Chemical Equation Balancer
Balance chemical equations such as Fe + O2 -> Fe2O3, C3H8 + O2 -> CO2 + H2O or Al + HCl -> AlCl3 + H2. The calculator parses neutral formulas, parentheses, brackets and hydrate dots, solves the coefficient system with exact rational arithmetic, and shows the atom count on each side so you can verify conservation of mass.
How the chemical equation balancer works
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1
Enter the unbalanced reaction
Use a single arrow between reactants and products, with plus signs between compounds. Existing leading coefficients are ignored so the equation can be solved from the formulas.
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2
The parser counts each element
Element symbols, multipliers, grouped formulas such as Fe2(SO4)3, brackets and hydrate notation such as CuSO4.5H2O are expanded into element counts.
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3
Read the smallest integer coefficients
The solver builds a conservation matrix, finds an exact null-space vector and reduces it to the smallest positive whole-number coefficients.
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4
Check atoms on both sides
The result table lists every element with its left-side and right-side atom totals, making it easy to spot a typo before you copy the balanced equation.
What balancing a chemical equation means
A chemical equation is balanced when every element appears in the same total amount on the reactant side and the product side. The formulas themselves do not change; only the coefficients in front of each compound change. That is why Fe + O2 -> Fe2O3 becomes:
4 Fe + 3 O2 -> 2 Fe2O3
The coefficient 4 means four iron atoms, 3 O2 means six oxygen atoms, and 2 Fe2O3 contains four iron atoms plus six oxygen atoms. Each element matches on both sides.
Worked example: propane combustion
For C3H8 + O2 -> CO2 + H2O, the balanced equation is:
C3H8 + 5 O2 -> 3 CO2 + 4 H2O
| Element | Left atoms | Right atoms | Why it matches |
|---|---|---|---|
| C | 3 | 3 | 3 CO2 gives 3 carbon atoms |
| H | 8 | 8 | 4 H2O gives 8 hydrogen atoms |
| O | 10 | 10 | 5 O2 gives 10 oxygen atoms; products have 6 + 4 |
Supported formula syntax
- Element symbols with normal capitalization:
NaCl,Fe2O3,Ca(OH)2. - Parentheses, square brackets and braces for groups:
Fe2(SO4)3,K4[Fe(CN)6]. - Hydrate dots with an ASCII period:
CuSO4.5H2O. - Optional state labels at the end of a formula:
(s),(l),(g)or(aq).
For best results, remove ionic charges and redox half-reaction electron notation before balancing. The tool is designed for neutral molecular formulas and common classroom or lab-prep equations.
Why exact arithmetic matters
Many chemical equations balance to fractions during the solving step. This calculator keeps those fractions exact, then multiplies by the least common denominator and reduces by the greatest common divisor. That avoids rounding errors and gives the smallest whole-number coefficient set whenever a positive balance exists.
Frequently Asked Questions
Yes. Groups such as Ca(OH)2, Al2(SO4)3 and K4[Fe(CN)6] are expanded before balancing, so group multipliers are counted correctly.
You can, but the solver ignores leading integer coefficients and recomputes the smallest valid set. For example, entering 2 H2 + O2 -> H2O still returns 2 H2 + O2 -> 2 H2O.
No. It balances neutral formula equations by atom conservation. Half-reactions with electrons, charges or acidic/basic medium steps should be handled with a dedicated redox balancer.
Usually one formula has a typo, an unsupported charge marker, a missing product/reactant, or an element that appears on only one side. Check the per-formula syntax and try again.
No. The parser and balancer run in the page request and only return the result for your session.
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