Arrhenius Equation Calculator
Calculate how a rate constant changes with temperature using the Arrhenius equation.
About Arrhenius Equation Calculator
Rate depends exponentially on temperature through the Boltzmann factor. For a typical activation energy of 50 kJ/mol the rate roughly doubles for every 10 K rise, which is the origin of the Q10 rule of thumb. The exponential dependence is why refrigeration is so effective at slowing spoilage and why runaway reactions accelerate so violently.
Formula
Arrhenius Equation
k = A e^(−Ea/RT); ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁)
- Ea
- Activation energy, the barrier the reaction must clear
- Q10
- Factor by which rate changes for a 10 K rise, about 2 to 3 for most reactions
Worked example
With the default values below, Arrhenius Equation Calculator returns Rate Constant at Temperature 2 of 0.001924265. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Activation energyminimum 0 kJ/mol
- 50 kJ/mol
- Temperature 1minimum -272 C
- 25 C
- Temperature 2minimum -272 C
- 35 C
- Rate constant at temperature 1minimum 0
- 0.001
Results
- Rate Constant at Temperature 2
- 0.001924265
- Rate Increase Factor
- 1.92426 x
- Rate Change per 10 Degrees
- 1.9243 x
- Pre-Exponential Factor
- 574,938.003486
- Temperature Rise That Doubles the Rate
- 10.246 K
Step by step
- 1Values used
- 2Arrhenius Equation
- 3Rate Constant at Temperature 2= 0.001924265
- 4Rate Increase Factor= 1.92426 x
- 5Rate Change per 10 Degrees= 1.9243 x
- 6Pre-Exponential Factor= 574,938.003486
- 7Temperature Rise That Doubles the Rate= 10.246 K
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
- Figures are rounded for display to 9 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Arrhenius Equation calculated?
k = A e^(−Ea/RT); ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁) Rate depends exponentially on temperature through the Boltzmann factor. For a typical activation energy of 50 kJ/mol the rate roughly doubles for every 10 K rise, which is the origin of the Q10 rule of thumb.
Why does Arrhenius Equation matter?
The exponential dependence is why refrigeration is so effective at slowing spoilage and why runaway reactions accelerate so violently.
What values do I need to enter?
This calculator takes 4 inputs: Activation energy, Temperature 1, Temperature 2, Rate constant at temperature 1. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.