# Arrhenius Equation Calculator

URL: https://speedycalculator.com/calculators/chemistry/arrhenius-equation/
Last updated: 2026-10-30

> The Arrhenius equation calculator solves k = A·e^(−Ea/RT) for any one of the rate constant, the pre-exponential factor, the activation energy or the temperature, in per-mole or per-molecule form, and draws the Arrhenius plot (ln k against 1/T) for your reaction.

## Inputs

- Solve for
- Form of the equation
- Pre-exponential factor A (s⁻¹, min⁻¹, h⁻¹, ms⁻¹ (per millisecond))
- Activation energy Ea (per mole) (kJ/mol, J/mol, kcal/mol, cal/mol, eV (per particle))
- Activation energy Ea (per molecule) (J, eV, zJ (10⁻²¹ J))
- Temperature T (K, °C, °F)
- Rate constant k (s⁻¹, min⁻¹, h⁻¹, ms⁻¹ (per millisecond))
- Chart
- Chart from temperature (K, °C, °F)
- Chart up to temperature (K, °C, °F)

## Results

- Rate constant k
- Pre-exponential factor A
- Activation energy Ea
- Temperature T
- Activation energy per molecule
- ln k (k in s⁻¹)
- Fraction of collisions with E ≥ Ea, e^(−Ea/RT)
- Rate increase for a 10 K rise
- Slope of the Arrhenius plot (−Ea/R)
- Arrhenius plot

## Formula

```
k = A·e^(−Ea/(R·T))  ·  per molecule: k = A·e^(−Ea/(kʙ·T))  ·  linear form: ln k = ln A − (Ea/R)·(1/T)
```

## Explanation

In 1889 Svante Arrhenius proposed that the rate constant of a reaction grows exponentially with temperature: k = A·e^(−Ea/RT). The exponential term is the fraction of collisions that carry at least the activation energy Ea; the pre-exponential factor A collects everything else – how often molecules meet and how often they meet in the right orientation. R is the gas constant, 8.314 J/(mol·K), and T is the absolute temperature.

When Ea is quoted per molecule (in joules or electronvolts) rather than per mole, the same equation uses the Boltzmann constant kʙ = 1.380649 × 10⁻²³ J/K instead of R. The two forms give identical rate constants because R = kʙ·N_A.

Taking logarithms turns the equation into a straight line, ln k = ln A − (Ea/R)(1/T). Plotting ln k against 1/T – the Arrhenius plot – therefore gives a line of slope −Ea/R and intercept ln A, which is how activation energies are measured. This calculator solves for whichever quantity you leave out and draws that plot (or k against T) across the temperature range you choose, marking your point on it.

### How to use the Arrhenius Equation Calculator

- **Solve for**
- **Form of the equation**
- **Pre-exponential factor A**
- **Activation energy Ea (per mole)**
- **Activation energy Ea (per molecule)**
- **Temperature T**
- **Rate constant k**
- **Chart**
- **Chart from temperature**
- **Chart up to temperature**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose what to solve for and the form of the equation, then enter the other three quantities. k and A share a unit (s⁻¹ for first-order reactions; for other orders the concentration part is the same for both). Temperatures are converted to kelvin before use.

### Worked example

A first-order reaction has A = 1.0 × 10¹³ s⁻¹ and Ea = 100 kJ/mol. At 25 °C (298.15 K), Ea/RT = 100 000 ÷ (8.3145 × 298.15) = 40.34, so k = 10¹³ × e^(−40.34) ≈ **3.03 × 10⁻⁵ s⁻¹** (a half-life of about 6.4 hours). At 35 °C the same reaction has k ≈ 1.12 × 10⁻⁴ s⁻¹, 3.7 times faster.

Working backwards, if you measured k = 3.0 × 10⁻⁵ s⁻¹ at 25 °C for a reaction with A = 10¹³ s⁻¹, solving for Ea gives −RT·ln(k/A) ≈ 100.0 kJ/mol.

### Reading the Arrhenius plot

On the ln k vs 1000/T chart, hot temperatures are on the left (small 1/T) and cold on the right. A steep line means a large activation energy and a reaction that is very sensitive to temperature; a flat line means a small barrier. The y-intercept at 1/T = 0 is ln A. If your own data points bend away from a straight line, a single Ea does not describe the reaction over that whole range.

### Tips

- Check the equation is balanced before using coefficients.
- Find the limiting reagent before calculating a yield.
- Keep temperatures in kelvin for rate and equilibrium equations.
- Everything is calculated in your browser.

### Common mistakes to avoid

- Using the excess reagent to calculate theoretical yield.
- Including pure solids and liquids in equilibrium expressions.
- Entering temperatures in °C into the Arrhenius equation without converting.

## Worked example

Inputs — Solve for: Rate constant k; Form of the equation: Per mole – k = A·e^(−Ea/RT); Pre-exponential factor A: 10,000,000,000,000 s⁻¹; Activation energy Ea (per mole): 100 kJ/mol; Temperature T: 298.15 K; Chart: Arrhenius plot – ln k against 1/T; Chart from temperature: 273.15 K; Chart up to temperature: 373.15 K.

Results — **Rate constant k = 0.00003**; Pre-exponential factor A = 10,000,000,000,000; Activation energy Ea = 100; Temperature T = 298.15; Activation energy per molecule = 1.6605e-19; ln k (k in s⁻¹) = -10.4059.

## Key terms

- **Rate constant (k)**: Proportionality constant in the rate law; its value depends on temperature.
- **Pre-exponential factor (A)**: Collision-frequency and orientation term in the Arrhenius equation.
- **Activation energy (Ea)**: The energy barrier between reactants and the transition state.
- **Arrhenius plot**: Graph of ln k against 1/T; a straight line with slope −Ea/R.
- **Boltzmann constant (kʙ)**: 1.380649 × 10⁻²³ J/K, the gas constant per molecule.

## FAQ

**What does the Arrhenius equation tell you?**
How the rate constant depends on temperature: k grows exponentially as T rises, and the higher the activation energy, the steeper the growth.

**What are the units of A?**
The same as k: s⁻¹ for first-order, M⁻¹·s⁻¹ for second-order and M·s⁻¹ for zero-order reactions.

**Why must temperature be in kelvin?**
The equation uses absolute temperature; 25 °C must be entered as 298.15 K. The unit menu converts °C and °F for you.

**What is the difference between the R and kʙ forms?**
R = 8.314 J/(mol·K) is used when Ea is per mole; kʙ = 1.380649 × 10⁻²³ J/K when Ea is per molecule. Both give the same k.

**How much faster is a reaction at 35 °C than at 25 °C?**
For Ea = 100 kJ/mol and A = 10¹³ s⁻¹, k rises from 3.03 × 10⁻⁵ to 1.12 × 10⁻⁴ s⁻¹ – about 3.7 times faster.

**How do I find Ea and A from experimental data?**
Measure k at several temperatures, plot ln k against 1/T and fit a straight line: Ea = −slope × R and A = e^intercept.

**Does the Arrhenius equation always hold?**
It works well over modest temperature ranges for most elementary reactions. Curved Arrhenius plots signal a change of mechanism, tunnelling or a temperature-dependent A.

**What formula does the Arrhenius Equation Calculator use?**
k = A·e^(−Ea/(R·T))  ·  per molecule: k = A·e^(−Ea/(kʙ·T))  ·  linear form: ln k = ln A − (Ea/R)·(1/T).


## Sources

- [IUPAC Compendium of Chemical Terminology (Gold Book)](https://goldbook.iupac.org/)
- [NIST – Fundamental physical constants (CODATA)](https://physics.nist.gov/cuu/Constants/)
- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)