This Arrhenius equation calculator works the temperature law of reaction rates, k = A·e^(−Ea/RT), in both directions: rate constants from activation energy, and activation energy from rate constants at two temperatures.

Result –

Why Reactions Obey an Exponential in Temperature

Part of our Chemistry Calculators collection.

Worked Examples (Verified)

  • k from A (defaults): A = 10¹³, Ea = 75 kJ/mol, T = 298 K → k = 10¹³ × e^(−75000/(8.314 × 298)) = 0.713 — a healthy rate constant assembled from a huge A and a minuscule success fraction (7.1 × 10⁻¹⁴)
  • The 10-degree rule: Ea = 50 kJ/mol, 300 → 310 K → k₂/k₁ = 1.909× — not exactly doubling, but close enough to have organized a century of bench intuition (try Mode 3)
  • Refrigeration is Arrhenius applied: spoilage reactions at 4 °C run several-fold slower than at 25 °C — the fridge is a rate-constant reduction device

Arrhenius Discipline

  • Kelvin, always: a °C slip here isn’t a rounding error, it’s a different universe.
  • Ea from slope, not single points, when data allow: plot ln k against 1/T; slope = −Ea/R, intercept = ln A.
  • A (the frequency factor) carries the units of k and encodes collision frequency + orientation (steric) effects — it’s measured, not universal.
  • Deviations happen: tunneling (low-T, light atoms), enzyme denaturation (rates crash past an optimum) and multi-step mechanisms all bend the line — the equation governs elementary steps best.

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Frequently Asked Questions

What is the Arrhenius equation?

k = A · e^(−Ea/RT): the rate constant equals a pre-exponential factor A times the Boltzmann-weighted fraction of collisions exceeding the activation energy Ea, at absolute temperature T (R = 8.314 J/(mol·K)). This calculator evaluates k, Ea (two-temperature form) and rate ratios.

How do you find activation energy from two rate constants?

With ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁), solved for Ea. Rates that triple over a 10 K rise near 300 K imply Ea ≈ 80+ kJ/mol; rates that barely move imply a small barrier. Mode 2 of this tool computes it directly.

Why do reaction rates roughly double every 10 °C?

Plug typical numbers in: Ea ≈ 50 kJ/mol at ~300 K gives k₂/k₁ ≈ 1.9 for a 10 K rise (verified in Mode 3 of this calculator). It’s an empirical shadow of the exponential — exact only for that Ea and temperature neighborhood.

What is the pre-exponential factor A?

The rate constant’s ceiling: collision frequency (how often molecules meet, ~10¹³ /s scale for unimolecular) discounted by orientation/steric requirements. It shares k’s units and is extracted from the intercept of the Arrhenius plot.

Does Arrhenius apply to equilibrium?

No — it governs rates (kinetics), not positions of equilibrium (thermodynamics). Temperature shifts equilibria via van ‘t Hoff; it shifts rates via Arrhenius. A catalyst lowers Ea (faster both directions) without moving the equilibrium at all.

Is this Arrhenius calculator free?

Yes — free, instant, no sign-up.