Chemical Equation Balancer
Balance any chemical equation — combustion, redox, ionic (with charges) or hydrates — by the matrix method and get the smallest whole-number coefficients with an atom-by-atom check of both sides.
How it works
Unknown coefficients x₁ … xₙ for every substance · one equation per element: Σ(atoms in reactants × x) = Σ(atoms in products × x) (plus one for total charge in ionic equations) · solve the homogeneous system A·x = 0 (exact integer Gaussian elimination) → the 1-dimensional null space · scale to the smallest positive whole numbers
Balancing by inspection works for simple reactions, but the algebraic (matrix) method always works: each element gives a linear equation saying its atoms are conserved, and the coefficients are the smallest positive integer solution of that system. The balancer parses formulas with parentheses, brackets, hydrates and ionic charges, solves the system with exact integer arithmetic (no rounding), and shows a table proving every element — and the charge — is equal on both sides. If the system has no solution, or more than one independent one, it tells you instead of guessing.
Worked example
Propane combustion C3H8 + O2 = CO2 + H2O: carbon gives 3 CO₂, hydrogen gives 4 H₂O (8 H), and the products then hold 3 × 2 + 4 = 10 O atoms, so 5 O₂ are needed. Balanced: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O, coefficients 1, 5, 3, 4, with 3 C, 8 H and 10 O on each side (21 atoms).
Sources: IUPAC Gold Book — stoichiometric number · Chemistry LibreTexts — Balancing Chemical Equations
Frequently asked questions
How do I balance a chemical equation step by step?
Write the unbalanced equation, balance the element that appears in the fewest substances first (often a metal or carbon), then hydrogen, then oxygen last, and finally reduce the coefficients to the smallest whole numbers. If you get stuck, the algebraic method used here — one equation per element — always finds the answer.
Why are formulas case-sensitive?
Because Co is cobalt and CO is carbon monoxide, Si is silicon and SI would be sulfur + iodine. Type element symbols with a capital first letter and a lowercase second letter.
Can it balance redox and ionic equations?
Yes. Add charges with ^ or braces (Fe^3+, MnO4^-, Cr2O7{2-}) and electrons as e^-; the charge is balanced as an extra equation. For half-reactions in acidic solution include H^+ and H2O, in basic solution OH^- and H2O.
Why does it say the equation can be balanced in more than one way?
That happens when the substances allow two or more independent reactions (for example H2 + O2 = H2O + H2O2). The equation then has no unique balance; split it into separate reactions or remove a product.
Do I change the subscripts to balance an equation?
Never — subscripts define the substance (H₂O vs H₂O₂). Only the coefficients in front of each formula change. The balancer leaves your formulas intact and only adds coefficients.
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