Compute k, Ea and A with the Arrhenius equation and linearized visualization
Energy barrier of the chemical process
Effective collision frequency
Evaluation temperature
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s-1— rate constant | — pre-exponential factor | — activation energy | = 8.314 J mol⁻¹ K⁻¹ | — absolute temperature (K)
Plotting vs yields a straight line with slope and intercept . This is the basis of the graphical Arrhenius method used in laboratories.
Derived algebraically from the linearised form evaluated at two experimental temperatures. Exact when the model holds; numerically unstable when (see limitations).
The exponential factor is the fraction of molecular collisions carrying energy ≥ , derived from the Maxwell–Boltzmann energy distribution. It is the physical core of the Arrhenius equation.
Svante Arrhenius (1889) observed that reaction rates grow exponentially with temperature — far faster than any linear model predicts. His equation encodes two independent factors: A, the collision frequency in the correct geometric orientation, and the Boltzmann factor , the probability that a collision carries enough energy to break or rearrange bonds. Only collisions satisfying both conditions lead to products.
is the minimum energy barrier that reactants must overcome to reach the transition state (activated complex). Typical values range from 40–200 kJ mol⁻¹ for thermally activated reactions. Values below ~10 kJ mol⁻¹ suggest diffusion control or radical recombination. A negative apparent is physically possible in multi-step mechanisms where a fast equilibrium precedes the rate-limiting step, making the effective barrier decrease with temperature.
(also called the frequency factor) encodes collision frequency and steric requirements. Transition State Theory (Eyring, 1935) refines this as , where is the transmission coefficient, is the activation entropy, and . For unimolecular reactions A typically falls between 10¹² and 10¹⁶ s⁻¹; values far outside this range warrant physical scrutiny.
Three mechanisms can produce an apparent negative :
The Arrhenius equation assumes and are temperature-independent — an approximation that holds well over narrow T ranges but breaks down for wide intervals. Curved Arrhenius plots (non-linear vs ) signal this breakdown and may indicate a change of mechanism, quantum tunnelling (relevant below ~200 K for H-transfer reactions), or non-Boltzmann energy distributions. In those cases the extended Eyring–Evans–Polanyi (Transition State Theory) formulation is more appropriate.
The two-point method amplifies experimental error when, because the denominator approaches zero while the numerator retains finite rounding error — a classic ill-conditioned subtraction. The calculator warns about this instability instead of blocking it, to support educational use cases. Similarly, the direct mode warns when (above the molecular vibration frequency ceiling) or (below any measurable timescale), since those results carry no physical meaning regardless of mathematical correctness.