Arrhenius equation formulas and interpretation
The Arrhenius equation models the temperature dependence of many reaction rate constants.
Activation energy and the gas constant must use compatible energy units.
How to use the Arrhenius equation calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
The rate constant equals the frequency factor multiplied by an exponential activation term.
k = A exp(−Eₐ/RT)- k — Rate constant
- Temperature-dependent reaction constant (reaction dependent)
- A — Pre-exponential factor
- Frequency and orientation factor (same as k)
- Eₐ — Activation energy
- Reaction energy barrier (J/mol)
- T — Temperature
- Absolute temperature (K)
Rate constant example
Use A = 1×10¹³ s⁻¹, Eₐ = 80 kJ/mol, and T = 500 K.
- A
- 1×10¹³ s⁻¹
- Eₐ
- 80,000 J/mol
- T
- 500 K
- k = 1×10¹³ exp(−80000/(8.314×500))
Result: k is approximately 4.39×10⁴ s⁻¹.
The result is sensitive to temperature because temperature occurs in the exponent.
Understanding your results
Interpreting the result
Use the result only for the reaction model and temperature range represented by the inputs.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.