Balance a chemical equation
Type an equation with an arrow; get the smallest whole-number coefficients.
Work it out
A worked example
KMnO₄ + HCl → KCl + MnCl₂ + H₂O + Cl₂
2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 8H₂O + 5Cl₂
- 1Six species and four elements give four equations in six unknowns.
- 2Eliminating leaves one free coefficient, so the answers are fixed relative to each other.
- 3Clearing the fractions and dividing by the common factor gives 2, 16, 2, 2, 8, 5.
- 4Check: K 2 and 2, Mn 2 and 2, O 8 and 8, H 16 and 16, Cl 16 and 16.
What this assumes
- Balancing conserves atoms and nothing else. A balanced equation is not evidence the reaction happens, that those are the products, or that the conditions exist — it is arithmetic about the formulae you supplied.
- Some equations have more than one independent balance, as in C + O₂ → CO + CO₂. There is genuinely no single right answer, so this reports the ambiguity rather than picking one.
- Ionic charges are not read. Half-equations with electrons and free charges need a redox method this does not implement.
The terms used here
- Stoichiometric coefficient
- The number in front of a species. It multiplies every atom in that formula.
- Conservation of mass
- Atoms are neither created nor destroyed, so each element must appear the same number of times on both sides.
- Subscript against coefficient
- A subscript belongs to the formula and cannot be changed; a coefficient is what balancing is allowed to alter.
Where to next
Theoretical yield and limiting reagent
The coefficients from here are exactly what that calculation needs.
Molar mass calculator
Turn a balanced equation into masses to weigh out.
Predict a reaction outcome
Not sure what the products are? Balancing cannot tell you — this can propose them, with its evidence.
The other calculators
Molar mass calculator
Enter a formula and get its molar mass, broken down by element.
Molarity calculator
Relate concentration, volume and moles. Leave the unknown blank.
Dilution calculator (C₁V₁ = C₂V₂)
C₁V₁ = C₂V₂. Leave the unknown blank.
Percent yield calculator
Actual over theoretical, as a percentage. Leave the unknown blank.
Beer–Lambert law calculator
A = εlc. Leave the unknown blank.
pH, pOH and [H⁺] calculator
Convert between pH, pOH, [H⁺] and [OH⁻]. Leave the unknown blank.
This calculator runs in your browser. Nothing you type is sent anywhere, and no account is needed. If you want to go further than arithmetic — look a structure up, see what a reaction has been recorded as giving, or follow a mechanism — the library is open too.