Arrhenius Equation & Q10 Calculator

Understanding the Arrhenius equation and Q10 calculator — concept and principle

The Arrhenius equation describes how fast a reaction speeds up when the temperature rises. This calculator takes an activation energy and two temperatures and returns how many times faster the reaction runs at the higher one, plus the Q10 coefficient, the rate change per 10 °C. It is used in chemistry, in accelerated shelf-life and ageing tests, in food science and in biology.

A 10 °C rise lets roughly twice as many molecules over a 50 kJ/mol barrier: k₂/k₁ = 1.92.

How it is calculated

k = A × e^(−Ea/RT), so for two temperatures:

k₂/k₁ = exp[−(Ea/R) × (1/T₂ − 1/T₁)]

Q10 = (k₂/k₁)^(10/(T₂ − T₁))

Ea is entered in kJ/mol and multiplied by 1000 to give J/mol. R = 8.314462618 J/(mol·K). T₁ and T₂ are entered in °C and converted to kelvin by adding 273.15. The pre-exponential factor A cancels in the ratio, so you do not need to know it.

The principle

Molecules must collide with at least the activation energy to react. According to the Boltzmann distribution, the fraction of molecules with that much energy is proportional to e^(−Ea/RT). A modest temperature rise increases this fraction a lot, because the high-energy tail of the distribution grows faster than the average energy. The larger Ea is, the more sensitive the rate is to temperature. Taking logarithms gives ln k = ln A − Ea/(RT), a straight line in 1/T (the Arrhenius plot), whose slope −Ea/R is how Ea is measured.

Worked example

Inputs: Ea = 50 kJ/mol, T₁ = 25 °C, T₂ = 35 °C.
T₁ = 298.15 K, T₂ = 308.15 K; 1/T₂ − 1/T₁ = −0.000108844 K⁻¹.
Ea/R = 50 000 ÷ 8.314462618 = 6013.62 K.
k₂/k₁ = exp(6013.62 × 0.000108844) = exp(0.65455) = 1.924.
T₂ − T₁ = 10 °C, so Q10 = 1.924^1 = 1.924.

Each point is the calculator re-run with only “T₂ (°C)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

T₂ (°C)	Rate ratio k₂/k₁
8.75	0.3126479218
17.5	0.5942438667
26.2	1.087856382
35	1.924264816
43.8	3.29822197
52.5	5.491857538
70	14.08377444

How to read the result

A ratio of 1.92 means the reaction runs 92% faster at 35 °C than at 25 °C. The familiar rule "rates double every 10 °C" corresponds to Ea of about 53 kJ/mol near room temperature. Many biological processes have Q10 between 2 and 3; physical processes such as diffusion are often closer to 1.2–1.5.

Common mistakes

Using °C directly in 1/T instead of kelvin.
Entering Ea in J/mol when the box expects kJ/mol (a factor of 1000 error).
Assuming Q10 is constant over a wide range; for a fixed Ea it falls slowly as temperature rises.

Keep in mind: The Arrhenius model assumes one dominant mechanism with constant Ea. Enzymes denature, materials change phase, and multi-step processes switch rate-limiting steps, so extrapolating far beyond the measured range, as in some accelerated ageing claims, can be badly wrong.

Frequently asked questions

How do I find Ea from two measured rate constants?

Rearrange: Ea = R × ln(k₂/k₁) ÷ (1/T₁ − 1/T₂), with temperatures in kelvin.

What does a catalyst change in the Arrhenius equation?

It provides a pathway with a lower activation energy, so the rate constant is larger at the same temperature.

Why does refrigeration slow food spoilage?

Lower temperature cuts the fraction of molecules or microbial reactions with enough energy, slowing rates by the Arrhenius factor.

Sources: S. Arrhenius, Zeitschrift für Physikalische Chemie 4, 226 (1889) · IUPAC Compendium of Chemical Terminology (Gold Book), "Arrhenius equation"

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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