Arrhenius Equation Calculator
Arrhenius equation calculator: rate constant, activation energy, pre-exponential factor or temperature from k = A·e^(−Ea/RT).
k = A · e−Ea/(R·T)
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
The Arrhenius equation k = A·e−Ea/(RT) describes how a rate constant k grows with temperature. Ea is the activation energy and A the pre-exponential (frequency) factor.
A common rule of thumb is that many reactions near room temperature double their rate for every 10 °C, which corresponds to Ea of about 50 kJ/mol.
Formula
k = A · e−Ea/(R·T)
| Symbol | Quantity | Units |
|---|---|---|
| A | Pre-exponential factor | s⁻¹, min⁻¹, h⁻¹ |
| Ea | Activation energy | kJ/mol, J/mol, kcal/mol, cal/mol |
| T | Temperature | K, °C, °F, °R |
| k | Rate constant | s⁻¹, min⁻¹, h⁻¹ |
Constants used: R = 8.314462618 J·mol⁻¹·K⁻¹
Worked example
Given: A = 1 × 1013 s⁻¹ · Ea = 100 kJ/mol · T = 25 °C
k = A · e−Ea/(R·T)
Result: k = 3.02523 × 10-5 s⁻¹
Frequently asked questions
How do I find Ea from two temperatures?
Use ln(k₂/k₁) = −(Ea/R)·(1/T₂ − 1/T₁). Equivalently, compute A at one temperature with this calculator and solve for Ea with the other point.
What units does A have?
The same as k. For a first-order reaction that is s⁻¹.