Arrhenius Equation Calculator
Choose what to solve for and enter temperatures in kelvin or Celsius. Activation energy is in kJ/mol; the rate constant comes out in the units of A or k1.
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Formula
k = A × exp(-Ea / (R × T))
R = 8.314462618 J/(mol K),Tin kelvin (K = °C + 273.15),Eain joules per mole (the form takes kJ/mol).- Two temperatures give the activation energy:
Ea = R × ln(k2 / k1) / (1/T1 - 1/T2). - And the rate constant at a second temperature:
k2 = k1 × exp(-(Ea / R) × (1/T2 - 1/T1)). - The Boltzmann factor
exp(-Ea / RT)is the fraction of collisions with at least the activation energy.
Worked example
A = 1 × 10^13, Ea = 75 kJ/mol, T = 298.15 K:
Ea / RT = 75000 / (8.314462618 × 298.15) = 30.254exp(-30.254) = 7.2538 × 10^-14k = 1 × 10^13 × 7.2538 × 10^-14 =0.72538
Frequently asked questions
What is the Arrhenius equation?
k = A × exp(-Ea / RT), where A is the pre-exponential factor, Ea the activation energy in J/mol, R = 8.314462618 J/(mol K) and T the absolute temperature. With A = 1 × 10^13, Ea = 75 kJ/mol and T = 298.15 K, k = 0.725.
How do I find activation energy from two rate constants?
Ea = R × ln(k2 / k1) / (1/T1 - 1/T2). If k rises from 0.001 at 298.15 K to 0.01 at 318.15 K, Ea = 8.3145 × ln 10 / 0.000211 = 90.8 kJ/mol.
How much faster is a reaction when it gets warmer?
Use k2 = k1 × exp(-(Ea/R)(1/T2 - 1/T1)). With k1 = 0.001, Ea = 50 kJ/mol and a rise from 298.15 K to 308.15 K, k2 = 0.00192, nearly double.
Why must the temperature be in kelvin?
The exponent uses absolute temperature. This calculator adds 273.15 when you choose Celsius, so 25 °C is 298.15 K. Ea must not be negative here, so a rate that falls as temperature rises is reported as out of range.