Solve the Arrhenius equation for k, A, Ea, or T
An Arrhenius equation calculator connects a reaction rate constant k, pre-exponential factor A, activation energy Ea, and absolute temperature T. Select the quantity to find and enter the other three. The page rearranges the same equation for each mode, converts activation-energy units explicitly, and shows the exponential or logarithmic step so the result can be checked rather than treated as a black-box prediction.
The Arrhenius model is widely used in chemical kinetics to describe how a rate constant changes with temperature over a suitable range. It supports classroom calculations and transparent estimates when A and Ea are known or fitted for a particular reaction. It does not determine the reaction order, mechanism, concentration-time profile, equilibrium position, or safety of running a reaction at the calculated temperature.
Understand every form of the Arrhenius formula
The primary equation is k = A × exp(−Ea/RT), where R = 8.314462618 J mol−1 K−1. Rearrangement gives A = k × exp(Ea/RT), Ea = −RT × ln(k/A), and T = −Ea ÷ [R × ln(k/A)]. Activation energy must be expressed in J/mol inside the exponent; an entered kJ/mol value is multiplied by 1,000 before calculation.
Both k and A must be positive because logarithms of zero or negative values are undefined. They must also use the same rate-constant unit, making k/A dimensionless. For a first-order reaction both may be s−1; another reaction order can use a different shared unit. Temperature is absolute and must be greater than zero kelvin. Celsius is converted to kelvins before it appears in the formula.
Follow an Arrhenius equation example
Let A = 1.00 × 10^13 s−1, Ea = 75.0 kJ/mol, and T = 298 K. First convert Ea to 75,000 J/mol. The exponent is −75,000 ÷ (8.314462618 × 298), approximately −30.27. Therefore k = 1.00 × 10^13 × exp(−30.27), or roughly 0.72 s−1. The displayed working keeps A’s unit with the final rate constant.
A reverse check divides k by A, takes the natural logarithm, and multiplies by −RT. It should recover the activation energy within rounding. When solving for A, substitute the answer back into k = A exp(−Ea/RT). When solving for temperature, use the unrounded logarithm and verify that the resulting kelvin value reproduces k; reciprocal or logarithmic rounding can otherwise create visible mismatch.
Handle logarithm domains and extreme exponent values
With positive Ea and finite positive T, exp(−Ea/RT) lies between zero and one, so k should be less than A. If k is greater than A, solving for Ea gives a negative apparent value; review whether that interpretation fits the system or signals inconsistent data. If k equals A, ln(k/A) is zero. Ea then calculates as zero, but solving for a finite T by dividing by that zero logarithm is undefined.
Very large positive or negative exponents can overflow or underflow ordinary decimal output even when the symbolic relationship is meaningful. Scientific notation and logarithms are safer for wide ranges. An extremely small displayed k may be below numeric resolution, while an enormous calculated A or T may expose an input-unit mistake. Check k and A units, the 1,000-fold J/kJ conversion, and the kelvin scale before interpreting an extreme result.
Arrhenius-model limits, reaction safety, and privacy
A single A and Ea pair may fail across phase changes, catalyst changes, diffusion limits, competing pathways, enzyme denaturation, tunnelling regimes, or other non-Arrhenius behavior. Parameters are specific to the reaction and conditions from which they were obtained. Do not extrapolate far beyond validated data for shelf life, process design, thermal runaway, storage, or hazard decisions; use measured kinetics, uncertainty analysis, and qualified chemical or process-safety review.
The values are calculated in the current browser tab. NexaCurrent does not upload the quantities, formulas, chemical names, element choices, or other information entered here, and no account is needed. Copying is a deliberate action after the answer and working are visible. Refreshing or leaving the page clears the current calculation, so keep a copied result if it is needed for later study.