Calculator Tools
Chemical Equation Balancer
Balance any chemical equation in your browser. Exact rational arithmetic, parentheses, hydrates, charges, and full element conservation check.
Type or paste an unbalanced equation. Use + between species and -> (or =) for the arrow.
Species
-
Elements
-
Status
ERROR
Parsed species
Each species split from the input, with its element count parsed and ready for balancing.
| Side | Species | Elements |
|---|---|---|
| Reactant | Fe2O3 | Fe: 2, O: 3 |
| Reactant | Al | Al: 1 |
| Product | Al2O3 | Al: 2, O: 3 |
| Product | Fe | Fe: 1 |
Cannot balance
Internal: non-positive denominator.
Try a preset
Classic equations from a chemistry course. Click one to load it.
How the balancer works
The solver writes element conservation as a linear system. For each element, the total number of atoms on the reactant side equals the total on the product side. With one coefficient per species, this is a homogeneous system A x = 0 with rows indexed by element and columns indexed by species (positive for reactants, negative for products). Every step uses exact rational arithmetic (BigInt numerators and denominators), so there is no floating-point error: reactions with fifty-digit coefficients balance perfectly.
After row-reducing to RREF, the dimension of the null space tells you what kind of equation you have. Dimension 1 is the normal case: a single integer ratio that balances everything. Dimension 0 means the atom counts cannot be matched at all. Dimension 2 or more means the equation contains two or more independent reactions stacked together, and you need to split it before a unique balance exists. The basis vector is scaled by the LCM of its denominators and divided by the GCD of the resulting numerators to give the smallest set of positive integer coefficients, the standard chemistry convention.
Parentheses, square brackets, curly braces, multi-letter element symbols, charges, and the centered-dot hydrate notation (CuSO4 . 5 H2O) are all supported. Charges are ignored for mass balance because they do not affect element counts. Everything runs in your browser; no equation, formula, or homework problem leaves your device.
How to use
- Type or paste the equation with reactants on the left, an arrow in the middle, and products on the right. Use + to separate species and -> or = for the arrow.
- Watch the Balanced equation card update as you type. The element conservation table verifies that every element has the same atom count on both sides.
- Use a preset like Octane combustion (C8H18 + O2 -> CO2 + H2O) or Photosynthesis (CO2 + H2O -> C6H12O6 + O2) for a one-click example.
- Parentheses, brackets, multi-letter symbols (Fe, Cl, Mg), charges, and the centered-dot hydrate notation (CuSO4 . 5 H2O) are all supported.
- Copy the balanced equation or the full text summary with the buttons under the result card.
About this tool
Chemical Equation Balancer takes any chemistry equation (reactants on the left, products on the right, with an arrow in between) and computes the smallest set of positive integer coefficients that balance it. It reads the equation, parses each species into an element count map (with full support for parentheses, square brackets, curly braces, multi-letter element symbols like Fe and Cl, charges that are ignored for mass balance, and the centered-dot hydrate notation CuSO4 . 5 H2O), and writes element conservation as a homogeneous linear system A x = 0 with one row per element and one column per species. The system is row-reduced to RREF using exact rational arithmetic (BigInt numerators and denominators) so there is no floating-point drift even on equations with very large coefficients. The null-space dimension classifies the equation: dimension 1 is the normal case and yields a single stoichiometric ratio; dimension 0 means no nontrivial solution exists and the equation cannot balance as written; dimension 2 or more means the equation contains two or more independent reactions stacked together and must be split before a unique balance exists. From the basis vector the tool scales by the LCM of all denominators and divides by the GCD of the resulting numerators to obtain the smallest positive integer coefficients, the standard chemistry convention. The result panel shows the balanced equation ready to copy, a coefficient table for every reactant and product, and an element conservation table that verifies each element has the same total atom count on both sides. Useful for chemistry students checking homework, lab demonstrators preparing experiments, teachers writing problem sets, college freshmen tackling stoichiometry, and anyone reading a textbook reaction who wants to confirm the coefficients without working out the algebra by hand. Eight preset reactions cover the patterns a typical course needs: water synthesis, octane combustion, the thermite reaction, acid-base neutralization, photosynthesis, the Haber-Bosch ammonia process, rust formation, and potassium permanganate decomposition. Everything runs in your browser. No equation, formula, or homework problem is uploaded.
Free to use. Works in your browser. No signup, no login.
Related tools
You may also like
Molar Mass Calculator
Molar mass and percent composition from a chemical formula, with grams-to-moles.
Open tool
CalculatorPeriodic Table
All 118 elements with search, category filter, and a detail panel for each cell.
Open tool
CalculatorGCD and LCM Calculator
GCD and LCM for any set of integers, with Euclidean steps and prime factorization.
Open tool
CalculatorSystem of Equations Solver
Solve 2 or 3 linear equations with exact-fraction steps and full classification.
Open tool
CalculatorQuadratic Equation Solver
Roots, discriminant, vertex, factored form, and step-by-step working for any quadratic.
Open tool
CalculatorBig Number Calculator
Exact integer math at any size: power, factorial, modular exponent, GCD, and LCM.
Open tool