How this instrument works
The Arrhenius equation, k = A·exp(−Ea/RT), predicts how fast a chemical reaction proceeds at a given absolute temperature T. A is the pre-exponential (or frequency) factor — roughly, how often molecules collide in a favourable orientation, independent of temperature. Ea is the activation energy, the energy barrier those collisions must clear. The exponential term exp(−Ea/RT) is the fraction of collisions energetic enough to clear that barrier at temperature T, and it is extraordinarily sensitive to both Ea and T: small changes in either can move the rate constant by orders of magnitude.
This instrument runs the equation forward — given A, Ea and T, it returns k directly. That is the complementary direction to this site's activation-energy instrument, which runs the same underlying physics backward: given two measured rate constants at two temperatures, it solves for Ea instead. Together they cover both directions a chemist needs — predicting a rate constant from known kinetic parameters, or extracting the activation energy from experimental rate data.
Because the relationship is exponential, k is far more sensitive to Ea than to A. Doubling A simply doubles k, but doubling Ea can shrink k by many orders of magnitude, since Ea sits divided by RT inside the exponent. This is also why reaction rates so reliably increase with temperature: raising T shrinks the magnitude of −Ea/RT, which pushes the exponential — and therefore k — upward, often dramatically for reactions with a sizeable activation energy.
- Enter the collision-frequency term into Pre-exponential factor, A (per unit time) — this carries the same time unit as the rate constant you expect back.
- Enter the reaction's energy barrier into Activation energy, Ea (J/mol) — convert from kJ/mol by multiplying by 1000 if that's how your source reports it.
- Enter the absolute temperature into Temperature (K) — kelvin only; add 273.15 first if you have a Celsius value.
- Read the predicted rate constant off Rate constant, k, expressed in whatever time unit A used.
- Small changes in Ea or T can shift k by orders of magnitude, so double-check both are in the right units before trusting the result.
Worked example — a 75 kJ/mol barrier at room temperature
Enter 1e13 into Pre-exponential factor, A (per unit time), 75000 into Activation energy, Ea (J/mol), and 298 into Temperature (K) — a textbook-typical collision frequency and a 75 kJ/mol barrier at room temperature. Rate constant, k reads 0.713219 per second.
By hand: the exponent is −Ea/(R·T) = −75000/(8.314 × 298) = −75000/2477.57 ≈ −30.272, and e^−30.272 ≈ 7.13 × 10⁻¹⁴. Multiplying by A gives k = 1×10¹³ × 7.13×10⁻¹⁴ ≈ 0.713 per second — a moderate, everyday reaction rate emerging from a barrier that, on its own, looks intimidatingly large.
Questions
What is the pre-exponential factor A, physically?
It's a proxy for how often reactant molecules collide with roughly the right orientation to react, independent of whether they have enough energy to actually react. In collision theory it's tied to collision frequency and a steric (orientation) factor; in transition-state theory it relates to the entropy of forming the activated complex. Either way, it carries the same time units as the rate constant k it multiplies.
Why is k so sensitive to activation energy?
Because Ea sits inside an exponent divided by RT, not as a simple linear term. Doubling A only doubles k, but doubling Ea can shrink the exponential term — and therefore k — by many orders of magnitude, since exp(x) changes far more steeply than x itself for large negative x. This is the mathematical reason a modest-looking energy barrier can make the difference between a reaction finishing in seconds or taking years.
How is this different from the activation-energy calculator on this site?
This instrument runs the Arrhenius equation forward: given A, Ea and T, it predicts k. The activation-energy instrument runs the same equation backward: given two measured rate constants (k1, k2) at two temperatures (T1, T2), it solves for Ea instead. Both use the identical underlying formula, k = A·exp(−Ea/RT); they simply solve for a different unknown.
Why must temperature be in kelvin, not Celsius?
The Arrhenius equation divides Ea by R×T, and that division only makes physical sense on an absolute temperature scale where zero means zero thermal energy. Celsius has an arbitrary zero point (the freezing point of water), so plugging a Celsius value straight into this formula would give a wrong, meaningless rate constant — always convert with T(K) = T(°C) + 273.15 first.
What does it mean if k comes out as an extremely tiny number?
It means the reaction is predicted to proceed very slowly at the temperature you entered — a large Ea relative to RT makes the exponential term, and so k, vanishingly small. This is exactly why many reactions that are thermodynamically favourable still barely happen at room temperature until you add heat, a catalyst, or both to make that exponential term less punishing.