Arrhenius Equation Calculator

The Arrhenius equation

The Arrhenius equation describes how the rate constant k of a chemical reaction depends on temperature:

k = A · e^(−Ea / (R · T))

• A — the pre-exponential (frequency) factor, related to how often correctly oriented collisions occur. It carries the same units as k.
• Ea — the activation energy, the minimum energy reactant molecules need to react. Entered here in kJ/mol and converted to J/mol (× 1000) inside the calculator.
• R — the universal gas constant, 8.314 J/(mol·K).
• T — the absolute temperature in kelvin (K).

The exponential term e^(−Ea / (R · T)) is the fraction of molecules with enough energy to react. Because it sits in an exponent, even modest temperature increases can raise k sharply.

Worked example

Suppose a reaction has A = 1 × 10¹³ s⁻¹, Ea = 50 kJ/mol and T = 298 K.

First convert: Ea = 50 × 1000 = 50000 J/mol. Then the exponent is −Ea / (R · T) = −50000 / (8.314 × 298) ≈ −20.18. So:

k = 1 × 10¹³ · e^(−20.18) ≈ 1.7 × 10⁵ s⁻¹

Raise the temperature to T = 308 K and the exponent becomes ≈ −19.53, giving k ≈ 3.3 × 10⁵ s⁻¹ — roughly double the rate for just a 10 K rise, the classic “rate doubles every 10 °C” rule of thumb.

How temperature changes k

Common pitfalls

• Mixing energy units. Ea is entered in kJ/mol here but R is in J/mol·K, so the value must be multiplied by 1000. This tool does that for you — just enter kJ/mol.
• Using °C instead of K. Temperature must be absolute. Convert: T(K) = T(°C) + 273.15. Using Celsius gives nonsense.
• Forgetting A is temperature-sensitive. In the simple Arrhenius form A is treated as constant; the modified form k = A · Tⁿ · e^(−Ea / RT) accounts for its mild temperature dependence.
• Comparing k across reactions blindly. The units of k (and A) depend on the reaction order, so a first-order k (s⁻¹) is not directly comparable to a second-order k (M⁻¹·s⁻¹).