Arrhenius Equation Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The Arrhenius equation relates a chemical reaction rate constant to temperature: k = A × exp(−Ea ÷ (R × T)), where Ea is the activation energy and T the absolute temperature. For a frequency factor of 1×10¹³ and an activation energy of 75,000 J/mol at 25°C, the resulting rate constant is about 0.724 (in the unit of A).
Explanation
The Arrhenius equation, proposed in 1889, explains why most chemical reactions speed up markedly with temperature: as T rises, a larger fraction of molecules has enough energy to clear the activation barrier Ea, and the rate constant k grows. This calculator directly complements our 1st-order half-life calculator, which takes the rate constant k as an already-measured input, without explaining how it varies with temperature: the Arrhenius equation is precisely that missing link, the one that shows why a reaction speeds up in hot water and slows down in the fridge. The factor A (frequency factor, or pre-exponential factor) roughly represents the frequency of correctly oriented molecular collisions; the exponential term exp(−Ea÷(R×T)) represents the fraction of those collisions with enough energy to actually react. A well-known practical consequence in chemical kinetics, often cited as a rule of thumb: a temperature rise of just 10°C can, depending on the value of Ea, multiply a reaction's rate by a factor on the order of 2 to 3 — a direct illustration of k's exponential (not linear) sensitivity to temperature, verifiable by comparing this calculator's results at two nearby temperatures, and closely related to the exponential decay seen in our radioactive decay calculator, even though the underlying physics differ.
Example: a reaction at room temperature
Inputs
Frequency factor (A): 1×10¹³. Activation energy (Ea): 75,000 J/mol. Temperature: 25°C.
Calculation
T = 25 + 273.15 = 298.15 K. k = 1×10¹³ × exp(−75,000 ÷ (8.314 × 298.15)) = 1×10¹³ × exp(−30.2996...) ≈ 1×10¹³ × 7.2416×10⁻¹⁴ ≈ 0.7242.
Result
The rate constant obtained at 25°C is about 0.724 (in the unit of A).
Frequently asked questions
What unit is the resulting rate constant k in?
k's unit is always the same as the frequency factor A entered, since the exponential term exp(−Ea÷(R×T)) is dimensionless. The actual unit of k depends on the reaction's order (s⁻¹ for 1st order, as in our 1st-order half-life calculator, L/(mol·s) for 2nd order, etc.) — so it's up to the user to supply a factor A consistent with the order of the reaction being studied.
Why does a small temperature change affect a reaction's rate so much?
Because temperature sits inside an exponential, not linearly: a small rise in T significantly reduces the value of −Ea÷(R×T), so it strongly increases exp(−Ea÷(R×T)). It's this exponential sensitivity that explains the well-known chemical kinetics rule of thumb that a 10°C rise often multiplies a reaction's rate by 2 to 3 — a factor that in reality depends on the precise activation energy Ea specific to each reaction, not a universal constant.
Can the activation energy Ea be negative?
For the vast majority of elementary chemical reactions, no: Ea represents an energy barrier to clear, so it's a positive or zero quantity. Apparently negative values only appear for complex, multi-step reaction mechanisms (overall effective kinetics), a special case outside the scope of this calculator, which applies the Arrhenius equation in its standard physical sense.