Activation Energy Calculator: Arrhenius Ea From Two Points or a Plot
Find activation energy from two rate constants, a single Arrhenius data point, or a least-squares Arrhenius plot. Kelvin-guarded, correctly-signed Ea in kJ/mol, with R and every convention shown.
At a glance
- Computes
- Activation energy from two rate constants, one Arrhenius point, or a least-squares plot.
- You supply
- Rate constants with their temperatures, or k, A, and T for a single point.
- Use when
- You have rate data at known temperatures and need Ea with the correct sign.
- Assumes
- Arrhenius behaviour over the range, and temperatures converted to kelvin first.
Find the activation energy Ea from two rate constants at two temperatures, a single Arrhenius data point, or a table of rate constants fit by least squares. Temperature always converts to kelvin before the math runs, and a negative Ea (anti-Arrhenius kinetics) is reported unclamped, never hidden.
natural log of rate constant against reciprocal temperature, 1000 per kelvin; least-squares fit
Solved value
Enter your data
Choose a mode and calculate.
| Metric | Value |
|---|
Ea = R*ln(k2/k1) / (1/T1 - 1/T2)
How?
How this is calculated
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)
Sources
- OpenStax Chemistry 2e, 12.5 Collision Theory. OpenStax. Retrieved .
- LibreTexts Physical and Theoretical Chemistry, 6.2.3 The Arrhenius Law. LibreTexts. Retrieved .
- NIST CODATA Fundamental Physical Constants. NIST. Retrieved .