Arrhenius equation calculator
This Arrhenius equation calculator solves k = A·e^(−Ea/RT) for you: enter two measurements to get the activation energy Ea, or Ea and one rate constant to get k at a new temperature.
Example: Calculate: Activation energy from two measurements · Temperature unit: Kelvin (K) · Temperature T1 650 · Rate constant k1 1.66 · Temperature T2 700 · Rate constant k2 7.39 → Result: Activation energy Ea = 113.0 kJ/mol (112,980 J/mol). Source: OpenStax Chemistry 2e, section 12.5: Arrhenius equation k = A·e^(−Ea/RT), R = 8.314 J/mol/K, two-point form ln(k1/k2) = (Ea/R)(1/T2 − 1/T1); N2O5 example 1.66 and 7.39 L/mol/s at 650 and 700 K (read 13.10.2026). Updated: .
How it is calculated
Arrhenius equation: k = A · e^(−Ea / RT). k is the rate constant, A the frequency factor, Ea the activation energy in J/mol, R = 8.314 J/mol/K and T the absolute temperature in kelvin (OpenStax Chemistry 2e).
Two-point form
With rate constants k1 at T1 and k2 at T2 the equation becomes ln(k2 / k1) = (Ea / R) · (1/T1 − 1/T2), so Ea = R · ln(k2 / k1) ÷ (1/T1 − 1/T2).
Worked example
OpenStax gives the decomposition of N2O5 with k = 1.66 L/mol/s at 650 K and 7.39 L/mol/s at 700 K. Then Ea = 8.314 · ln(7.39 / 1.66) ÷ (1/650 − 1/700) ≈ 112980 J/mol, about 113.0 kJ/mol (the book states 1.1 × 105 J/mol). The rate constant grows by a factor of 4.452.
How much faster is 10 K warmer?
For a reaction starting at 300 K, the factor k(T2) / k(300 K) depends strongly on Ea:
| Ea in kJ/mol | at 310 K | at 320 K |
|---|---|---|
| 25 | 1.382 | 1.871 |
| 50 | 1.909 | 3.501 |
| 75 | 2.638 | 6.549 |
| 100 | 3.645 | 12.254 |
A second example: with k1 = 0.01 at 300 K and Ea = 50 kJ/mol the rate constant at 310 K is 0.01909. Gases on the same absolute scale are covered by the ideal gas law calculator; for decay processes see the half-life calculator.
Limits
The equation holds when Ea and A are constant over the temperature range; over wide temperature ranges or for complex mechanisms, measured values can deviate.
Frequently asked questions
What is the Arrhenius equation?
k = A · e^(−Ea/RT): it relates the rate constant k of a reaction to the temperature T and the activation energy Ea.
How do I find the activation energy from two rate constants?
Ea = R · ln(k2/k1) ÷ (1/T1 − 1/T2), with T in kelvin. For k = 1.66 at 650 K and 7.39 at 700 K that is about 113 kJ/mol.
Which value of R do I use?
8.314 J/mol/K when Ea is in J/mol (OpenStax); here you enter Ea in kJ/mol and the tool converts it.
Why must temperatures be in kelvin?
The exponent contains 1/T, which only makes sense on an absolute scale; the tool adds 273.15 to °C.
Does a reaction really double every 10 K?
Only for certain Ea values. At 300 K, Ea = 50 kJ/mol gives a factor of 1.909 for +10 K, Ea = 100 kJ/mol gives 3.645.
Sources and legal basis
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