# Chemical Kinetics Calculator - Rate Law, Reaction Order, Half-Life & Arrhenius Activation Energy

> Free chemical kinetics calculator: reaction orders and k with units by initial rates, zero, first and second-order rate laws, and Ea from the Arrhenius plot.

- URL: https://qilingtools.com/en/math/kinetics
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Chemistry](https://qilingtools.com/en/tags/chemistry)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Chemical kinetics is about how fast reactions go. The orders in a rate law, rate = k[A]^m[B]^n, can only be found by experiment. With the method of initial rates you compare two runs in which only one concentration changes: if doubling [A] quadruples the rate, m = ln 4 / ln 2 = 2. This tool fits all your runs at once with a multiple least-squares regression of ln(rate) on ln(concentration), rounds each order to the nearest 0, ½, 1, 2 (and reports how good the fit is), then computes k from every run and writes its units automatically: M^(1−n)·s⁻¹ for overall order n, e.g. L·mol⁻¹·s⁻¹ for second order. The integrated rate law tab solves [A], [A]₀, t or k for zero order ([A] = [A]₀ − kt), first order (ln[A] = ln[A]₀ − kt) and second order (1/[A] = 1/[A]₀ + kt), accepts a half-life instead of k (t½ = ln2/k for first order, [A]₀/2k for zero order, 1/(k[A]₀) for second order) and plots both the concentration curve and the straight-line form. Paste concentration–time data and the tool plots [A], ln[A] and 1/[A] against t, compares the R² values and picks the order; for NO₂ decomposing at 300 °C the 1/[A] plot has R² = 0.99998, so the reaction is second order with k ≈ 0.544 M⁻¹·s⁻¹. The Arrhenius tab uses ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂): a rate that doubles between 300 K and 310 K means Ea ≈ 53.6 kJ/mol. It also predicts k at a new temperature, or fits Ea and the pre-exponential factor A from an ln k vs 1/T plot of several points. A final tab draws an energy profile with the transition state, ΔH, reverse activation energy and a catalysed pathway.

## How to use

1. Pick a tab: initial rates, integrated rate law, order from data, Arrhenius or energy diagram, or load an example
2. Enter your experiments or known values; you can paste concentration–time or temperature–k tables from a spreadsheet
3. Read the reaction order, rate law, k with units, half-life or activation energy, with every step of the working and the graphs

## Features

- Method of initial rates: ratio method plus multiple least-squares regression, up to 4 reactants
- Writes the rate law and the units of k (both M⁻¹·s⁻¹ and L·mol⁻¹·s⁻¹ styles)
- Zero, first and second-order integrated rate laws: solve [A], [A]₀, t or k, or use a half-life instead of k
- Order from data: [A], ln[A] and 1/[A] vs t plotted side by side and ranked by R²
- Two-point Arrhenius: solve Ea, k₂ or T₂, with a check of the '10 °C doubles the rate' rule of thumb
- Arrhenius plot fit of several (T, k) points for Ea and the pre-exponential factor A
- Energy profile diagram with reactants, products, transition state, Ea, reverse Ea, ΔH and catalysed path
- Links to the half-life calculator for radioactive decay

## FAQ

### Can I read reaction orders from the balanced equation?

Usually not. Orders equal the stoichiometric coefficients only for an elementary step; most reactions happen in several steps, so orders must be measured and can be zero, fractional or even negative. For example NO₂ + CO → NO + CO₂ follows rate = k[NO₂]² and is zero order in CO. Use initial rates or concentration–time data to find them.

### How do I work out the units of the rate constant?

Rate has units of M·s⁻¹ and the concentration terms contribute M^n, where n is the overall order, so k has units of M^(1−n)·s⁻¹: M·s⁻¹ for zero order, s⁻¹ for first order, M⁻¹·s⁻¹ (L·mol⁻¹·s⁻¹) for second order and M⁻²·s⁻¹ for third order. Conversely, the units of k tell you the overall order.

### How do I find the order from concentration–time data?

Plot [A], ln[A] and 1/[A] against time. Whichever gives a straight line tells you the reaction is zero, first or second order, with slopes −k, −k and +k respectively. The tool measures straightness with R² and picks the best. If all three R² values are close to 1, the data cover too little of the reaction; follow it to at least 70% conversion.

### How do I calculate activation energy from rate constants at two temperatures?

Use the two-point Arrhenius equation ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂) with temperatures in kelvin and R = 8.314 J·mol⁻¹·K⁻¹. If k doubles from 300 K to 310 K, Ea = 8.314 × ln 2 / (1/300 − 1/310) ≈ 53,600 J/mol = 53.6 kJ/mol. That is why the 'rate doubles every 10 °C' rule only holds for activation energies around 50 kJ/mol.

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