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Science / Chemistry

Chemical Equation Balancer

Enter an unbalanced chemical equation using formulas such as Fe + O2 -> Fe2O3. The calculator parses each compound, conserves every element, and returns the simplest whole-number coefficients.

Balanced equation
4 Fe + 3 O2 -> 2 Fe2O3
Coefficient pattern
4 : 3 -> 2
Atom check
Fe: NaN = 4, O: NaN = 6

The balancer builds an element-by-compound matrix and solves for the coefficient ratio that makes each element count equal on both sides. It then reduces the result to the smallest positive whole numbers.

Source: Based on the law of conservation of mass and exact rational linear algebra.

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Written by
Inchs Calculator Team
Editorial Team

Balancing a chemical equation means making the number of atoms of every element equal on the reactant and product sides. That is the practical expression of conservation of mass: atoms are rearranged during a reaction, not created or destroyed. This calculator accepts a typed reaction instead of limiting you to one special reaction family.

How to Balance a Chemical Equation (step by step)

Step One: Write formulas and separate the sides

Enter each substance with its correct chemical formula, put plus signs between substances on the same side, and use one arrow between reactants and products.

unbalanced equation = Fe + O2 -> Fe2O3
input = Fe + O2 -> Fe2O3

Step Two: Count each element in every compound

The parser reads subscripts and parentheses as atom counts. A missing subscript means one atom, while a subscript after parentheses multiplies the entire group.

Fe = 1 Fe
O2 = 2 O
Fe2O3 = 2 Fe + 3 O
element rows = Fe, O
compound columns = Fe, O2, Fe2O3

Step Three: Solve the conservation equations

The calculator finds coefficients that make each element total match on both sides. It uses exact fractions internally, so a temporary fractional ratio does not create rounding errors.

iron balance: Fe coefficient = 2 x Fe2O3 coefficient
oxygen balance: 2 x O2 coefficient = 3 x Fe2O3 coefficient
coefficient ratio = 4 : 3 : 2

Step Four: Reduce the coefficients to whole numbers

Multiply through by the smallest common factor, then divide out any common divisor. Coefficients of one are omitted in the displayed equation.

balanced equation = 4 Fe + 3 O2 -> 2 Fe2O3
coefficient pattern = 4 : 3 -> 2
atom check = Fe: 4 = 4, O: 6 = 6

What your results mean

The balanced equation is the reaction written with the smallest whole-number mole ratio. The default example says that 4 moles of iron react with 3 moles of oxygen to form 2 moles of iron(III) oxide. Those coefficients can be carried into a stoichiometry calculator when you need masses, limiting reactants, or theoretical yield.

The coefficient pattern shows the numbers in input order, first for reactants and then for products. The atom check is a quick audit of the result: every listed element should have the same total on each side. For mass-based work, calculate each compound’s formula weight with a molar mass calculator before converting the mole ratio into grams.

Input limits and common mistakes

Use valid formulas and do not change subscripts to force a balance. The parser supports normal element symbols, nested parentheses or brackets, hydrate notation with a middle dot, and common state labels. It does not interpret reaction conditions, catalysts, electron-transfer notation, or unusual charge notation as separate balancing entities, so verify redox reactions and ionic equations carefully.

About the formula: The balancer builds an element-by-compound matrix and solves for the coefficient ratio that makes each element count equal on both sides. It then reduces the result to the smallest positive whole numbers.

Frequently Asked Questions

What format should I enter?+

Enter formulas separated by plus signs with one reaction arrow, such as Fe + O2 -> Fe2O3. You can also include starting coefficients, parentheses, brackets, hydrate dots, and common state labels such as (aq) or (s).

Does a coefficient change a chemical formula?+

No. A coefficient multiplies the entire formula and changes the amount of that substance. Never change subscripts to balance an equation because that creates a different compound.

Why does the calculator return the smallest whole-number ratio?+

Chemical equations describe mole ratios, so any common multiple represents the same reaction. Reducing the coefficients removes unnecessary duplication and gives the conventional form.

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