Chemical Equation Balancer

What is a Balanced Chemical Equation?

A balanced chemical equation has equal numbers of each type of atom on both sides of the reaction arrow, satisfying the Law of Conservation of Mass. Matter is neither created nor destroyed in a chemical reaction.

Balancing Method

This tool uses a matrix-based algorithm (Gaussian elimination) to find the null space of the element composition matrix. This produces the smallest set of whole-number coefficients that balance the equation.

1. Parse each compound into its element composition
2. Build a matrix where rows are elements and columns are compounds (reactants positive, products negative)
3. Apply Gaussian elimination to find the null space vector
4. Scale the result to the smallest whole-number coefficients

Example Walkthrough

Unbalanced: CH₄ + O₂ → CO₂ + H₂O

Balanced: CH₄ + 2O₂ → CO₂ + 2H₂O

Element	Left Side	Right Side
C	1	1
H	4	4
O	4	4

Input Format

• Element symbols with counts: H2O, CO2, NaCl
• Parentheses for groups: Ca(OH)2, Fe2(SO4)3, Al2(CO3)3
• Separate compounds with +
• Use ->, =, or → between reactants and products

Tips

• Element symbols are case-sensitive: Co (cobalt) vs CO (carbon + oxygen)
• Coefficients of 1 are implied and not shown
• The tool finds the simplest integer ratio of coefficients

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