Chemical Equation Balancer

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Chemical equation:

Separate species with + and sides with ->, =, or →. Explicit ionic charges use braces, for example Fe{2+}.

Samples replace only the equation source.

Conservation model:

Keep the default for ionic equations. Atoms only intentionally ignores explicit charge suffixes.

The coefficient ratio is reduced to the smallest positive integers. This checks the supplied formulas and charges; it does not predict products, feasibility, conditions, safety, or yield.

Conserved quantity	Reactants	Products	Status	Copy
{{ row.label }}	{{ row.reactants }}	{{ row.products }}	Balanced

The chart renderer is unavailable. Coefficients remain available in the summary and balanced equation.

A chemical equation names the substances involved in a reaction, but it becomes quantitatively useful only when the amounts on both sides agree. Reactants appear before the arrow, products after it, and coefficients state their relative numbers. Balancing finds coefficients that conserve every represented element without changing any chemical formula.

Subscripts and coefficients do different jobs. The subscript in H₂O says that each water unit contains two hydrogen atoms, so changing it would create a different substance. A coefficient such as 2H₂O keeps water unchanged and counts two units, contributing four hydrogen atoms and two oxygen atoms.

Molecular equation: Shows compounds as complete formulas and balances their atom counts.
Complete ionic equation: Shows strong electrolytes as ions, including species that remain unchanged.
Net ionic equation: Removes spectator ions and keeps the species that take part in the chemical change.

Ionic equations add a second conservation requirement. The total charge on the reactant side must equal the total charge on the product side, even though each side need not be neutral. A redox equation can have +24 elementary charges on both sides and still be charge-balanced.

A balanced equation describes stoichiometric proportion, not reaction speed, equilibrium position, yield, or whether the proposed reaction actually occurs. It also cannot repair a missing species or an incorrect formula. If an element appears on only one side, the chemical statement must be corrected before coefficients can solve it.

How to Use This Tool:

Enter one complete reaction and choose whether explicit ionic charge is part of the conservation test.

Type formulas in Chemical equation, separate species with plus signs, and use ->, =, or → once between the two sides. Parentheses, square-bracket groups, hydrate dots, and state suffixes such as (aq) are supported.
Write an ionic charge in braces after the formula, such as Fe{2+} or Cr2O7{2-}. Keep Atoms and supplied charges for ionic equations.
Read Balanced equation, then check Conservation ledger. Every listed element should have equal reactant and product totals, and charge totals should match when charge checking is active.
If the equation is rejected, correct the named formula, group, arrow, or species mismatch. Balancing changes coefficients only, so adding a missing substance requires changing the entered reaction.

Interpreting Results:

The returned coefficients are the smallest positive whole-number ratio for the supplied species. A coefficient of 1 is left unwritten. Multiplying every coefficient by the same number would preserve balance, but it would no longer be the reduced form.

Treat Atoms only as an intentional exception. It can produce matching atom totals while ignoring an explicit charge imbalance. For an ionic or redox equation, use the charge-aware result and confirm both atom and charge rows before using the stoichiometric ratio.

Technical Details:

Each species becomes a column in a conservation matrix. Every element supplies one row; the charge-aware mode adds another row for elementary charge. Reactant counts are positive and product counts negative, so a valid coefficient vector makes every row sum to zero.

Formula Core:

The coefficient vector must satisfy the homogeneous conservation system and then be reduced to its primitive positive-integer form.

A c = 0, c_{j} \in Z^{+}, \gcd (c_{1}, \dots, c_{n}) = 1

A holds signed element counts and, when selected, charge counts. c holds one coefficient per supplied species. Positive integers require every species to participate, while the greatest-common-divisor rule produces the smallest equivalent ratio.

Transformation Core:

Chemical equation balancing stages
Stage	Transformation	Failure that stops the balance
Parse	Separate reaction sides and expand element counts through grouped formulas and hydrates.	Unknown element, mismatched group, unsupported character, or missing side.
Build constraints	Create one signed row per element and optionally one charge row.	An element occurs on only one side.
Solve	Reduce the exact rational matrix and find its null-space direction.	No nonzero solution, multiple independent balances, or no all-positive solution.
Normalize	Clear denominators and divide all coefficients by their greatest common divisor.	A required coefficient exceeds 1,000,000.

For methane combustion, CH₄ + O₂ → CO₂ + H₂O becomes CH₄ + 2O₂ → CO₂ + 2H₂O. Carbon totals 1 on each side, hydrogen 4, and oxygen 4.

One equation may contain at most 16 supplied species. Formula and charge multipliers are positive integers up to 100,000, and the entered equation is limited to 2,000 characters. Initial coefficients are accepted as input decoration but are replaced by the independently solved smallest ratio.

References:

Chemical reaction equation, IUPAC Compendium of Chemical Terminology.
Writing and Balancing Chemical Equations, OpenStax Chemistry.