Balance chemical reactions instantly with lowest integer stoichiometric coefficients, element-by-element atom count audits, molar mass breakdowns, and reaction type classification using our free Chemical Equation Balancer.
Use standard chemical formulas with uppercase/lowercase letters (e.g. Ca(OH)2, Fe2(SO4)3, KMnO4). Separate sides with =, ->, or →.
Stoichiometric Coefficients: 1 : 5 → 3 : 4
| Element | Reactant Atoms | Product Atoms | Balance Check |
|---|
Sum of Reactants
Sum of Products
Conservation Exact
In chemical stoichiometry, a Chemical Equation Balancer is a mathematical tool that determines the lowest irreducible whole integer coefficients (\(a, b, c, d\)) for all reactant and product molecules in a chemical reaction. Balancing is governed by Antoine Lavoisier's fundamental Law of Conservation of Mass:
Matter cannot be created or destroyed in ordinary chemical transformations. Chemical bonds break and reform, but atomic nuclei remain unaltered. An unbalanced equation represents an impossible physical process; balancing provides the exact stoichiometric mole ratios needed for chemical synthesis, percent yield calculations, and industrial reactor scale-up.
Eliminates endless manual guessing on complex reactions with 4+ elements or polyatomic groups by solving exact matrix linear equations.
Correctly parses compound parentheses like \(\text{Ca(OH)}_2\) or \(\text{Fe}_2(\text{SO}_4)_3\), preventing missed atom multipliers.
Provides a live element-by-element atom count matrix and total mass balance verification to guarantee \(100\%\) conservation.
Converts any chemical equation into a homogeneous matrix of linear equations and computes the lowest positive integer nullspace.
Automatically categorizes reactions into Combustion, Synthesis, Decomposition, Single Displacement, Double Displacement, or Redox.
Calculates standard molecular weights (\(\text{g/mol}\)) for all reactants and products using high-precision IUPAC standard atomic weights.
Renders balanced chemical equations, stoichiometric fractions, and algebraic substitution steps with professional LaTeX typography.
| Reaction Type | General Formula | Key Identifying Characteristics | Classic Example |
|---|---|---|---|
| Combustion | \(\text{C}_x\text{H}_y + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}\) | Hydrocarbon rapidly oxidizes with oxygen gas releasing heat, \(\text{CO}_2\), and water vapor | \(\text{C}_3\text{H}_8 + 5\text{O}_2 \to 3\text{CO}_2 + 4\text{H}_2\text{O}\) |
| Synthesis (Combination) | \(\text{A} + \text{B} \to \text{AB}\) | Two or more simpler substances combine into a single compound | \(\text{N}_2 + 3\text{H}_2 \to 2\text{NH}_3\) |
| Decomposition | \(\text{AB} \to \text{A} + \text{B}\) | A single reactant breaks down into two or more smaller products | \(2\text{KClO}_3 \to 2\text{KCl} + 3\text{O}_2\) |
| Single Displacement | \(\text{A} + \text{BC} \to \text{AC} + \text{B}\) | A more reactive free element replaces a less reactive element in a compound | \(\text{Zn} + 2\text{HCl} \to \text{ZnCl}_2 + \text{H}_2\) |
| Double Displacement | \(\text{AB} + \text{CD} \to \text{AD} + \text{CB}\) | Two ionic compounds exchange cations/anions in aqueous solution to form a precipitate or water | \(\text{AgNO}_3 + \text{NaCl} \to \text{AgCl}(s) + \text{NaNO}_3\) |
Type or paste your unbalanced equation (e.g. C3H8 + O2 = CO2 + H2O) or click a reaction preset.
The Gaussian matrix engine solves the linear algebraic system in milliseconds without trial-and-error delays.
Verify that reactant atoms equal product atoms across all elements, and inspect molecular weights for each compound.
Click "Copy" to paste the balanced equation directly into chemistry reports, homework assignments, or lab notebooks.
Problem: Balance the unbalanced combustion reaction: \(\text{C}_3\text{H}_8 + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}\).
1. Balance Carbon: 3 carbons on left require \(3\text{ CO}_2\) on right.
2. Balance Hydrogen: 8 hydrogens on left require \(4\text{ H}_2\text{O}\) on right (\(4 \times 2 = 8\)).
3. Balance Oxygen: Right side has \((3 \times 2) + (4 \times 1) = 10\text{ O}\) atoms, requiring \(5\text{ O}_2\) on left.
Problem: Balance \(\text{Ca(OH)}_2 + \text{H}_3\text{PO}_4 \to \text{Ca}_3(\text{PO}_4)_2 + \text{H}_2\text{O}\).
1. Balance Calcium: 3 Ca on right requires \(3\text{ Ca(OH)}_2\) on left.
2. Balance Phosphate (\(\text{PO}_4\)): 2 \(\text{PO}_4\) on right requires \(2\text{ H}_3\text{PO}_4\) on left.
3. Balance Hydrogen/Oxygen: \(3 \times 2 = 6\text{ OH}^-\) plus \(2 \times 3 = 6\text{ H}^+\) form \(6\text{ H}_2\text{O}\).
Never modify subscripts within a chemical formula to balance atoms (e.g. changing \(\text{H}_2\text{O}\) to \(\text{H}_2\text{O}_2\)). Subscripts define chemical identity; only stoichiometric coefficients in front of formulas may be adjusted.
Element symbols are case-sensitive. The first letter is uppercase and the second is lowercase. Typing CO means Carbon Monoxide, while Co means metallic Cobalt.
In their standard elemental states, hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine, and iodine exist as diatomic molecules: \(\text{H}_2, \text{N}_2, \text{O}_2, \text{F}_2, \text{Cl}_2, \text{Br}_2, \text{I}_2\).
Always simplify coefficients to their lowest whole number ratio. For example, \(2\text{H}_2 + 1\text{O}_2 \to 2\text{H}_2\text{O}\) is correct, whereas \(4\text{H}_2 + 2\text{O}_2 \to 4\text{H}_2\text{O}\) is reducible.
In blast furnaces, iron(III) oxide is reduced by carbon monoxide: \(\text{Fe}_2\text{O}_3 + 3\text{CO} \to 2\text{Fe} + 3\text{CO}_2\). Exact stoichiometric balancing ensures sufficient \(\text{CO}\) reducing gas is generated to prevent unreacted ore loss while controlling furnace carbon emissions.
Coal-fired power stations scrub acidic \(\text{SO}_2\) exhaust using calcium carbonate slurries: \(2\text{CaCO}_3 + 2\text{SO}_2 + \text{O}_2 \to 2\text{CaSO}_4 + 2\text{CO}_2\). Balancing determines limestone quarry consumption and commercial wallboard gypsum (\(\text{CaSO}_4\)) production yields.
Authoritative answers to common questions about balancing chemical reaction equations and stoichiometry.
