Chemical Equation Balancer

Type a chemical equation and get the smallest whole-number coefficients that balance it. For example, Fe + O₂ = Fe₂O₃ balances to 4Fe + 3O₂ → 2Fe₂O₃. Each step of the algebra method is shown, with an atom count check and a mass check.

How to use the chemical equation balancer

1. Type the reactants, an equals sign or arrow, then the products. Separate substances with +.
2. Write formulas with capital letters for element symbols: CO₂ is CO2, cobalt is Co.
3. For ions, add the charge after a caret, such as Fe^3+ or SO4^2-. Use e for electrons in half-reactions.
4. Press Balance. You get the balanced equation, the coefficients, the algebra steps, an atom count for each element and a mass check.

How balancing works: the algebra method

A balanced equation has the same number of atoms of every element on both sides (and the same total charge for ionic equations). Give each substance an unknown coefficient and write one equation per element.

For \(a\,\mathrm{Fe} + b\,\mathrm{O_{2}} \rightarrow c\,\mathrm{Fe_{2}O_{3}}\):

• Iron: \(a = 2c\)
• Oxygen: \(2b = 3c\)

Set \(c = 1\): then \(a = 2\) and \(b = \frac{3}{2}\). Multiply every coefficient by 2 to clear the fraction: \(a = 4,\ b = 3,\ c = 2\). The balanced equation is \(4\,\mathrm{Fe} + 3\,\mathrm{O_{2}} \rightarrow 2\,\mathrm{Fe_{2}O_{3}}\).

The calculator solves the same system exactly with fractions (it finds the null space of the element matrix), so it works for long equations where trial and error is slow.

Worked example: combustion of propane

\(a\,\mathrm{C_{3}H_{8}} + b\,\mathrm{O_{2}} \rightarrow c\,\mathrm{CO_{2}} + d\,\mathrm{H_{2}O}\)

With \(a = 1\): \(\mathrm{C_{3}H_{8}} + 5\,\mathrm{O_{2}} \rightarrow 3\,\mathrm{CO_{2}} + 4\,\mathrm{H_{2}O}\). Check: 3 C, 8 H and 10 O on each side.

Balancing by inspection (by hand)

1. Start with the element that appears in the fewest substances, usually a metal.
2. Balance hydrogen and oxygen last, since they often appear in several substances.
3. Treat a polyatomic ion that stays together (like SO₄) as one unit.
4. If you end with a fraction, multiply every coefficient by its denominator.
5. Never change subscripts: that would change the substance itself.

Ionic and redox equations

For equations with ions, charge must balance as well as atoms. The calculator adds a charge equation to the system. In the permanganate–iron(II) reaction, the total charge on each side is +17:

\(\mathrm{MnO_{4}}^{-} + 5\,\mathrm{Fe}^{2+} + 8\,\mathrm{H}^{+} \rightarrow \mathrm{Mn}^{2+} + 5\,\mathrm{Fe}^{3+} + 4\,\mathrm{H_{2}O}\)

For a half-reaction, include electrons as e, for example Cr2O7^2- + H^+ + e = Cr^3+ + H2O.

Common mistakes

• Changing subscripts instead of coefficients.
• Lowercase symbols: co2 is not carbon dioxide; type CO2.
• Forgetting diatomic elements: oxygen gas is O2, hydrogen H2, nitrogen N2, chlorine Cl2.
• Leaving coefficients that share a factor: 2H2 + 2O2 … should be reduced to the smallest whole numbers.
• An element on only one side: then the equation cannot balance; a formula is wrong or a product is missing.

Balancing chemical equations quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you balance a chemical equation?

Give each substance a coefficient, count the atoms of each element on both sides, and choose coefficients so every element (and the total charge, for ions) is equal on both sides. Use the smallest whole numbers.

Can this balancer handle ions and redox reactions?

Yes. Write charges after a caret, like Fe^3+ or MnO4^-, and electrons as e. The calculator balances charge along with the atoms.

Why can my equation not be balanced?

Usually a formula is wrong or a substance is missing: an element appears on only one side, or the only solution needs a coefficient of zero. Check the formulas and the products.

Do I type subscripts?

Type them as plain numbers after the element or bracket: H2SO4, Ca(OH)2, Fe2(SO4)3. Hydrates use * or ·, like CuSO4*5H2O.

What does the mass check show?

The total molar mass of the reactants equals that of the products, which shows the law of conservation of mass for the balanced equation.

Sources

• OpenStax Chemistry 2e: Writing and Balancing Chemical Equations
• IUPAC CIAAW: Standard atomic weights
• PubChem Periodic Table of Elements

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