Chemical Equation Balancer
Free online chemical equation balancer. Balance any chemical reaction automatically using linear algebra on atom counts. 100% client-side.
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What is Chemical Equation Balancer?
A Chemical Equation Balancer takes an unbalanced chemical reaction and finds the smallest whole-number coefficients that conserve every atom on both sides. You enter an equation like H2 + O2 → H2O and the tool parses each formula, counts atoms element-by-element, builds a system of linear conservation equations, and solves it with exact rational arithmetic (BigInt fractions). The parser supports parentheses groups, square brackets, multiple terms, and common state annotations. The result is the fully balanced equation plus a detailed coefficient breakdown table. All calculations run locally in your browser with no data upload.
Key Benefits
- Exact BigInt rational arithmetic eliminates floating-point rounding errors
- Smart parser handles parentheses groups and square brackets with multipliers
- Supports complex multi-term reactions with any number of reactants and products
- Smallest whole-number coefficients, reduced by greatest common divisor
- Atom conservation verification for every element in the equation
Common Use Cases
- •Chemistry homework: balance equations for stoichiometry and limiting reagent problems
- •Lab work: verify mole ratios for reactant and product calculations
- •Redox reactions: balance complex equations with many terms like KMnO4 + HCl
- •Educational reference: understand how coefficients conserve atoms in reactions
- •Quick verification: double-check hand-balanced equations for mistakes
How to Use the Chemical Equation Balancer
- Enter your equation: Type the unbalanced equation using + between terms and an arrow (→ or ->) between reactants and products. For example: H2 + O2 → H2O.
- Use an example if needed: Click any example chip (combustion, single replacement, redox, etc.) to quickly load a common reaction and see how it works.
- Read the balanced equation: The result card shows the fully balanced equation with the smallest whole-number coefficients. Each term displays its coefficient in the breakdown table.
- Verify and copy: The tool verifies atom conservation for every element. Click Copy to save the balanced equation as text for your homework or lab notes.
Key Features
- Exact BigInt rational arithmetic for zero floating-point rounding errors
- Smart parser handles parentheses groups like Ca(OH)2 and Fe2(SO4)3
- Multi-term reactions with any number of reactants and products
- Smallest whole-number coefficients, reduced by greatest common divisor
- Atom conservation verification with detailed coefficient breakdown table
- 100% client-side - no data uploaded, works offline
Frequently Asked Questions
How does the Chemical Equation Balancer work?
The balancer parses each reactant and product formula to count atoms element-by-element, then builds a system of linear equations where each row enforces conservation of one element (reactant atoms equal product atoms). It solves this system using Gaussian elimination with exact rational arithmetic (BigInt fractions) and converts the result to the smallest whole-number coefficients.
What notation should I use for the arrow and plus signs?
Use + between terms on the same side and an arrow between reactants and products. Both the Unicode right arrow (→) and ASCII (->) are accepted. An equals sign (=) also works. Ensure there is at least one term on each side. Example: H2 + O2 → H2O.
Does it support parentheses and complex formulas?
Yes. The parser handles parentheses groups with multipliers, such as Ca(OH)2 (one calcium, two oxygens, two hydrogens) and Fe2(SO4)3. Square brackets like [Co(NH3)6] are also supported. State annotations like (s), (l), (g), and (aq) are ignored automatically.
Why are my coefficients different from my textbook?
Chemical equations have infinitely many valid coefficient sets (you can multiply all coefficients by any positive integer). This tool always returns the smallest whole-number ratio, reduced by the greatest common divisor. Textbooks use the same convention, so the results should match. If they differ, double-check your formulas for typos.