol.

What is the pre-exponential factor A in the Arrhenius equation?

A, also called the frequency factor or attempt frequency, represents the rate at which collisions occur with the correct orientation, independent of energy. Its units match those of k (e.g. s⁻¹ for first-order reactions). A large A means molecules collide favorably very often.

How do I use the two-temperature form of the Arrhenius equation?

When you have rate constants k₁ and k₂ measured at temperatures T₁ and T₂, you can use ln(k₂/k₁) = (Eₐ/R)(1/T₁ − 1/T₂) to solve for Eₐ, or rearrange to find k₂ given k₁ and Eₐ. Both temperatures must be in Kelvin.

What is the linearized (ln) form of the Arrhenius equation?

Taking the natural log of both sides gives ln k = ln A − (Eₐ/R)(1/T). This is a straight-line equation in the form y = mx + b, where a plot of ln k versus 1/T yields a slope of −Eₐ/R and a y-intercept of ln A — known as the Arrhenius plot.

Why must temperature be entered in Kelvin?

The Arrhenius equation requires an absolute temperature scale because it uses temperature in the exponent (division). Zero on the Celsius or Fahrenheit scale does not represent zero molecular kinetic energy. Convert Celsius to Kelvin by adding 273.15.

What is the gas constant R used in the Arrhenius equation?

R is the universal gas constant with a value of 8.314 J/(mol·K). Because Eₐ is often given in kJ/mol, it must be multiplied by 1000 before dividing by R·T to keep units consistent.

Can the Arrhenius equation be used for all chemical reactions?

The Arrhenius equation works well for most elementary reactions over moderate temperature ranges. It can break down for reactions with complex mechanisms, quantum tunneling effects, or very wide temperature ranges where A or Eₐ themselves vary with temperature.