Balance a chemical equation online

Enter the whole reaction including the products. The calculator finds the smallest whole-number coefficients, checks the atom balance (and the charge for ions) and computes molar masses. Works for redox, combustion and ionic equations.

Reaction equation

Read as: KMnO₄ + HCl → KCl + MnCl₂ + Cl₂ + H₂O

Separate the sides with «=», «->» or «→» and the substances with «+». Ion charge with ^: Fe^3+, SO4^2-. Hydrate: CuSO4·5H2O. If you do not know the products, use the «Complete a reaction» calculator.

Balanced equation

2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 5Cl₂ + 8H₂O

Coefficients: 2 : 16 : 2 : 2 : 5 : 8

Check: atoms on each side

Element	Left	Right
K	2	2 ✓
Mn	2	2 ✓
O	8	8 ✓
H	16	16 ✓
Cl	16	16 ✓

Molar masses and conservation of mass

Substance	M, g/mol	ν·M, g
KMnO₄	158.032	316.064
HCl	36.458	583.328
KCl	74.548	149.096
MnCl₂	125.838	251.676
Cl₂	70.900	354.500
H₂O	18.015	144.120

Mass of reactants 899.392 g = mass of products 899.392 g (for amounts in moles equal to the coefficients). Atomic masses are IUPAC standard values.

Solution

Assign an unknown coefficient to each substance: 6 substances, 5 balance equations (one per element and, for ions, one for charge).
The number of atoms of each element on the left equals that on the right, which gives a system of linear equations.
Solve it exactly in fractions (Gaussian elimination) and scale to the smallest positive whole numbers.
Answer: 2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 5Cl₂ + 8H₂O

How to balance a chemical equation

By the law of conservation of mass atoms are neither created nor destroyed, so each element must have the same number of atoms on both sides. Coefficients are chosen to make this true, and the smallest whole numbers are used.

Balancing by inspection

Start with the element that appears in the fewest substances, usually the metal.
Then balance the acid groups, then hydrogen; check oxygen last.
If you get a fraction (such as ½O₂), multiply all coefficients by the denominator.

Example: C₃H₈ + O₂ → CO₂ + H₂O. Three carbons give 3CO₂; eight hydrogens give 4H₂O; oxygen on the right is 3·2 + 4 = 10, so 5O₂.

How the calculator does it

Each substance gets an unknown coefficient, and each element gives an equation «left equals right». This is a homogeneous system of linear equations. The calculator solves it exactly in rational numbers (no rounding) and scales the solution to the smallest whole numbers, so it also handles redox reactions: 2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 5Cl₂ + 8H₂O.

For ionic equations one more condition is added: the total charge on the left equals the total charge on the right.

When it cannot be balanced

If the system has no positive solution, there is a mistake in the formulas or products. If there are infinitely many solutions, the record actually contains several independent reactions: for example, with hydrogen peroxide the coefficients depend on how much oxygen came from the oxidising agent and how much from the peroxide itself. Then the half-reaction (electron balance) method is needed.

FAQ

How do I balance a chemical equation?

Each element must have the same number of atoms on both sides. Start with the metal, then balance acid groups and hydrogen, and check oxygen last. The calculator does the same exactly: it sets up the balance equations and finds the smallest whole-number coefficients.

Can it balance redox reactions?

Yes. If the products are known, the coefficients follow from the atom balance: for example, 2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 5Cl₂ + 8H₂O. The electron balance steps are not shown yet.

Why does it say «infinitely many solutions»?

This happens when the record contains several independent reactions, for example redox with hydrogen peroxide. The atom balance does not fix the coefficients uniquely. Use the electron balance or specify the products more precisely.

How do I enter an ionic equation with charges?

Write the charge with ^: MnO4^- + Fe^2+ + H^+ = Mn^2+ + Fe^3+ + H2O. The calculator balances both atoms and charge.

Which atomic masses are used?

IUPAC abridged standard atomic weights: H 1.008, C 12.011, O 15.999, Cl 35.45, Cu 63.546. School problems often round them to whole numbers (35.5 for chlorine), so answers may differ in the first decimal place.