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Arrhenius Equation Calculator

Find a rate constant with the Arrhenius equation.

How it is calculated

The tool evaluates k = A × e^(−Ea / (R·T)). A is the pre-exponential factor, which has the same unit as k (for a first-order reaction, 1/s). Ea is the activation energy in kJ/mol, which the tool converts to J/mol. R is the gas constant 8.314462618 J/(mol·K), and T is the temperature. You enter the temperature in °C and the tool adds 273.15 to get kelvin.

Besides k, which is shown in scientific notation with four decimals, the tool shows the exponent −Ea / (R·T). A must be greater than zero, and the temperature must be above absolute zero (−273.15 °C), otherwise there is no result. Scientific notation such as 1e10 is accepted for A.

Worked example

Take A = 1e10 per second, Ea = 75 kJ/mol and 25 °C. The temperature is 25 + 273.15 = 298.15 K. The exponent is −75000 / (8.314462618 × 298.15) = −75000 / 2478.96 = −30.2547. Then e^(−30.2547) ≈ 7.25e-14, and multiplying by A gives 7.2538 × 10⁻⁴ (per second). At 35 °C the same inputs give 1.9363 × 10⁻³.

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Common mistakes

  • Entering Ea in J/mol instead of kJ/mol; 75000 instead of 75 makes the exponent 1000 times larger and k effectively zero.
  • Typing the temperature in kelvin although the field is in °C, which adds 273.15 a second time.
  • Using the A and Ea of a different reaction order or rate expression; k only has the unit that A has, so the result must be read in that unit.
  • Ea given in kcal/mol from older literature without converting (1 kcal = 4.184 kJ).
  • Extrapolating far beyond the temperature range where A and Ea were fitted; the Arrhenius form is an empirical fit and can fail at extremes, for example when an enzyme denatures.

About this calculator

This calculator finds a chemical reaction's rate constant using the Arrhenius equation: k = A·e^(−Ea/RT), where A is the pre-exponential (frequency) factor, Ea is the activation energy, R is the gas constant, and T is absolute temperature. It captures why reaction rates rise sharply with even modest temperature increases.

Chemists, chemical engineers, and food scientists use it to predict how fast a reaction — or a spoilage or degradation process — will proceed at a given temperature, and to compare rate constants across temperatures when only Ea and A are known from an Arrhenius plot.

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Comments (1)

  • Editorial team

    You can compare temperatures even when A is unknown, because A cancels in the ratio of two rate constants. With Ea = 50 kJ/mol, going from 25 °C to 35 °C raises k from 17.393 to 33.469 for A = 1e10, a factor of about 1.9. A lower Ea gives a smaller jump, a higher one a larger jump. Which process are you modelling, a reaction in the lab or something like food spoilage?

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