Balance chemical equations automatically with step-by-step matrix method. Supports redox half-reactions and combustion.
Enter a skeletal chemical reaction, and the Chemical Equation Balancer finds coefficients that give matching element totals on both sides. It presents the balancing process through a matrix method, including support for combustion equations and redox half-reactions. For a half-reaction, charge and electrons must be considered along with atom counts. The common mistake is changing a formula's subscripts to make totals match. Balancing changes only the coefficients placed before formulas; changing a subscript changes the chemical species itself.
A concrete input and expected output from the current implementation.
Input
Fe + O2 -> Fe2O3
Expected output
4 Fe + 3 O2 -> 2 Fe2O3
Two Fe2O3 formula units contain four iron atoms and six oxygen atoms. Four Fe atoms and three O2 molecules supply those same totals, and the coefficient ratio 4:3:2 is already reduced.
The element symbols define conservation rows, and the entered compounds define coefficient columns. A signed composition matrix records each element's count on the reactant and product sides. Solving the resulting homogeneous system finds coefficient ratios that make every row sum to zero. The displayed steps expose this linear algebra setup without changing any chemical formula.
After a nonzero ratio is found, fractional values can be multiplied by a common denominator and reduced to the lowest whole-number ratio. For Fe + O2 -> Fe2O3, conservation gives one relation for iron and another for oxygen. The normalized solution is 4:3:2, balancing four iron atoms and six oxygen atoms on each side.
Yes, the tool supports redox half-reactions. Enter charges and electrons unambiguously, then check both atom totals and net charge in the result. The surrounding medium still matters: water, H+, or OH- may participate depending on whether conditions are acidic or basic, so an incomplete skeleton may not specify a unique half-reaction.
No. Its coefficients give relative stoichiometric amounts, such as moles of one species per mole of another. Actual product quantity also depends on the starting amounts, limiting reactant, purity, reaction completion, and yield. Use the balanced coefficients as ratios, then perform the separate mass or mole calculation.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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