Calculate the reaction rate constant k using the Arrhenius equation: k = A · e−Ea/(RT). Enter the pre-exponential factor, activation energy, and temperature. Switch to the two-temperature mode to find k at a new temperature from a known value.
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Method verified 2025
Arrhenius equation as stated in IUPAC recommendations. R = 8.314 J/(mol·K).
1. Reaction Parameters
s⁻¹ (or appropriate)
kJ/mol
2. Temperature
K
k = A · exp(−Ea ÷ (R · T))
Arrhenius Result
Temperature (K)
-
Absolute temperature
Rate Constant k
-
Arrhenius result
ln(k)
-
Natural log of k
Calculation Steps
A (pre-exponential factor)-
Ea (activation energy)-
T (temperature)-
R (gas constant)8.314 J/(mol·K)
Ea / (R · T)-
e−Ea/(RT)-
k = A · e−Ea/(RT)-
Worked Example
A1 × 1013 s−1
Ea75 kJ/mol (75,000 J/mol)
T298 K (25 °C)
Ea/(RT)75000 / (8.314 × 298) = 30.27
e−30.277.13 × 10−14
k0.713 s−1
Result:Enter values above to calculate the rate constant.
1. Known State (k1 at T1)
K
2. Target State
kJ/mol
K
ln(k2/k1) = (Ea/R) · (1/T1 − 1/T2)
Two-Temperature Result
k1 (at T1)
-
Known rate constant
k2 (at T2)
-
Calculated rate constant
k2 / k1 ratio
-
Speed-up factor
Calculation Steps
Ea in J/mol-
T1 (K)-
T2 (K)-
1/T1 − 1/T2-
(Ea/R) · (1/T1 − 1/T2)-
k2/k1 = eabove-
k2 = k1 × (k2/k1)-
Worked Example
k10.713 s−1 at 298 K
Ea75 kJ/mol (75,000 J/mol)
T2323 K (50 °C)
1/298 − 1/3232.597 × 10−4 K−1
(Ea/R) · Δ(1/T)2.343
k2/k1 = e2.34310.41
k27.42 s−1
Result:Enter values above to calculate k2.
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.
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.
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