Chemical Equation Balancer

Type an unbalanced chemical equation and the balancer finds the smallest whole-number coefficients that make the number of atoms of each element the same on both sides. It reads formulas with parentheses and brackets, such as Ca(OH)2 or K4[Fe(CN)6], and hydrates written with a dot. The result shows the balanced equation and a table and chart of atom counts on each side, so you can see that mass is conserved. It is meant for checking work and learning; try balancing by hand first.

for each element: Σ (coefficient × atoms in each reactant) = Σ (coefficient × atoms in each product)

Each element gives one linear equation in the unknown coefficients. The balancer writes these as a matrix and solves it exactly with fractions, finding the set of coefficients that satisfies every equation, then scales them to the smallest whole numbers. If the equations have no positive solution, a compound is probably missing or a formula is wrong; if they have more than one independent solution, the equation combines separate reactions and needs to be split.

For most equations, inspection is quicker than algebra. Balance elements that appear in only one compound on each side first, leave hydrogen and oxygen until last, and adjust coefficients, never subscripts, since changing a subscript changes the substance.

For propane, C3H8 + O2 → CO2 + H2O: three carbons need 3 CO2; eight hydrogens need 4 H2O; that makes 6 + 4 = 10 oxygen atoms on the right, so 5 O2 on the left. The balanced equation is C3H8 + 5O2 → 3CO2 + 4H2O.

1. Type the reactants separated by plus signs, then an arrow (->, = or →), then the products.
2. Use correct capitalization: Co is cobalt, while CO is carbon monoxide. Element symbols start with a capital letter.
3. Write subscripts as ordinary numbers, such as H2O, and groups in parentheses, such as Al2(SO4)3.
4. Leave out existing coefficients and states; the balancer works them out.

Combustion reactions combine a fuel with oxygen to make carbon dioxide and water. Synthesis reactions join simple substances into a compound, as when iron and oxygen form rust. Decomposition reactions break a compound apart, single replacement reactions swap one element for another, and double replacement reactions, including neutralizations of acids and bases, exchange partners between two compounds. Recognizing the type helps you predict the products before balancing.

• It does not predict products. Enter both sides of the reaction you want to balance.
• Ionic equations with charges are not balanced for charge; charges written as ^2+ are ignored, so balance net ionic equations by hand or add spectator ions.
• States of matter such as (aq) or (g) should be left out.
• A balanced equation shows ratios, not whether a reaction actually happens or how fast.

Coefficients give the mole ratios between substances, which are the starting point for quantitative chemistry. Use the molar mass calculator to convert grams to moles, the stoichiometry calculator to find how much product a given amount of reactant can make, the limiting reagent calculator when reactants are mixed in arbitrary amounts, and the percent yield calculator to compare an experiment with the theoretical result.