#1 Free Arrhenius Equation Calculator 2025

The Arrhenius equation is a formula for the temperature dependence of reaction rates. Proposed by Svante Arrhenius in 1889, it provides a quantitative basis for the observation that many reaction rates increase with temperature.

The equation introduces the concept of Activation Energy (E_a), which is the minimum energy required for a chemical reaction to occur. Only molecules possessing energy equal to or greater than E_a can overcome the energy barrier and form products.

The Pre-exponential Factor (A), also known as the frequency factor, represents the frequency of collisions between reactant molecules in the correct orientation. It is related to the entropy of activation.

Increasing temperature has two effects:

1. Increases the average kinetic energy of molecules, leading to more frequent collisions.
2. More significantly, it dramatically increases the fraction of molecules that possess energy greater than or equal to E_a, as described by the Boltzmann distribution.

1. Basic Arrhenius Equation (for k):

k = A * exp(-Ea / (RT))

2. Two-Point Form (for E_a or k₂):

This form is derived by taking the natural logarithm of the basic equation at two different temperatures and subtracting:

ln(k₂) - ln(k₁) = (-Ea / RT₂) - (-Ea / RT₁)

ln(k₂ / k₁) = (Ea / R) * (1/T₁ - 1/T₂)

• To find E_a: Ea = R * ln(k₂ / k₁) / (1/T₁ - 1/T₂)
• To find k₂: k₂ = k₁ * exp[(Ea / R) * (1/T₁ - 1/T₂)]

3. For Pre-exponential Factor (A):

A = k / exp(-Ea / (RT)) or A = k * exp(Ea / (RT))

4. For Temperature (T):

ln(k/A) = -Ea / (RT) => T = -Ea / (R * ln(k/A))

This can be rewritten as: T = Ea / (R * ln(A/k)) (Requires A > k for positive T if E_a > 0)

Where:

• k, k₁, k₂ = Rate constants (units depend on reaction order, but must be consistent)
• A = Pre-exponential factor (units same as k)
• Ea = Activation energy (typically in J/mol or kJ/mol)
• R = Ideal gas constant (8.314 J mol⁻¹ K⁻¹ or 0.008314 kJ mol⁻¹ K⁻¹)
• T, T₁, T₂ = Absolute temperature (in Kelvin, K)
• exp(x) = e^x (Euler's number raised to the power of x)
• ln(x) = Natural logarithm of x

1. Select Calculation Mode:

• Choose what you want to calculate from the radio buttons: Rate Constant (k), Activation Energy (E_a), k₂ at T₂, Pre-exponential Factor (A), or Temperature (T).

2. Enter Input Values:

• Based on the selected mode, specific input fields will appear.
• Temperatures (T, T₁, T₂): Enter temperature values and select their units (°C or K). The calculator will convert to Kelvin for calculations.
• Activation Energy (E_a): Enter E_a and select its units (J/mol or kJ/mol). The calculator will convert to J/mol.
• Rate Constants (k, k₁, k₂): Enter rate constant values. Be consistent with units if multiple k values are used (e.g., if k₁ is in s⁻¹, k₂ will also be in s⁻¹). The calculator does not convert k units.
• Pre-exponential Factor (A): Enter the value of A. Its units must be consistent with the rate constant k.

3. Select Output Units (if applicable):

• For E_a calculation, select the desired output unit (J/mol or kJ/mol).
• For T calculation, select the desired output unit (K or °C).

4. Calculate:

• Click the "Calculate" button corresponding to your selected mode.

5. View Results:

• The calculated value will be displayed prominently.
• A detailed step-by-step solution will show how the result was derived, including unit conversions and formula application.
• Error messages will appear for invalid inputs or calculation issues (e.g., division by zero, non-physical results like negative absolute temperature).

6. Reset:

• Click the "Reset" button to clear all input fields and results.