Arrhenius Equation Calculator
Enter a pre-exponential factor, an activation energy, and an absolute temperature to get the reaction rate constant — and see why a few degrees can change a reaction rate so dramatically.
Rate constant in one step
Enter A, the activation energy, and the temperature in kelvin and the Arrhenius equation calculator returns the rate constant k = A · exp(−Ea / (R · T)) in 1/s.
What is the Arrhenius equation?
Temperature dependence of a rate constant
The Arrhenius equation calculator turns three numbers — the pre-exponential factor A, the activation energy Ea, and the absolute temperature T — into the rate constant k of a chemical reaction. The Arrhenius equation, k = A · exp(−Ea / (R · T)), describes how steeply a reaction speeds up as it gets warmer: the rate constant rises because more molecules carry enough energy to clear the activation barrier. Here R is the molar gas constant (8.314462618 J/(mol·K)), the activation energy is in joules per mole, and the temperature is in kelvin, so the rate constant comes back in reciprocal seconds (1/s) for a first-order reaction.
Enter the pre-exponential factor, the activation energy in J/mol, and the temperature in kelvin to get the rate constant instantly.
The rate constant is the pre-exponential factor multiplied by an exponential term that depends on the activation energy and the temperature.
k = A × exp(−Ea / (R × T))The exponent −Ea / (R · T) is always negative, so the exponential term is between zero and one and the rate constant never exceeds A. A larger activation energy makes the exponent more negative and the reaction slower; a higher temperature makes the exponent less negative and the reaction faster. Because the temperature sits inside the exponent, the rate constant is extremely sensitive to it.
Suppose a first-order reaction has a pre-exponential factor of 1e13 1/s and an activation energy of 75,000 J/mol at 298.15 K (25 °C).
Build the exponent
−75,000 / (8.314462618 × 298.15) = −30.260 — the dimensionless exponent −Ea / (R · T).
Take the exponential
exp(−30.260) ≈ 7.254 × 10⁻¹⁴ — the fraction of collisions with enough energy.
Multiply by A
1e13 × 7.254 × 10⁻¹⁴ ≈ 0.725385 1/s — the rate constant at this temperature.
The rate constant tells you how fast the reaction proceeds at the temperature you entered: for a first-order reaction, k = 0.725385 1/s means the reactant concentration falls by a factor of e roughly every 1.4 seconds. The real power of the Arrhenius equation is in comparison. Raise the temperature from 298.15 K to 308.15 K — just ten degrees — and the same reaction's rate constant climbs to about 1.94 1/s, roughly 2.7 times faster, which is the familiar rule of thumb that many reactions double or triple in rate for every 10 °C. That steep climb comes entirely from the exponential: a small change in T moves the exponent only a little, but the exponential amplifies it. The activation energy is the lever that sets the sensitivity — a higher Ea means a steeper temperature response — while the pre-exponential factor A simply scales the whole curve up or down without changing its shape.
The equation is a model, so a few assumptions are worth keeping in mind.
Constant activation energy and consistent units
This calculator assumes the activation energy Ea is constant over the temperature range and uses the simple two-parameter Arrhenius form, not the modified A·Tⁿ·exp(−Ea / (R · T)) version. Keep your units consistent: the temperature must be in kelvin, the activation energy in joules per mole, and the gas constant R is 8.314462618 J/(mol·K). The unit of the rate constant matches the pre-exponential factor A — here 1/s, appropriate for a first-order reaction.