Arrhenius equation calculator
Choose one of three tasks. Enter the pre-exponential factor, the activation energy and the temperature to get the rate constant; or a known rate constant and Ea to get k at another temperature; or two rate constants at two temperatures to get the activation energy.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose the task: rate constant, rate constant at another temperature, or activation energy.
- Enter A or a known rate constant, the activation energy with its unit, and the temperature or temperatures.
- Pick °C, K or °F; temperatures are converted to kelvin.
- Read k, k₂ or Ea, and the ratio between the two rates.
- k = A × e^(−Ea / RT)
- k₂ = k₁ × e^(−Ea/R × (1/T₂ − 1/T₁))
- Ea = R × ln(k₂ / k₁) ÷ (1/T₁ − 1/T₂)
R = 8.314462618 J/(mol·K); 1 kcal = 4.184 kJ. The fraction e^(−Ea/RT) is the share of molecular collisions energetic enough to react.
Worked example
A = 10¹³ s⁻¹, Ea = 100 kJ/mol, 25 °C = 298.15 K: Ea ÷ RT = 100,000 ÷ (8.314462618 × 298.15) = 40.34, so k = 10¹³ × e^−40.34 = 0.00003025227 s⁻¹.
Two measurements, k₁ = 0.0123 at 300 K and k₂ = 0.0573 at 320 K: Ea = 8.314462618 × ln(4.6585) ÷ (1/300 − 1/320) = 61.409 kJ/mol.
Tips
- Always use kelvin. Plugging in °C gives nonsense; the calculator converts for you.
- Same units for k₁ and k₂. Only their ratio enters the activation energy.
- Catalysts lower Ea, which is why a small drop in activation energy can speed a reaction up many times.
Frequently asked questions
What is the Arrhenius equation?
k = A × e^(−Ea ÷ (R × T)), where k is the rate constant, A the pre-exponential factor, Ea the activation energy, R = 8.314462618 J/(mol·K) the gas constant and T the absolute temperature in kelvin.
How do I find the activation energy from two temperatures?
Use the two-point form, ln(k₂ ÷ k₁) = (Ea ÷ R) × (1/T₁ − 1/T₂), so Ea = R × ln(k₂ ÷ k₁) ÷ (1/T₁ − 1/T₂). The calculator also works out A from it.
Does the rate really double every 10 °C?
Only for activation energies near 53 kJ/mol around room temperature. With Ea = 52.9 kJ/mol, going from 25 to 35 °C multiplies the rate by about 2.0; higher activation energies are more sensitive to temperature.
What unit does k have?
It depends on the reaction order (1/s for first order, L/(mol·s) for second order). A always has the same unit as k, and the calculator keeps whatever unit you use.