Arrhenius Rate Constant Calculator
The Arrhenius equation links the rate constant of a chemical reaction to its activation energy and temperature. Small changes in temperature produce large changes in rate because the dependence is exponential. This calculator takes the pre-exponential factor A, the activation energy Ea, and the absolute temperature T, and returns the rate constant k. It also reports the exponential term and the ratio Ea over RT so you can see how far the reaction sits above the activation barrier. Enter the gas constant in units consistent with your activation energy.
Arrhenius equation formula
k = A * exp(-Ea / (R * T))
RT = R * T
ratio = Ea / (R * T)
exponential term = exp(-ratio)
k = A * exponential term
A is the pre-exponential factor (frequency factor) and carries the same units as k. Ea is the activation energy in joules per mole. R is the molar gas constant and T is absolute temperature in kelvin. The exponential term is the fraction of collisions with enough energy to react.
Using the calculator
- Keep Ea and R in matching energy units: J/mol with R = 8.314, or kJ/mol with R = 0.008314.
- Temperature must be in kelvin. Add 273.15 to a Celsius reading.
- k inherits the units of A: a first-order A is in per second, a second-order A is in L per mol per second.
- Raising temperature lowers Ea/RT, which raises the exponential term and speeds the reaction.
- The gas constant default is the exact CODATA 2018 value, fixed by the 2019 SI redefinition.
Arrhenius equation: frequently asked questions
What is the Arrhenius equation?
The Arrhenius equation describes how the rate constant k of a chemical reaction depends on temperature: k = A times exp(-Ea / (R times T)), where A is the pre-exponential (frequency) factor, Ea is the activation energy, R is the molar gas constant, and T is the absolute temperature in kelvin. It was proposed by Svante Arrhenius in 1889.
What value of the gas constant does this use?
It uses the CODATA recommended molar gas constant R = 8.314462618 J per mol per kelvin, which is now an exact value following the 2019 redefinition of the SI base units. You can edit it if your activation energy is expressed in different units.
What units should I use for activation energy?
Enter activation energy in joules per mole (J/mol) to match the default gas constant. If your source gives Ea in kilojoules per mole (kJ/mol), multiply by 1,000 first, or change R to 0.008314462618 kJ per mol per kelvin so the units are consistent.
Why must temperature be in kelvin?
The Arrhenius equation is derived from statistical thermodynamics where temperature is an absolute quantity. Using Celsius would give a negative or zero value near the freezing point of water and break the exponential. Convert by adding 273.15 to a Celsius temperature.
Official sources
- NIST: CODATA value of the molar gas constant R.
- NIST Chemistry WebBook: kinetics and thermochemical reference data.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.