Arrhenius Equation Calculator
Compute a chemical reaction rate constant from the Arrhenius equation k = A · exp(−Eₐ/(R·T)). The standard tool for predicting how reaction rates depend on temperature, used everywhere from catalyst design to pharmaceutical stability testing.
Last updated: May 2026
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About this calculator
The Arrhenius equation k = A · exp(−Eₐ / (R · T)) describes how a reaction rate constant k varies with absolute temperature T. Variables: A is the pre-exponential factor (also called the frequency factor) with units matching k (typically s⁻¹ for first-order, M⁻¹·s⁻¹ for second-order); Eₐ is the activation energy in J/mol (the energy barrier reactants must overcome to form products); R = 8.314 J/(mol·K) is the universal gas constant; T is absolute temperature in K (never °C — converting wrong gives nonsense). The pre-exponential factor A reflects the collision frequency and orientation factor; the exp(−Eₐ/RT) term reflects the Boltzmann distribution probability that any given collision has enough energy to overcome the barrier. As temperature increases, this exponential term grows rapidly, which is why most chemical reactions roughly double in rate for every 10 K rise (a rule of thumb true for typical Eₐ around 50 kJ/mol near room temperature). Edge cases: T must be in K and > 0; very low T gives essentially zero rate (frozen kinetics); very high T gives k approaching A (every collision succeeds). Eₐ typically falls between 30 and 250 kJ/mol for normal chemistry; values below 30 kJ/mol indicate barrierless reactions (radical recombination, ion-molecule); values above 250 kJ/mol suggest bond-breaking that's rate-limited by extreme temperatures. The two-temperature Arrhenius plot: ln(k₁/k₂) = −Eₐ/R · (1/T₁ − 1/T₂) lets you extract Eₐ from rate constants measured at two temperatures. Real reactions sometimes deviate from simple Arrhenius (modified Arrhenius k = A·T^n·exp(−Eₐ/RT), Eyring transition-state theory) but the simple form is adequate for most engineering and analytical applications over modest temperature ranges.
How to use
Example 1 — Standard reaction at moderate temperature. A reaction with pre-exponential factor A = 10⁶ s⁻¹ and activation energy Eₐ = 50,000 J/mol at T = 350 K. Enter Pre-exponential = 1000000, Activation Energy = 50000, Temperature = 350. k = 10⁶ × exp(−50000 / (8.314 × 350)) = 10⁶ × exp(−17.18) = 10⁶ × 3.45 × 10⁻⁸ ≈ 0.0345 s⁻¹. ✓ At 350 K the reaction proceeds with a rate constant of about 0.035/s; the characteristic time scale is 1/k ≈ 29 seconds for a first-order reaction. Example 2 — Effect of temperature. Same reaction at higher temperature, T = 400 K. Enter 1000000, 50000, 400. k = 10⁶ × exp(−50000 / (8.314 × 400)) = 10⁶ × exp(−15.04) = 10⁶ × 2.93 × 10⁻⁷ ≈ 0.293 s⁻¹. ✓ The rate constant has increased about 8.5× for a 50 K temperature rise — much more than the "doubles every 10 K" rule of thumb because both the temperature change and the Eₐ value here favour strong sensitivity. This is exactly why thermal stability of pharmaceuticals is tested at elevated temperatures: short tests at 60 °C can predict shelf life at 25 °C, using the Arrhenius equation to extrapolate.
Frequently asked questions
How does the Arrhenius equation work physically?
Chemical reactions need to overcome an energy barrier (activation energy Eₐ) between reactants and products. At any temperature T, the molecules in a sample have a distribution of kinetic energies (Maxwell-Boltzmann distribution); the fraction with enough energy to clear the barrier is proportional to exp(−Eₐ/RT). Multiplying this fraction by the collision frequency A (which captures how often molecules meet with the right orientation) gives the rate constant k = A · exp(−Eₐ/RT). Higher temperature exponentially increases the fraction of high-energy collisions, while A is relatively temperature-insensitive. The factor A typically ranges from 10⁹ to 10¹⁴ s⁻¹ for unimolecular reactions; deviations from these typical values reflect unusual transition-state geometry, steric requirements, or quantum tunneling effects. Higher Eₐ means a steeper temperature dependence — small temperature changes have outsized effects on rate.
Why does the "rate doubles every 10°C" rule of thumb work?
For a reaction with Eₐ around 50–60 kJ/mol (typical for many organic reactions near room temperature), a 10 K temperature rise from 298 K to 308 K gives k(308)/k(298) = exp[Eₐ/R · (1/298 − 1/308)] = exp[50000/8.314 · (1.085 × 10⁻⁴)] = exp(0.653) ≈ 1.92 — almost exactly doubling. The rule works for this range of Eₐ in this temperature window; for lower Eₐ the multiplier is smaller (10 K rise might only increase rate 30–50%), for higher Eₐ it can be 3× or more per 10 K. Many enzyme-catalyzed and biological reactions have Eₐ around 50 kJ/mol, which is why "rate doubles per 10 K" works well for many biological and thermal-degradation contexts (food spoilage, drug stability, etc.).
How do I find activation energy from experimental rate data?
Measure rate constants at two or more temperatures, then plot ln(k) vs 1/T. From the Arrhenius equation, ln(k) = ln(A) − (Eₐ/R) · (1/T), so the plot is a straight line with slope −Eₐ/R and intercept ln(A). For two measurements at T₁ and T₂: Eₐ = −R · [ln(k₂/k₁)] / (1/T₂ − 1/T₁). Example: k = 0.01/s at 300 K and 0.04/s at 320 K. Eₐ = −8.314 · ln(4) / (1/320 − 1/300) = −8.314 · 1.386 / (−2.083 × 10⁻⁴) = 55,300 J/mol ≈ 55 kJ/mol. For accurate Eₐ determination, use at least 4–5 temperatures spanning a wide range; the linear regression gives both Eₐ and A and their uncertainties. Deviations from linearity in the Arrhenius plot indicate non-Arrhenius behaviour (curved plot) or mechanism changes.
What are the most common mistakes using the Arrhenius equation?
The first is using °C instead of K — exp(−Eₐ/RT) with T = 25 (°C) instead of T = 298 (K) gives a wildly different result. Always convert. The second is mismatching units of Eₐ and R — Eₐ in J/mol requires R = 8.314 J/(mol·K); Eₐ in kJ/mol requires R = 8.314 × 10⁻³ kJ/(mol·K); Eₐ in cal/mol uses R = 1.987 cal/(mol·K). Mismatches produce wildly off rates. The third is extrapolating Arrhenius behaviour far outside the measured temperature range; activation energies can change at very high or low temperatures, mechanisms can shift, and the simple equation breaks down. The fourth is assuming Arrhenius applies to all reactions — diffusion-controlled reactions, tunneling-dominated reactions (H-atom transfer at low T), and many enzyme-catalyzed reactions show non-Arrhenius behaviour. The fifth is computing rate from k without specifying the rate law (k for a first-order reaction has units of s⁻¹, for second-order M⁻¹·s⁻¹) — the calculator returns k but you need to know the order to convert k to actual rate.
When should I not use this calculator?
Skip it for reactions known to deviate from Arrhenius behaviour — diffusion-controlled reactions at high T (k plateau when reaction is limited by reactant encounter, not energy barrier); H-atom or proton transfer at low T (quantum tunneling makes rates much higher than Arrhenius predicts); enzymes near their optimum temperature (denaturation curves rates downward at high T). Don't use it for non-elementary reactions where the apparent activation energy depends on multiple elementary-step barriers; the simple Arrhenius fit can still describe behaviour empirically but the Eₐ doesn't correspond to a single barrier. It's the wrong tool for surface and catalytic reactions where the rate depends on adsorption isotherms as well as kinetics; use Langmuir-Hinshelwood or Eley-Rideal mechanism-specific rate laws. Avoid it for very wide temperature ranges (factor of 5 or more in T) where the assumption of constant Eₐ likely fails; use modified Arrhenius k = A·T^n·exp(−Eₐ/RT) or Eyring transition-state theory. Finally, don't use it to predict reaction rates with kinetic uncertainty for safety-critical applications (runaway reactions, energetic-material decomposition) without experimental confirmation and safety margins.