Chemical Equation Balancer (Coefficient Calculator)
Enter an unbalanced chemical equation like H2 + O2 -> H2O and instantly get the smallest positive integer coefficients that satisfy conservation of mass.
Examples of commonly balanced equations
Common reactions from middle and high school chemistry, along with their balanced coefficients — useful for checking your work before you solve one yourself.
| Reaction | Unbalanced equation | Balanced equation |
|---|---|---|
| Combustion of hydrogen | H2 + O2 → H2O | 2H2 + O2 → 2H2O |
| Rusting (oxidation) of iron | Fe + O2 → Fe2O3 | 4Fe + 3O2 → 2Fe2O3 |
| Complete combustion of methane | CH4 + O2 → CO2 + H2O | CH4 + 2O2 → CO2 + 2H2O |
| Complete combustion of propane | C3H8 + O2 → CO2 + H2O | C3H8 + 5O2 → 3CO2 + 4H2O |
| Redox reaction of potassium permanganate with hydrochloric acid | KMnO4 + HCl → KCl + MnCl2 + H2O + Cl2 | 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2 |
Usage tips
- You do not need to type coefficients yourself — any numbers already in your equation are ignored and recalculated from scratch.
- The arrow can be written as "->", "=", or "→", so pasting a Unicode arrow character works fine too.
- Formulas with parentheses (e.g. Fe2(SO4)3) are supported, so more complex salts can be balanced as well.
- If an equation "should" balance but does not, double-check that every element listed on the reactant side also appears on the product side.
- Try loading one of the sample equations first to see how the result table is laid out before typing your own equation.
Frequently asked questions
Side Note — the algorithm behind balancing and the law of conservation of mass
The idea of balancing a chemical equation with coefficients rests on the law of conservation of mass, proposed in the 18th century by the French chemist Antoine Lavoisier. By precisely measuring combustion reactions inside sealed vessels, he demonstrated that total mass does not change during a reaction, overturning the earlier phlogiston theory, which held that burning caused a loss of mass.
When students first balance equations by hand in school chemistry, the most common stumbling block is confusing coefficients with subscripts. A coefficient scales the whole compound, while a subscript counts atoms within a single molecule — changing the latter creates an entirely different substance. The algorithm behind this tool (finding the null space of a system of linear equations) strictly respects that distinction while mechanically deriving the correct coefficients.
For more complex redox reactions — such as potassium permanganate reacting with hydrochloric acid — working out coefficients by hand can be tedious and often requires specialized techniques like the half-reaction method, which tracks the transfer of electrons. The Gaussian-elimination-based algorithm used here can solve even these equations purely from the requirement that atom counts match on both sides, without needing to track electron transfer at all.