Chemical Equation Balancer

Balancing by inspection works for water and rust. It falls apart on anything with five or six substances, where changing one coefficient breaks two others and the search turns into guesswork. This balancer does not guess. It writes the equation as a small system of linear equations, one per element, and solves it exactly.

Type the substances with an arrow between the two sides and you get the smallest whole-number coefficients, the equation with proper subscripts, a table proving every element matches, and a mass check. Ionic and redox equations work too, because charge is balanced alongside the atoms.

Worked Example: Burning Propane

The page opens on C3H8 + O2 -> CO2 + H2O. The result isC₃H₈ + 5O₂ → 3CO₂ + 4H₂O: 3 carbon, 8 hydrogen and 10 oxygen atoms on each side. The mass check reads 204.087 g on both sides per mole of reaction as written, using IUPAC standard atomic weights.

Load Sample then steps through potassium permanganate with hydrochloric acid (2, 16, 2, 2, 8, 5), an ionic redox equation where the charge column has to come out equal as well, calcium phosphate with brackets, a hydrate losing its water, and aluminium burning to its oxide.

How the Math Finds the Coefficients

Each element becomes a row and each substance a column, with reactants counted as positive and products as negative; a charge row is added when any species is charged. The coefficients are the solution of that matrix equal to zero. The tool reduces it with exact fractions, sets the one free coefficient to 1, then scales everything to the smallest whole numbers.

That method also explains its error messages. If an element appears on only one side, nothing can balance it, and the page says so by name:“Mg appears only on the right side, so no coefficients can balance it.” If the matrix leaves two free coefficients, the equation is really two reactions written as one, and you are asked to split it rather than shown an arbitrary answer.

Input Format for Charges, Hydrates and Brackets

• The arrow can be ->, =, →, <=> or ⇌. Substances are separated by +.
• Charges go after a caret, as in Fe^3+ or MnO4^-, or as superscripts like Fe³⁺. Electrons are e-, so half-equations such as Fe^3+ + e- -> Fe^2+ balance too.
• Brackets nest (K4[Fe(CN)6]), and hydrates use a dot: CuSO4·5H2O or CuSO4.5H2O.
• Coefficients you type are ignored and worked out again, so 2H2 + 3O2 -> 7H2O still comes back as 2, 1, 2.
• Up to 12 substances per equation. Copy the answer with subscripts (H₂O) for documents, or as plain text (H2O) for anywhere subscripts would break.