Chemical equation balancer
Type the reactants and products; the balancer finds the smallest whole-number coefficients.
How the equation is balanced
Each element gives one equation: the atoms of that element in the reactants must equal those in the products. With one unknown coefficient per substance, these equations form a table, or matrix, with one row per element and one column per substance (products entered with a minus sign). A balanced equation is a column of positive coefficients that makes every row add to zero.[1][2] The balancer solves the table by Gauss–Jordan elimination in exact fractions, so no rounding can creep in, and scales the solution to the smallest whole numbers. When ions appear, a charge row is added, so charge balances too.
The five possible answers
- Balanced. Exactly one set of coefficients, up to scale, conserves every element: the usual case.
- Cannot be balanced. Only zero coefficients work. A formula is wrong or a substance is missing (for example CO2 + H2O → C6H12O6 without the O2 that photosynthesis releases).
- Balances only without a species. One substance must have coefficient zero: it takes no part.
- Balances only with a species moved. A coefficient comes out negative: that substance belongs on the other side.
- More than one answer. The equation is two or more independent reactions written as one, so infinitely many balanced versions exist. The balancer lists the independent reactions instead of picking one. Counting cannot choose between them, not even counting electrons (for neutral substances, every atom-balanced version is electron-balanced too). What decides is which reactions actually happen: chemical knowledge, or a measured ratio of the products.[2]
Many online balancers return a single answer for the last case without saying that others exist. For KMnO4 + H2O2 + H2SO4 → K2SO4 + MnSO4 + O2 + H2O, both 2, 5, 3 → 1, 2, 5, 8 and 2, 1, 3 → 1, 2, 3, 4 conserve every atom. Only the first is the reaction that happens. Both balance electrons as well as atoms; the first is the one in which every O2 molecule comes from the peroxide, and whether the reaction really goes that way is a question for chemistry and experiment, which no amount of counting can settle.
What you can type
Separate substances with + and the two sides with an arrow: ->, →, = or <=> (a reversible arrow is balanced like a forward one). Formulas follow the rules of the Molar mass calculator: capitals matter, brackets and hydrates are allowed. Charges need a caret, Fe^3+, or superscripts, Fe³⁺, so that the charge's + is never read as a separator. An electron is e^-. If you type coefficients, the balancer checks them and shows the ledger for your version as well. Up to 10 substances per side and 16 in all.
Worked examples
| Reaction | Balanced |
|---|---|
| Methane burns | CH4 + 2O2 → CO2 + 2H2O |
| Iron rusts | 4Fe + 3O2 → 2Fe2O3 |
| Permanganate and hydrochloric acid | 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 5Cl2 + 8H2O |
| Copper in dilute nitric acid | 3Cu + 8HNO3 → 3Cu(NO3)2 + 2NO + 4H2O |
| Permanganate and iron(II), in acid | MnO4− + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O |
| Fermentation of glucose | C6H12O6 → 2C2H5OH + 2CO2 |
A balanced equation records the net change, not the mechanism, and says nothing about whether, how fast or how far a reaction goes.[3]
Sources
- (1982). Chemical equation balancing: A general method which is quick, simple, and has unexpected applications. Journal of Chemical Education 59(9), 728. doi:10.1021/ed059p728. paper
- (1997). On balancing chemical equations: past and present. Journal of Chemical Education 74(11), 1359. doi:10.1021/ed074p1359. paper
- (2019). Chemistry 2e. OpenStax, Rice University. book §1.5 Measurement uncertainty, accuracy, and precision; §3.1 Formula mass and the mole concept; §4.1 Writing and balancing chemical equations; §4.3 Reaction stoichiometry; §4.4 Reaction yields.