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Arrhenius Rate, Temperature & Activation Energy

Solve the Arrhenius relation for activation energy, first-order rate constant, frequency factor or absolute temperature with reversible unit conversion.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

At 300 K, a rate constant of 1 per second and frequency factor e per second give an activation energy of 2.4942 kJ/mol using R = 8.314 J/(mol·K).

k = A exp(−Ea / RT); Ea = −RT ln(k/A), with R = 8.314 J/(mol·K)

Worked example

Enter these known values and leave the other values blank.

Reaction temperature
26.85 °C
First-order rate constant k
1 1/ sec
Frequency factor A
2.718281828459045235360287471352662497757247093699959574966967628 1/ sec
Apparent activation energy Ea
2.494 kJ /mol

Assumptions and limitations

  • Temperature must exceed absolute zero. Celsius and Fahrenheit entries are converted to kelvins before calculation. Both k and A must be positive.
  • The supported rate units are reciprocal time, appropriate for a first-order rate constant and its matching frequency factor. Other reaction orders require compatible concentration dimensions that are not offered here.
  • This model retains R = 8.314 J/(mol·K), a rounded gas constant. Its results therefore have that constant’s precision limit.
  • A and activation energy are treated as constant over the considered temperature range. A fitted apparent activation energy can be negative; the calculation does not infer a reaction mechanism.
  • At k = A and Ea = 0, temperature cannot be determined uniquely. Enter a positive temperature to calculate the zero-energy case.

Common questions

Must k and A use the same time unit on screen?

No. Each rate is converted to reciprocal seconds before their ratio is taken. For example, 60 per minute equals 1 per second.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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