Activation Energy Calculator

Calculate activation energy Ea from two rate constants at two temperatures using the Arrhenius equation. Find k at a new temperature or determine the pre-exponential factor A.

K
K
Activation Energy Ea (kJ/mol)
Ea (J/mol)
Arrhenius Plot Slope (−Ea/R)
Extended More scenarios, charts & detailed breakdown
K
K
Ea (kJ/mol)
Professional Full parameters & maximum detail
K
K
K
Activation Energy Ea (kJ/mol)
Pre-exponential ln(A)
Pre-exponential factor A
k at T₃
Fraction molecules ≥ Ea (at T₁)
Effect of 20% lower Ea on k

How to Use This Calculator

  1. Enter k₁ at T₁ and k₂ at T₂ (same units).
  2. The calculator returns Ea in kJ/mol and J/mol.
  3. Use the Find k at New Temp tab to extrapolate the rate constant to any temperature.

Formula

Ea = R × ln(k₂/k₁) × T₁T₂/(T₂−T₁)

Arrhenius: k = A·e^(−Ea/RT)

Plot: slope of ln k vs 1/T = −Ea/R

Example

Example: k₁ = 0.01 s⁻¹ at T₁ = 300 K, k₂ = 0.10 s⁻¹ at T₂ = 350 K. Ea = 8.314 × ln(10) × (300×350)/(350−300) = 8.314 × 2.303 × 2100 = 40.2 kJ/mol.

Frequently Asked Questions

  • Activation energy (Ea) is the minimum energy required for reactant molecules to successfully collide and form products. Higher Ea means a slower reaction at a given temperature.
  • k = A·exp(−Ea/(RT)), where k is the rate constant, A is the pre-exponential factor, Ea is activation energy in J/mol, R = 8.314 J/(mol·K), and T is temperature in Kelvin.
  • Ea = R × ln(k₂/k₁) × (T₁T₂)/(T₂−T₁). This two-point Arrhenius method assumes Ea and A are constant over the temperature range.
  • A plot of ln(k) vs 1/T gives a straight line with slope = −Ea/R. The activation energy is found from: Ea = −slope × R.
  • Most chemical reactions have Ea = 40–150 kJ/mol. Enzyme-catalyzed reactions typically 25–65 kJ/mol. Uncatalyzed biological reactions: 65–110 kJ/mol. A catalyst lowers Ea without changing ΔH.

Related Calculators

Sources & References (5)
  1. Arrhenius Equation — ACS Education — American Chemical Society
  2. OpenStax Chemistry 2e, Chapter 12 — The Arrhenius Equation — OpenStax
  3. IUPAC Gold Book — Activation Energy — IUPAC
  4. NIST Chemical Kinetics Database — NIST
  5. Atkins, P. & de Paula, J. — Physical Chemistry, 10th Ed., Ch. 17 — Arrhenius Parameters — Oxford University Press