Activation Energy Calculator: Arrhenius Ea From Two Points or a Plot

Method. The single-point Arrhenius equation is k = A*e^(-Ea/RT), rearranged for whichever quantity is unknown. The two-point form above comes from subtracting the equation at two temperatures; it is symmetric under swapping the two points, so it returns the identical, correctly signed Ea regardless of entry order and never requires T2 to exceed T1. The plot mode fits ln k against 1/T by ordinary least squares (the shared suite regression routine), then reads Ea = -slope*R and A = e^(intercept). All three routes use the CODATA gas constant R = 8.314462618 J/mol*K, matching the sibling ideal-gas-law tool and about 0.006% above the textbook 8.314.

Sign is never dropped. A rate constant that rises with temperature gives a positive Ea, the ordinary case. A rate constant that falls as temperature rises gives a genuinely negative Ea (anti-Arrhenius kinetics, real for barrierless and complex-mechanism reactions). Every mode reports that negative value unclamped, with a warning, rather than taking an absolute value.

Least squares versus endpoints. The two-point mode reads an Ea straight from two measurements; the plot mode fits every row by least squares, which is how Ea is measured experimentally. The two can disagree slightly on the same data: fitting the full 5-point OpenStax HI-decomposition table gives Ea = 185.3 kJ/mol by least squares against 185.4 kJ/mol from its two endpoints alone. OpenStax's own worked example prints Ea = 1.8e5 J/mol from a slope it rounds to -2.2e4 K first; that 180 is the same fit read to two significant figures, not a different answer.

Scope. Ea and A are treated as constant across the temperature range entered. A reaction whose Arrhenius plot curves (temperature-dependent Ea, competing mechanisms) is outside this linear model.

Formula: Ea = R*ln(k2/k1) / (1/T1 - 1/T2)

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