Chemical Equation Balancer

List every element that appears, then adjust whole-number coefficients in front of each formula until the count of each element is identical on both sides. For CH4 + O2 → CO2 + H2O, balancing carbon and hydrogen first (methane already gives 1 C and 4 H, so H2O needs a coefficient of 2) leaves 4 oxygen atoms needed, which requires 2O2. This calculator automates that trial-and-error using linear algebra.

The algebraic method assigns a variable coefficient to every species, writes one linear equation per element (atoms in equal atoms out), and solves the resulting system. Because a correctly balanced equation has one more unknown than independent equations, the system has a one-parameter family of solutions; fixing that parameter and clearing fractions gives the smallest whole-number coefficients. This calculator solves that system exactly using fractions, not decimal approximations.

A balanced equation obeys the law of conservation of mass: atoms are neither created nor destroyed in a chemical reaction, only rearranged. An unbalanced equation implies atoms appearing from nowhere or vanishing, which is physically impossible. Balanced coefficients also give the correct mole ratios needed for every stoichiometry calculation that follows.

Yes. One level of parentheses is expanded automatically, so Ca(OH)2, Al2(SO4)3, and similar formulas parse correctly. Nested parentheses (a group inside another group) are not supported; rewrite the formula without nesting if needed.

It means an element appears in the reactants but never in the products, or vice versa, which usually signals a typo in one of the formulas. Chemically valid equations always have the same set of elements on both sides, since atoms are only rearranged, not created or destroyed.

Up to 6 total species combined (reactants plus products). This covers the overwhelming majority of introductory and intermediate chemistry equations, including multi-product redox reactions such as KMnO4 + HCl → KCl + MnCl2 + H2O + Cl2.

Coefficients represent counts of molecules or moles, which cannot be fractional in a physically meaningful balanced equation. The calculator solves the underlying system in exact fractions, then scales every coefficient by the least common multiple of the denominators so the final answer is always the smallest possible set of whole numbers.

A subscript (the small number inside a formula, like the 4 in CH4) is fixed by the compound's identity and can never be changed when balancing. A coefficient (the number placed in front of a formula, like the 2 in 2H2O) is what balancing adjusts. Changing a subscript would describe a different substance entirely.

Yes. Combustion reactions (a hydrocarbon plus O2 producing CO2 and H2O) are one of the most common uses. Enter the fuel and O2 as reactants, CO2 and H2O as products, for example C3H8, O2 as reactants and CO2, H2O as products for propane combustion.

This calculator balances atoms only, not electrical charge, so it works for standard molecular equations but not for balancing half-reactions or net ionic equations that require charge balancing alongside atom balancing. For charge-balanced redox half-reactions, balance atoms first with this tool, then balance charge separately by adding electrons.

No practical limit within the 6-species scope. Some redox equations naturally require larger coefficients, for example 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2, and the calculator finds these exactly the same way as smaller examples.

Yes. This tool balances a given set of reactants and products, it does not predict what products a reaction will form. Predicting products requires knowledge of reaction type (combustion, synthesis, decomposition, single or double displacement) which is a separate chemistry skill from balancing.