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Arrhenius Equation Calculator

Calculate a reaction's rate constant at two temperatures, and how much faster it runs between them, from its activation energy via the Arrhenius equation k = A·e^(−Ea/RT).

Rate constant at T1
0
Rate constant at T2
0
Rate ratio (T2 ÷ T1)
1.9243×

How it works

The Arrhenius equation, k = A·e^(−Ea/RT), describes how a reaction's rate constant k depends on absolute temperature T: Ea is the activation energy (the energy barrier reacting molecules need to clear), A is the pre-exponential factor (the rate constant that temperature would approach if that barrier didn't exist), and R is the molar gas constant, 8.31446261815324 J/(mol·K) — an exact defined value since the 2019 SI redefinition fixed the Boltzmann constant and Avogadro's number precisely. This calculator evaluates k at two temperatures you choose and reports their ratio.

Dividing the two Arrhenius expressions cancels A completely, leaving rateRatio = e^[(Ea/R)·(1/T1 − 1/T2)] — the temperature sensitivity depends only on the activation energy and how far apart the two temperatures are, not on A. That's why A defaults to 1 here: if you don't know your reaction's actual pre-exponential factor, leaving it at 1 still gives correct, meaningful rate constants in the same arbitrary units, and an exactly correct ratio.

FAQ

Why does this ask for two temperatures instead of one?

A single rate constant on its own isn't very meaningful without knowing A's actual value and units for your specific reaction, which varies enormously between reactions. The ratio between two temperatures is the practically useful, A-independent number — it directly answers "how much faster does this reaction run if I heat it from T1 to T2?"

Does this match the "rate doubles every 10°C" rule of thumb?

Yes, for the kind of activation energy (around 50 kJ/mol) that rule of thumb is based on: a 10 K rise from 298.15 K to 308.15 K at Ea = 50 kJ/mol gives a rate ratio of about 1.92, close to the commonly cited factor of 2. That rule is only a rough approximation, though — the real ratio depends on both the activation energy and the starting temperature, which this calculator computes exactly rather than approximating.

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