Rate Constant (Arrhenius) Calculator
This calculator works out the reaction rate constant k using the Arrhenius equation, the standard way chemists predict how much faster or slower a reaction runs as temperature changes. In single-temperature mode, you enter the pre-exponential factor A, the activation energy Ea in kJ/mol or J/mol, and the temperature in Kelvin or Celsius. It returns the rate constant k, its natural log ln(k), and a step-by-step breakdown showing the Ea/(RT) ratio and the Boltzmann factor that produced it. Switch to two-temperature mode when you already know a rate constant k1 at one temperature T1 and want to find k2 at a different temperature T2 for the same activation energy; this mode returns k1, k2, and the k2/k1 ratio, showing how many times faster or slower the reaction runs at the new temperature. Both panels include a worked example matching the default inputs, so you can check your own figures follow the same steps. This is useful for planning laboratory experiments, checking coursework, or understanding why reaction rates climb so sharply with heat, since even a modest activation energy makes k extremely sensitive to temperature. The equation assumes A and Ea stay constant with temperature, which holds well for most simple reactions but can break down at very high or very low temperatures, so treat the output as a theoretical estimate rather than a substitute for measured laboratory data.
1. Reaction Parameters
2. Temperature
Calculation Steps
Worked Example
What Is the Arrhenius Equation?
The Arrhenius equation describes the temperature dependence of chemical reaction rate constants. Published by Svante Arrhenius in 1889, it remains the standard way to predict how much faster a reaction proceeds when temperature increases. The equation is:
k = A · e−Ea / (R · T)
Where:
- k is the rate constant (units depend on reaction order)
- A is the pre-exponential factor (same units as k), representing the maximum collision frequency
- Ea is the activation energy in joules per mole (J/mol)
- R is the universal gas constant: 8.314 J/(mol·K)
- T is the absolute temperature in Kelvin (K = °C + 273.15)
How to Use This Calculator
Single temperature mode: enter A, Ea, and T to find k directly. This is the most common use case for laboratory calculations.
Two-temperature mode: if you already know k at one temperature and want to find k at another temperature, use this mode. It applies the linearised Arrhenius equation:
ln(k2 / k1) = (Ea / R) · (1/T1 − 1/T2)
This avoids needing to know A separately.
Worked Example
A first-order reaction has A = 1 × 1013 s−1 and Ea = 75 kJ/mol. What is k at 25 °C (298 K)?
- Convert Ea to J/mol: 75 kJ/mol × 1,000 = 75,000 J/mol
- Compute Ea/(RT) = 75,000 / (8.314 × 298) = 30.27
- Compute e−30.27 = 7.13 × 10−14
- Multiply: k = 1 × 1013 × 7.13 × 10−14 = 0.713 s−1
This matches the calculator output for the default inputs.
Units of k and A
| Reaction Order | Units of k | Units of A |
|---|---|---|
| Zero order | mol L−1 s−1 | mol L−1 s−1 |
| First order | s−1 | s−1 |
| Second order | L mol−1 s−1 | L mol−1 s−1 |
The units of A must always match those of k. The Boltzmann factor e−Ea/(RT) is dimensionless, so it does not affect the units.
The 10-Degree Rule
A common approximation in chemistry is that reaction rates roughly double for every 10°C rise in temperature. This is a useful rule of thumb, but the Arrhenius equation gives a more accurate answer because the actual ratio depends on the activation energy. A reaction with Ea = 75 kJ/mol and T1 = 298 K has k2/k1 = 10.4 when T rises by 25 K to 323 K, as shown in the worked example above.
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Sources and method: Arrhenius, S. (1889). "Uber die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Sauren." Zeitschrift fur Physikalische Chemie. IUPAC compendium of chemical terminology (Gold Book): rate of reaction and rate constant. Atkins, P.; de Paula, J. (2014). Physical Chemistry (10th ed.), Oxford University Press.
This calculator provides results based on the standard Arrhenius equation for educational and laboratory-planning purposes. It assumes ideal conditions where A and Ea are temperature-independent. For some reactions, particularly at very high or very low temperatures, deviations from Arrhenius behaviour may occur. The pre-exponential factor A is typically determined from experimental data.