Chemical Equation Balancer
Enter reactant and product formulas to calculate the smallest whole-number stoichiometric coefficients and verify atom conservation element by element.
Reaction input
Balanced result
Atom balance check
| Element | Reactant atoms | Product atoms | Difference | Check |
|---|---|---|---|---|
| C | 4 | 4 | 0 | Balanced |
| H | 12 | 12 | 0 | Balanced |
| O | 14 | 14 | 0 | Balanced |
The table multiplies each formula's atom counts by its calculated coefficient. Every difference must equal zero for a valid balance.
How to use the chemical equation balancer
What this calculator does
This calculator finds stoichiometric coefficients that conserve each chemical element across a reaction. It treats every compound formula as fixed, builds an element-by-compound matrix, solves the resulting homogeneous linear system, and reduces the answer to the smallest positive whole-number ratio. It verifies atom counts, but it does not determine whether the reaction is chemically feasible, predict products, identify reaction conditions, or account for ionic charge unless charge is explicitly represented as a conserved species.
When to use it
Use it to check homework, prepare a stoichiometry calculation, verify a reaction before converting moles or masses, or audit a manually balanced equation. It is especially useful for formulas with parentheses, such as Ca(OH)2, where a subscript multiplies every atom inside the group.
How to calculate
- The calculator opens with the demonstration equation C2H6 + O2 → CO2 + H2O, a complete balanced result, and an immediately available XLSX workbook.
- Replace the text in Unbalanced chemical equation. Separate compounds with plus signs and separate the two sides with ->, =, or →.
- Read Balanced result, then confirm that every row in Atom balance check shows equal reactant and product atom totals.
- Select Download Excel to export the current formulas, coefficients, balanced equation, and atom audit. Select Reset to clear the demonstration; export remains disabled until a complete valid equation is entered again.
Input guide
Unbalanced chemical equation is required text. Enter valid element symbols with correct capitalization, optional whole-number subscripts, parentheses or brackets, and ordinary hydrate dots. Example: Ca(OH)2 + H3PO4 -> Ca3(PO4)2 + H2O. Do not alter subscripts merely to make counts match; subscripts define the substances themselves. Changing a formula changes the composition matrix and therefore the calculated coefficient ratio. Common mistakes include lowercase element symbols, missing closing parentheses, more than one reaction arrow, or placing a plus sign inside an unsupported charge notation.
Output guide
Balanced result is the reaction written with the smallest positive integer coefficients; an omitted coefficient means 1. Coefficient ratio lists those integers in the same left-to-right order as the compounds. Coefficient sum adds them and is mainly a compact complexity indicator, not a chemical property. Elements conserved reports how many distinct elements have equal totals on both sides. Solution form confirms that a common divisor has been removed. In the Atom balance check table, Reactant atoms and Product atoms are coefficient-weighted totals, Difference is product minus reactant, and Check must read Balanced. These values are exact identities for the parsed formulas rather than experimental estimates.
Worked example
For the startup equation C2H6 + O2 → CO2 + H2O, the calculator returns coefficients 2, 7, 4, and 6. Carbon becomes 2 × 2 = 4 atoms on the left and 4 × 1 = 4 on the right. Hydrogen becomes 2 × 6 = 12 on the left and 6 × 2 = 12 on the right. Oxygen becomes 7 × 2 = 14 on the left and 4 × 2 + 6 × 1 = 14 on the right. The first-open result is therefore 2 C2H6 + 7 O2 → 4 CO2 + 6 H2O, with a coefficient sum of 19.
Learn more
The balancing rule follows conservation of atoms: coefficients may change, but chemical formulas may not. The LibreTexts guide to writing and balancing equations explains the inspection method and coefficient meaning in more detail.
How the balancing model works
For every element, the calculator creates one conservation equation. Reactant atom counts receive negative signs and product atom counts receive positive signs. The coefficient vector must lie in the null space of this matrix, meaning the matrix-vector product equals zero. Exact rational arithmetic is used so fractional intermediate values do not introduce floating-point rounding errors. The final rational vector is multiplied by the least common multiple of its denominators and divided by the greatest common divisor of all coefficients.
For each element i: Σ(reactant atoms × coefficient) = Σ(product atoms × coefficient)
This linear-algebra interpretation is consistent with the standard mathematical description of chemical-equation balancing. See the system-of-linear-equations formulation and the IUPAC definition of stoichiometric number.
Interpretation and limitations
A balanced equation states relative amounts, not actual yield. Multiplying every coefficient by the same positive integer preserves balance, but conventional equations use the lowest whole-number ratio. A zero difference in every table row proves elemental conservation for the entered formulas; it does not prove that the formulas, products, phases, catalyst, temperature, or mechanism are correct. For ionic reactions, mass and electric charge should both be conserved, and half-reaction methods may be more appropriate. The OpenStax discussion of chemical reactions provides broader context for interpreting equations.