Chemical Equation Balancer
Type an unbalanced equation and get the smallest whole-number coefficients, a table that counts every atom and charge on both sides, and the matrix working behind the answer. It handles ions, electrons and redox equations, and when no single balance exists it tells you why. Runs entirely in your browser. Free, no sign-up.
Separate species with +, and reactants from products with ->, → or =. Write ions with a sign (Fe3+, SO4^2-, OH-) and electrons as e-. Coefficients and (s)/(aq) labels you type are ignored.
Result
Balanced equation
C3H8 + 5 O2 → 3 CO2 + 4 H2O
Coefficients
| Species | Side | Coefficient |
|---|---|---|
| C₃H₈ | Reactant | 1 |
| O₂ | Reactant | 5 |
| CO₂ | Product | 3 |
| H₂O | Product | 4 |
Atom check
| Element | Left side | Right side |
|---|---|---|
| C | 3 | 3 |
| H | 8 | 8 |
| O | 10 | 10 |
Every row matches, so atoms and charge are conserved.
The working
Each column is a species and each row an element. Reactant atoms count as positive and product atoms as negative, so coefficients balance the equation exactly when every row sums to zero.
| Row | C₃H₈ | O₂ | CO₂ | H₂O |
|---|---|---|---|---|
| C | 3 | 0 | -1 | 0 |
| H | 8 | 0 | 0 | -2 |
| O | 0 | 2 | -2 | -1 |
Null-space vector: (1/4, 5/4, 3/4, 1)
Multiply by 4 to clear fractions: (1, 5, 3, 4)
How to Use the Chemical Equation Balancer
- 1. Type the unbalanced equation. Put reactants on the left and products on the right, with + between species and an arrow (->, → or =) in the middle. Write formulas the usual way: C3H8, Ca(OH)2, CuSO4·5H2O.
- 2. Add charges and electrons if you have them. Write an ion with its sign, as in Fe3+, OH- or SO4^2-, and a free electron as e-. A charge row is added to the working automatically, so ionic and half-reaction equations balance too.
- 3. Read the result. The balanced equation appears at the top, with a coefficient table and an atom check that counts each element and the net charge on both sides.
- 4. Open the working. The matrix shows how the equation was turned into a linear system and solved exactly, so you can follow every step.
How the Null-Space Method Works
Balancing by inspection is trial and error. The null-space method turns the same problem into algebra. Give each species an unknown coefficient, then write one equation per element saying that the atoms on the left equal the atoms on the right. The coefficients that satisfy every equation at once are the null space of the matrix of atom counts.
In the matrix, each column is a species and each row is an element. Reactant atoms are counted as positive and product atoms as negative, so a set of coefficients balances the equation exactly when every row sums to zero. Charge is just one more row: the charge on each ion, signed the same way.
The solver uses exact fractions, not decimals, so there is no rounding to mistake for a real answer. For propane burning, C₃H₈ + O₂ → CO₂ + H₂O, the rows are:
| Row | C₃H₈ | O₂ | CO₂ | H₂O |
|---|---|---|---|---|
| C | 3 | 0 | −1 | 0 |
| H | 8 | 0 | 0 | −2 |
| O | 0 | 2 | −2 | −1 |
Its null space is one vector, (1, 5, 3, 4), so the balanced equation is C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. For H₂ + O₂ → H₂O the vector comes out as (1, ½, 1); multiplying by 2 clears the fraction and gives 2H₂ + O₂ → 2H₂O, the smallest whole numbers. The matrix is never larger than 30 elements by 20 species, so the answer is instant.
Balancing Ionic and Redox Equations
An ionic equation must balance twice: once for atoms and once for charge. Enter the ions with their charges and the balancer does both. For the permanganate–iron reaction in acid, MnO₄⁻ + Fe²⁺ + H⁺ → Mn²⁺ + Fe³⁺ + H₂O, it returns MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O, with +17 on each side.
Acidic and basic solutions
The balancer balances the species you list; it does not decide which to add. For a reaction in acid, include H⁺ and H₂O. In base, include OH⁻ and H₂O. For a half-reaction, include e⁻ on the correct side, and the electron count comes out for you. To find the oxidation states that tell you which atoms gain or lose electrons, use the Oxidation Number Calculator.
When an Equation Has No Unique Balance
Most textbook equations have exactly one balance. When they do not, the null space tells you what went wrong:
- No balance at all. The only solution is zero of everything. This usually means an element appears on one side only — chlorine in NaCl → Na — and the tool names it.
- Several independent balances. In H₂ + O₂ → H₂O + H₂O₂, two reactions are tangled together, so any mix of them balances. The tool lists each one; split your equation into separate reactions.
- A species on the wrong side. In H₂ + H₂O → O₂ the only balance is 2H₂O → O₂ + 2H₂. The tool shows the corrected equation and says which species moved.
- A species that takes no part. In H₂ + O₂ + N₂ → H₂O the nitrogen has nowhere to go, so N₂ gets a coefficient of zero while 2H₂ + O₂ → 2H₂O balances without it. The tool names the idle species.
Frequently Asked Questions
- How do you balance a chemical equation step by step?
- Count the atoms of each element on both sides, then adjust the coefficients (never the subscripts) one element at a time until the counts match, leaving the smallest whole numbers. This calculator does the same job algebraically: it sets up one equation per element and solves the whole system at once, which works even when inspection gets stuck.
- Why can't you change the subscripts to balance an equation?
- A subscript is part of a substance's identity: H₂O is water, but H₂O₂ is hydrogen peroxide. Changing it describes a different compound. Coefficients only say how many units of the substance react, so they are the only numbers you are free to change.
- How do you balance an equation with charges?
- Balance the atoms and the net charge together. The total charge on the left must equal the total on the right, just as each element's count must. Write each ion with its charge (Fe3+, SO4^2-) and the balancer adds a charge row to its working, so ionic and redox equations come out balanced for both.
- What does 'no unique balance' mean?
- It means the coefficients are not fixed by the atoms alone. Either no positive coefficients work, or two or more independent reactions are written as one equation, so infinitely many mixes balance. Check for a missing species, a wrong formula, or two reactions that should be listed separately.
- How do I balance a redox reaction in acidic or basic solution?
- Include the extra species the half-reaction method would add: H⁺ and H₂O in acid, or OH⁻ and H₂O in base, plus e⁻ for a half-reaction. Enter the whole equation with those species on the correct sides and the balancer solves atoms and charge together. You still choose which species to add.
- Can coefficients be fractions?
- Only as a step in the working. The calculator first finds a vector that may contain fractions, such as (1, ½, 1), then multiplies by the least common denominator to give whole numbers. Some textbooks leave ½O₂ in thermochemical equations, but for balancing the standard answer is the smallest whole-number set.
- Does it accept state symbols like (aq) and (g)?
- Yes. Labels such as (s), (l), (g) and (aq) are stripped before balancing, and so are coefficients you typed in front of a formula. The balancer works out its own, so a wrong guess in your input does no harm.