Arrhenius Equation Calculator

Chemistry

Calculate the rate constant k of a chemical reaction with the Arrhenius equation, k = A · exp(−Eₐ ⁄ (R·T)). Enter the pre-exponential factor A, the activation energy Eₐ in kJ/mol, and the absolute temperature T in kelvin. The calculator returns the rate constant and the exponential (Boltzmann) factor, showing how strongly temperature and activation energy control reaction speed.

Formula

k = A x exp(-Ea / (R x T))
  • k is the rate constant, A is the pre-exponential (frequency) factor, Eₐ is the activation energy, R = 8.314 J/(mol·K) is the gas constant, and T is the absolute temperature in kelvin.
  • Enter the activation energy in kJ/mol; the calculator converts it to J/mol (× 1000) before dividing by R·T.
  • The exponential term exp(−Eₐ/RT) is the fraction of collisions with enough energy to react — it grows as temperature rises and shrinks as activation energy rises.
  • k carries the same units as A, which depend on the reaction order, so the calculator reports A and k as plain numbers.

Example: A = 1×10¹⁰, Eₐ = 50 kJ/mol, T = 298 K

Inputs
  • Pre-exponential factor A: 10000000000
  • Activation energy Ea (kJ/mol): 50
  • Temperature T (K): 298

At 298 K with Eₐ = 50 kJ/mol, the exponential factor is exp(−50000 / (8.314 × 298)) ≈ 1.7 × 10⁻⁹, so k ≈ 1×10¹⁰ × 1.7×10⁻⁹ ≈ 17 (in the units of A).

Frequently asked questions

What does the Arrhenius equation describe?
It links a reaction's rate constant to temperature, showing that reactions speed up as temperature increases or as the activation energy decreases.
What units should the activation energy be in?
Enter Eₐ in kilojoules per mole (kJ/mol). The calculator multiplies by 1000 to use joules per mole with R = 8.314 J/(mol·K).
Why must the temperature be in kelvin?
The Boltzmann factor exp(−Eₐ/RT) is only physically meaningful with absolute temperature, so use kelvin (°C + 273.15), never Celsius.
What is the pre-exponential factor A?
A reflects how often molecules collide with the correct orientation. It sets the maximum rate constant the reaction would have if every collision had enough energy.
What units does k have?
k takes the same units as A, which depend on the overall reaction order, so the result is shown as a unit-less number you interpret in context.

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