Chemical equation balancer

How do I balance a chemical equation?

Choose coefficients so every element has the same number of atoms on both sides — atoms are neither created nor destroyed. Propane burning: C3H8 + 5O2 → 3CO2 + 4H2O, with 3 carbon, 8 hydrogen and 10 oxygen atoms on each side.

How do I type the equation?

Write the formulas with + between them and = or -> between the sides: Fe + O2 = Fe2O3. Parentheses work too: Ca3(PO4)2. Numbers after a symbol are subscripts.

How does the balancer work?

It counts each element in every formula and solves the system of equations exactly, then scales the answer to the smallest whole numbers — 4Fe + 3O2 → 2Fe2O3.

Why does it say the reaction can be balanced more than one way?

Some inputs combine two independent reactions, such as H2 + O2 = H2O2 + H2O. Any mix of them balances, so write each reaction separately.

Does it handle ions and charges?

Not yet — enter neutral formulas. For redox reactions in solution, include the full compounds, like 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2.

Can I change the subscripts to balance an equation?

No. Subscripts are part of the formula of a substance: H2O is water, and H2O2 is hydrogen peroxide, a different compound. Only the coefficients in front of the formulas can change.

What is the law behind balancing?

The law of conservation of mass: atoms are neither created nor destroyed in a chemical reaction, so each element must appear the same number of times on both sides.

Does a balanced equation mean the reaction will happen?

No. Balancing only checks the atom count. Whether a reaction actually occurs, and at what rate, depends on the substances and conditions, which the equation does not show.

How the balancer works

Each formula is read into a count of atoms for every element, with parentheses and subscripts handled. These counts form a table of elements against substances, with the products entered as negative numbers. A set of coefficients balances the equation when every row of the table adds up to zero. The balancer solves this exactly with fractions, so there are no rounding errors, and then scales the answer to the smallest whole numbers. If the table has more than one independent solution, the equation combines separate reactions, and the balancer asks you to split it.

Worked example

Take Al + O2 = Al2O3. Aluminum appears once on the left and twice on the right, and oxygen twice on the left and three times on the right. The smallest whole numbers that make both sides equal are 4, 3, 2, giving 4Al + 3O2 → 2Al2O3. The check: 4 Al on each side, and 6 O atoms on each side (3 × 2 on the left and 2 × 3 on the right). A longer one: C2H6 + O2 = CO2 + H2O balances as 2C2H6 + 7O2 → 4CO2 + 6H2O, which has 4 C, 12 H and 14 O on each side.

Common mistakes

• Changing a subscript instead of a coefficient. Writing Al2O3 as AlO to fix the count changes the substance.
• Mixing up upper and lower case. Co is cobalt but CO is carbon monoxide. The capital letter starts a new element symbol.
• Leaving out a product. If the equation cannot be balanced, a product or reactant may be missing. Check the reaction before changing anything.

Sources and related calculators

Method: OpenStax Chemistry 2e, chapter 4, section 4.1 (Writing and Balancing Chemical Equations), with the matrix method from linear algebra. Related: molar mass calculator, percent yield calculator and average atomic mass calculator.