About the Chemical Equation Balancer
This chemical equation balancer finds the smallest whole-number coefficients that make the number of atoms of every element equal on both sides of a reaction. Type the unbalanced equation with an arrow between reactants and products — for example Fe + O2 -> Fe2O3 — and the balanced form appears instantly, together with an atom tally so you can see that nothing is created or destroyed.
It is designed for chemistry students checking homework, teachers preparing worksheets and anyone writing reaction equations for lab notes. Formulas can include parentheses and brackets such as Ca(OH)2 or K4[Fe(CN)6], hydrates such as CuSO4·5H2O, and state symbols like (aq) or (g), which are ignored during balancing.
Element symbols are case-sensitive: Co is cobalt, while CO is carbon monoxide. Ionic and redox equations are supported too: write each charge after a caret, such as Fe^3+, MnO4^- or SO4^2-, and electrons as e-. When charges are present the balancer makes both the atoms and the net charge equal on each side. It balances the species you type; it does not add missing H⁺, OH⁻ or H₂O for you, so include them as you would in an acidic or basic half-reaction.
How to use the chemical equation balancer
- 1Type the reactants separated by +, for example CH4 + O2.
- 2Add an arrow (-> or =) and then the products, for example CO2 + H2O.
- 3Check element symbols use the right capitalisation (Na, Cl, Co), and write any ionic charges with a caret (Fe^3+, e-).
- 4Read the balanced equation and the coefficient list.
- 5Use the atom balance table to confirm every element matches.
Formula and method
Balancing is solved as a system of linear equations. Each element gives one equation: the atoms it contributes on the left, multiplied by the unknown coefficients, must equal the atoms on the right. When the equation contains ions or electrons, the net charge adds one more row, so total charge must also match. Writing product counts as negative numbers produces a matrix A whose null space holds the balancing coefficients.
The calculator reduces the matrix with exact fraction arithmetic (no rounding), takes the single solution direction, and scales it by the least common denominator and then divides by the greatest common divisor so the coefficients are the smallest positive whole numbers. If there is no solution, or more than one independent solution, it tells you instead of guessing.
- A
- Element-by-compound atom count matrix, plus a charge row for ionic equations (products negative)
- x
- Vector of stoichiometric coefficients
Worked examples
Combustion of propane
Three carbons in propane need 3 CO₂ and eight hydrogens need 4 H₂O. That is 6 + 4 = 10 oxygen atoms on the right, so 5 O₂ are needed on the left.
Rusting of iron
Fe₂O₃ has an odd number of oxygens, so it must be doubled to match whole O₂ molecules: 2 Fe₂O₃ has 6 O (3 O₂) and 4 Fe.
Neutralisation with a polyatomic group
Calcium phosphate needs 3 Ca and 2 PO₄, so 3 Ca(OH)₂ and 2 H₃PO₄ react. That supplies 6 + 6 = 12 hydrogens, which form 6 H₂O.
Permanganate oxidising iron(II) in acid (net ionic)
Manganese drops from +7 to +2 (gains 5 electrons) while each iron rises from +2 to +3, so 5 Fe²⁺ are needed. The 4 oxygens become 4 H₂O, which needs 8 H⁺. Net charge is −1 + 10 + 8 = +17 on the left and +2 + 15 = +17 on the right.
Dichromate reduction half-reaction
Two Cr³⁺ and 7 H₂O balance chromium and oxygen; 14 H⁺ supply the hydrogen. The left then carries −2 + 14 = +12 and the right +6, so 6 electrons are added to the left to balance the charge.
Frequently asked questions
Why do chemical equations need to be balanced?+
The law of conservation of mass says atoms are neither created nor destroyed in a chemical reaction. A balanced equation has the same number of each kind of atom on both sides, which is also what makes stoichiometry calculations work.
Can I change subscripts to balance an equation?+
No. Subscripts define the substance — changing H2O to H2O2 turns water into hydrogen peroxide. Only the coefficients in front of each formula may be changed.
How do I enter parentheses and hydrates?+
Type them as written: Ca(OH)2, Al2(SO4)3 or K4[Fe(CN)6]. For hydrates use a middle dot, asterisk or full stop, such as CuSO4·5H2O or CuSO4*5H2O.
Why does it say the equation cannot be balanced?+
Usually an element appears on only one side, a formula has a typo, or a symbol has the wrong capitalisation (CO is carbon monoxide, Co is cobalt). Some equations combine two independent reactions and have no unique balance.
Does the balancer handle ionic charges and redox equations?+
Yes. Type charges after a caret — Fe^2+, MnO4^-, Cr2O7^2- — and electrons as e-. The balancer then matches the net charge as well as the atoms, so net ionic equations and half-reactions balance correctly. Include H^+ and H2O (acidic) or OH^- and H2O (basic) yourself, as it does not add them automatically.