Chemical Equation Balancer

Balance a chemical equation from a text string and return stoichiometric coefficients with the underlying element-balance equations.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

This calculator balances a chemical equation by building one conservation equation per element and solving for a non-trivial stoichiometric coefficient vector.

It combines Unbalanced Equation to estimate Balanced Equation, Coefficients, System Equations.

Formula & Method

The balancing step enforces conservation of each element. In matrix form, the stoichiometric vector

\mathbf{x}

satisfies

A\mathbf{x}=0

where each row of

A

represents one element-balance equation.

Notation used in the formulas: $R$ = Balanced Equation; $x_{1}$ = Unbalanced Equation.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you need quick stoichiometric coefficients and want to inspect the linear system implied by atom conservation.

Reference Book

Chemistry: The Central Science

Theodore E. Brown, H. Eugene LeMay, Bruce E. Bursten, Catherine Murphy, Patrick Woodward, and Matthew E. Stoltzfus · Pearson

A widely used general chemistry text covering stoichiometry, gases, solutions, acids and bases, and electrochemistry.

View Book

Inputs Used

Unbalanced Equation: Used directly in the calculation.

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