About the Arrhenius Equation Calculator
This Arrhenius equation calculator handles the three problems chemistry students and lab workers meet most often. Give it two rate constants measured at two temperatures and it returns the activation energy Ea and the pre-exponential factor A. Give it one rate constant, its temperature and Ea, and it predicts the rate constant at any other temperature. Or enter A, Ea and a temperature to get k directly.
It is useful for kinetics homework, for estimating how much faster a reaction, a spoilage process or a drug-degradation pathway runs when it gets warmer, and for checking the slope of an Arrhenius plot from lab data. Temperatures can be entered in Celsius, Kelvin or Fahrenheit; they are always converted to kelvin before use, which is the most common source of mistakes when solving by hand.
The calculator assumes Ea and A do not change over the temperature range, which holds well for most reactions over a few tens of degrees. Rate constants can be in any unit (s⁻¹, M⁻¹·s⁻¹, min⁻¹…) as long as both use the same one; A comes out in that same unit.
How to use the arrhenius equation calculator
- 1Choose whether you want the activation energy, a rate constant at a new temperature, or k from A and Ea.
- 2Pick the temperature unit you have — conversion to kelvin is automatic.
- 3Enter the rate constants and temperatures (or Ea in kJ/mol and A).
- 4Read the answer, then check the rate ratio and the Arrhenius plot.
Formula and method
The Arrhenius equation says a rate constant grows exponentially with temperature: k = A·e^(−Ea/RT). Taking the natural log of the equation at two temperatures and subtracting cancels A, leaving the two-point form ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁). Rearranged, it gives Ea from two measurements or k₂ from a known Ea.
Temperatures must be absolute (kelvin), R is 8.314462618 J/(mol·K), and Ea is converted from kJ/mol to J/mol before use. Once Ea is known, A is recovered from A = k₁·e^(Ea/RT₁). A plot of ln k against 1/T is a straight line with slope −Ea/R, which the chart shows.
- k
- Rate constant (any consistent unit)
- A
- Pre-exponential (frequency) factor, same unit as k
- Ea
- Activation energy, J/mol (entered in kJ/mol)
- R
- Gas constant, 8.314462618 J/(mol·K)
- T
- Absolute temperature in kelvin
Worked examples
Activation energy from two rate constants
k rises from 0.0012 to 0.0058 when the temperature goes from 25 °C (298.15 K) to 45 °C (318.15 K). Ea = 8.314 × ln(4.833) ÷ (1/298.15 − 1/318.15) ≈ 62.1 kJ/mol.
Rate constant at body temperature
With Ea = 50 kJ/mol, warming from 293.15 K to 310.15 K multiplies k by e^((50000/8.314)(1/293.15 − 1/310.15)) ≈ 3.08, so k₂ ≈ 0.0025 × 3.078 ≈ 0.00770.
Rate constant from A and Ea
k = 1×10¹¹ × e^(−75000 / (8.314 × 298.15)) = 1×10¹¹ × e^(−30.26) ≈ 0.00725 s⁻¹ at 25 °C — a half-life of roughly 95 seconds for a first-order reaction.
Frequently asked questions
How do you calculate activation energy from two temperatures?+
Measure the rate constant at two temperatures, convert both to kelvin and use Ea = R·ln(k₂/k₁) ÷ (1/T₁ − 1/T₂) with R = 8.314 J/(mol·K). Divide by 1000 to get kJ/mol.
Why must temperature be in kelvin?+
The Arrhenius equation uses 1/T, which only makes physical sense on an absolute scale. Using Celsius gives wrong answers and even division by zero at 0 °C, so always add 273.15 first.
Does the unit of the rate constant matter?+
Not for Ea, because only the ratio k₂/k₁ is used, so any unit cancels as long as both values share it. The pre-exponential factor A takes the same unit as k.
Is it true that reaction rates double every 10 °C?+
Only roughly. The doubling rule matches an activation energy of about 53 kJ/mol near room temperature. Reactions with higher Ea speed up more than twofold; low-Ea reactions speed up less.
What is a typical activation energy?+
Many solution-phase organic and biochemical reactions have Ea between about 40 and 120 kJ/mol. Enzymes lower Ea, which is why catalysed reactions run quickly at body temperature.
What does the pre-exponential factor A mean?+
A reflects how often molecules collide with the right orientation. It is the rate constant you would get at infinite temperature, where every collision has enough energy to react.