Chemical Equation Balancer
Type an unbalanced reaction such as Fe + O2 = Fe2O3 and get the smallest whole-number coefficients instantly. The balancer builds the element matrix, solves it with exact fractions and shows every step, including charge balance for ionic and redox equations.
Separate species with + and the two sides with =, -> or →. Use brackets like Ca(OH)2, hydrates like CuSO4·5H2O or CuSO4*5H2O, and charges like Fe^3+, MnO4^- or Fe{3+}. Write electrons as e-.
Atom check
Species
Show the matrix method step by step
How to use the Chemical Equation Balancer
- Type the equation with reactants on the left and products on the right, for example C3H8 + O2 -> CO2 + H2O.
- Use correct capitals for element symbols (Co is cobalt, CO is carbon monoxide). Add brackets, hydrate dots and charges where needed.
- Press Balance or Enter. The result also updates as you type.
- Read the result: the balanced equation, the coefficients and an atom check showing both sides match.
- Open the steps to see the element matrix, the row reduction and how the coefficients were scaled to whole numbers.
Worked example: balancing propane combustion with a matrix
Take C3H8 + O2 → CO2 + H2O and give the species coefficients a, b, c and d. Counting each element on both sides gives one equation per element:
| Element | Equation | Matrix row (a, b, c, d) |
|---|---|---|
| Carbon | 3a = c | 3, 0, −1, 0 |
| Hydrogen | 8a = 2d | 8, 0, 0, −2 |
| Oxygen | 2b = 2c + d | 0, 2, −2, −1 |
Three equations and four unknowns leave one free variable. Setting a = 1 gives c = 3 and d = 4, and then 2b = 6 + 4, so b = 5. The balanced equation is C3H8 + 5O2 → 3CO2 + 4H2O. Check: 3 C, 8 H and 10 O atoms on each side.
Common balanced equations
| Reaction | Balanced equation |
|---|---|
| Rusting of iron | 4Fe + 3O2 → 2Fe2O3 |
| Water formation | 2H2 + O2 → 2H2O |
| Methane combustion | CH4 + 2O2 → CO2 + 2H2O |
| Photosynthesis | 6CO2 + 6H2O → C6H12O6 + 6O2 |
| Haber process | N2 + 3H2 → 2NH3 |
| Copper and dilute nitric acid | 3Cu + 8HNO3 → 3Cu(NO3)2 + 2NO + 4H2O |
| Permanganate and hydrochloric acid | 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2 |
| Permanganate and iron(II), acidic | MnO4− + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O |
Tips for typing equations
- Capitalisation matters. Each element symbol is one capital letter, sometimes followed by one lowercase letter. NaCl, not nacl.
- Charges go after a caret or inside braces: SO4^2-, NH4^+, Fe{3+}. A single element followed by a number and a sign, such as Cu2+, is read as an ion with that charge.
- Hydrates use ·, * or a full stop: Na2CO3·10H2O.
- Coefficients you type in front of species are ignored. The balancer always works out its own.
- Redox half-reactions can include electrons: Fe^3+ + e- = Fe^2+.
Frequently asked questions
How do you balance a chemical equation?
Give each species an unknown coefficient and require that every element appears the same number of times on both sides. Each element gives one linear equation. Solving these equations and scaling to the smallest whole numbers gives the balanced equation, for example 4Fe + 3O2 → 2Fe2O3.
What is the matrix method for balancing equations?
Write a matrix with one row per element and one column per species, with reactant atom counts positive and product counts negative. The balanced coefficients are a vector in the null space of this matrix. Row-reducing it with exact fractions finds that vector, which is then multiplied up to whole numbers.
How do I enter ions and charges?
Put a caret or braces after the formula: Fe^3+, MnO4^-, SO4^2- or Fe{3+}. Single ions can also be written Na+ or Cl-. Electrons are written e-. The balancer then adds a charge row so total charge is conserved as well as atoms.
How do I enter a hydrate?
Separate the water of crystallisation with a middle dot, an asterisk or a full stop, with the number of water molecules in front: CuSO4·5H2O, CuSO4*5H2O or CuSO4.5H2O.
Why does it say my equation cannot be balanced?
Either an element appears on only one side, a formula is wrong, or no set of positive coefficients can conserve every element. Check the capitalisation of symbols, the charges and whether each species is on the correct side.
Why does it say there is more than one solution?
Some equations combine two or more independent reactions, such as H2 + O2 → H2O + H2O2. Many coefficient sets balance them, so there is no unique answer. Split the equation into separate reactions or remove a species.
Do the coefficients have to be whole numbers?
Yes, by convention balanced equations use the smallest set of positive whole numbers. A coefficient of 1 is not written. Fractions like ½O2 are sometimes used for thermochemistry, but this balancer always scales to integers.