Bohr Model Calculator
Calculate an ideal hydrogen-like energy change and photon wavelength between two Bohr levels.
Open toolArrhenius Equation Calculator
Calculate the chemical reaction rate constant k from pre-exponential factor A, activation energy Ea, and temperature T, or solve the two-point Arrhenius equation for Ea from (k₁, T₁) and (k₂, T₂).
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Enter the inputs, then select Calculate.
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How the Arrhenius Equation Calculator Works (Single-Point & Two-Point Modes)
Switch between single-temperature rate constant calculation and two-temperature experimental activation energy determination using the molar gas constant R = 8.314462618 J/(mol·K).
Mode 1 (Rate Constant): k = A x exp(-Ea / (R x T)). Mode 2 (Two-Point Activation Energy): ln(k₂ / k₁) = (Ea / R) x (1/T₁ - 1/T₂), which rearranges to Ea = R x ln(k₂ / k₁) / (1/T₁ - 1/T₂).
Activation energy Ea is entered and returned in joules per mole (J/mol; divide by 1,000 for kJ/mol). Temperatures T, T₁, and T₂ must be in absolute Kelvin (K = °C + 273.15).
Arrhenius Equation Parameters, Units, and Benchmark Values
Standard units and physical meaning for every variable in the single-point and two-point Arrhenius equations.
| Symbol | Parameter Name | Required Unit in Tool | Conversion / Typical Range |
|---|---|---|---|
| k (or k₁, k₂) | Reaction rate constant | Same units as A (e.g., s⁻¹ or M⁻¹s⁻¹) | k₂ / k₁ is dimensionless in two-point mode |
| A | Pre-exponential (frequency) factor | Same units as k | Typically 10⁸ to 10¹⁴ s⁻¹ for unimolecular reactions |
| Ea | Activation energy | J/mol (joules per mole) | 50 kJ/mol = 50,000 J/mol; 100 kJ/mol = 100,000 J/mol |
| R | Universal gas constant | 8.314462618 J/(mol·K) | Fixed SI CODATA value built into the calculator |
| T (or T₁, T₂) | Absolute temperature | Kelvin (K) | 25 °C = 298.15 K; 300 K = 26.85 °C; 350 K = 76.85 °C |
How to Calculate k or Activation Energy Ea Step by Step
Choose your known inputs mode and verify that Ea is in J/mol and temperature is in Kelvin.
Select Single-Point (find k) or Two-Point (find Ea) mode
Choose 'A, activation energy and temperature' to solve for the rate constant k, or choose 'Two measured rate constants and temperatures' to solve for Ea and A from two lab measurements.
Input and settings
Enter A, Ea (in J/mol), and T (in K) or k₁, T₁, k₂, T₂
Convert activation energy from kJ/mol to J/mol by multiplying by 1,000 (for example, 50 kJ/mol = 50000 J/mol), and convert Celsius temperatures to Kelvin by adding 273.15.
Tool result
Run the calculation and inspect the exponential factor
Select Calculate result to get the rate constant k (or activation energy Ea in J/mol and kJ/mol) and copy the output for your lab report.
Review the details
Worked Chemical Kinetics Examples
Verify both single-temperature rate constants and the classic 10 °C rate-doubling rule of thumb.
Mode 1: Rate constant k at 300 K (A = 10¹⁰ s⁻¹, Ea = 50,000 J/mol)
With Ea = 50,000 J/mol and T = 300 K, the dimensionless exponent is Ea / (R x T) = 50,000 / (8.314462618 x 300) = 20.0454. Thus k = 10¹⁰ x exp(-20.0454) = 19.697 s⁻¹.
Mode 2: Finding Ea when the rate doubles from 300 K to 310 K
Setting k₁ = 1, T₁ = 300 K, k₂ = 2, and T₂ = 310 K gives Ea = 8.314462618 x ln(2) / (1/300 - 1/310) = 53,603.5 J/mol (53.60 kJ/mol), illustrating the chemistry rule of thumb near room temperature.
High activation barrier sensitivity check (Ea = 100,000 J/mol)
When Ea is 100 kJ/mol (100,000 J/mol), raising T from 300 K to 350 K increases the Boltzmann factor exp(-Ea/RT) by over 300-fold.
How to Interpret the Boltzmann Factor exp(-Ea / RT)
Understand the physical meaning of A, Ea, and the fraction of reactive collisions.
The result is the selected rate constant or two-point activation energy. Explore the temperature relationship under an entered Arrhenius model.
Temperatures use kelvin; a two-point estimate is reported with its sign rather than clipped.
Numerical output shows up to 12 significant digits. Floating-point arithmetic and display rounding can affect the last digits.
- Example input
- Known Arrhenius inputs = A, activation energy and temperature; Pre-exponential factor A (same rate units) = 10000000000.0; Activation energy (J/mol) = 50000; Absolute temperature (K) = 300; Measured k1 (same units) = 1; Temperature T1 (K) = 300; Measured k2 (same units) = 2; Temperature T2 (K) = 320
- Example output
- Rate constant: 19.6968440582 (entered A units)
Common Unit Mistakes (kJ/mol vs. J/mol and °C vs. K)
Check these two unit conversions before trusting an Arrhenius calculation.
The #1 error in chemistry homework is entering Ea in kJ/mol (such as 50) while R is in J/(mol·K) (8.314). Always enter Ea in J/mol (50000 for 50 kJ/mol).
Never enter Celsius or Fahrenheit directly into T, T₁, or T₂. Absolute temperature in Kelvin (K = °C + 273.15) is strictly required (> 0 K).
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Open toolArrhenius Equation Calculator: Frequently Asked Questions
Answers about using Arrhenius Equation Calculator and understanding its results.
Should I enter activation energy Ea in J/mol or kJ/mol?
Enter Activation energy in joules per mole (J/mol) so its units match the molar gas constant R = 8.314462618 J/(mol·K). Multiply any kJ/mol value by 1,000 before entering it (for example, 65 kJ/mol = 65000 J/mol).
How do I calculate activation energy Ea from two temperatures and rate constants?
Switch the top dropdown to 'Two measured rate constants and temperatures', then enter k₁, T₁ (in K), k₂, and T₂ (in K). The tool applies Ea = R x ln(k₂ / k₁) / (1/T₁ - 1/T₂).
How do I convert Celsius (°C) to Kelvin (K) for this calculator?
Add 273.15 to the Celsius temperature. For example, 0 °C = 273.15 K, 25 °C = 298.15 K, and 100 °C = 373.15 K.
What units does the rate constant k have?
The rate constant k always has the exact same units as the pre-exponential factor A (s⁻¹ for first-order reactions, L·mol⁻¹·s⁻¹ for second-order reactions) because the exponential factor exp(-Ea/RT) is dimensionless.
Get the selected rate constant or two-point activation energy
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