Activation Energy Calculator Formula

Understand the math behind the activation energy calculator. Each variable explained with a worked example.

Use the Activation Energy Calculator

Formulas Used

Activation Energy (Ea)

ea_j = -(8.314 * log(k2 / k1)) / ((1 / t2) - (1 / t1))

Activation Energy

ea_kj = (-(8.314 * log(k2 / k1)) / ((1 / t2) - (1 / t1))) / 1000

Variables

VariableDescriptionDefault
k1Rate Constant at T₁ (k₁)0.001
t1Temperature T₁(K)300
k2Rate Constant at T₂ (k₂)0.01
t2Temperature T₂(K)350

How It Works

Arrhenius Equation for Activation Energy

Formula

ln(k₂/k₁) = -(Ea/R) × (1/T₂ - 1/T₁)

Solving for Ea: Ea = -R × ln(k₂/k₁) / (1/T₂ - 1/T₁)

Where:

  • Ea = activation energy (J/mol)
  • R = 8.314 J/(mol·K)
  • k₁, k₂ = rate constants at temperatures T₁, T₂
  • T₁, T₂ = absolute temperatures (K)

    • Worked Example

    A reaction has k₁ = 0.001 at 300 K and k₂ = 0.01 at 350 K.

    k1 = 0.001t1 = 300k2 = 0.01t2 = 350
    1. 01Ea = -R × ln(k₂/k₁) / (1/T₂ - 1/T₁)
    2. 02ln(0.01/0.001) = ln(10) = 2.3026
    3. 031/350 - 1/300 = 0.002857 - 0.003333 = -0.000476
    4. 04Ea = -8.314 × 2.3026 / (-0.000476)
    5. 05Ea = 40,200 J/mol = 40.2 kJ/mol

    Ready to run the numbers?

    Open Activation Energy Calculator