About the Chemical Equation Balancer
Balance any chemical equation using exact linear algebra, not trial and error.
What it is
Balancing a chemical equation means finding coefficients that make the number of atoms of each element equal on both sides. This tool builds a matrix from the element counts of every species โ reactants as positive columns, products as negative โ and finds the null space of that matrix using exact rational Gaussian elimination. The result is scaled to the smallest whole-number ratio, guaranteeing a mathematically correct answer rather than a guessed one.
Features
Free-text formula parsing
Handles nested parentheses and hydrates like CuSOโยท5HโO.
Matrix-based balancing
Solves the element-conservation matrix's null space with exact fraction arithmetic โ no rounding error.
Atom-count verification table
Confirms every element matches on both sides after balancing.
Already-balanced & cannot-balance detection
Recognizes equations that are already balanced, and clearly explains when no valid integer solution exists.