Chemistry
Chemical equation balancer
Type the reactants and products: the calculator finds the smallest whole-number coefficients and shows, element by element, that the atoms and the charge match on both sides.
How to balance an equation
In a chemical reaction atoms are neither created nor destroyed, they only change partners: so every element must appear the same number of times on both sides of the arrow. Balancing means finding the coefficients in front of the formulas, never touching the subscripts, which would change the substance.
Simple reactions are balanced by inspection: Fe + O₂ → Fe₂O₃ has 2 iron and 3 oxygen atoms in the product, and the least common multiple of the 2 oxygens in O₂ and the 3 in Fe₂O₃ leads to 4 Fe + 3 O₂ → 2 Fe₂O₃. The combustion of propane, C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O, is balanced carbon first, then hydrogen and oxygen last.
For redox reactions such as KMnO₄ + HCl, inspection struggles: the calculator writes one equation per element and solves it exactly, giving 2 KMnO₄ + 16 HCl → 2 KCl + 2 MnCl₂ + 8 H₂O + 5 Cl₂. In ionic equations the total charge must also match on both sides, and the table checks it along with the atoms.
Common mistakes
- Changing subscripts instead of coefficients: H₂O₂ in place of H₂O does not balance the reaction, it makes it a different one.
- Leaving coefficients unreduced, as in 4 H₂ + 2 O₂ → 4 H₂O: the smallest whole numbers are always used.
- Forgetting the charge in ionic equations: the atoms can match even when the electrons do not.
Frequently asked questions
Why can't the subscripts change?
Because the subscript is part of the formula: H₂O is water, H₂O₂ is hydrogen peroxide. The coefficient says how many molecules react, the subscript which ones.
How do I type ions?
With a caret and the charge: Fe^3+, SO4^2-, H^+. Pasting real superscripts such as Fe³⁺ works too, as do bracketed groups and hydrates with a dot, like CuSO4·5H2O.
What does it mean when a reaction has several balances?
That it is really the sum of two independent reactions, each balanced on its own, which can be combined in endless ratios. Write them separately.
How this calculation works
Each element gives one equation: the sum over reactants of coefficient times atoms of that element equals the same sum over products. Ionic equations add a charge equation. The homogeneous system is solved by Gaussian elimination in exact fractions: when the solution space has dimension 1, the vector with all coefficients positive is taken and reduced to the smallest integers by dividing by the GCD.
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