Chemical equation balancer

A chemical equation balancer finds the numbers to put in front of each formula so that every element has the same number of atoms on both sides. Propane burning, C₃H₈ + O₂ → CO₂ + H₂O, balances as C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. Our Equation Balancer balances molecular, ionic and half equations, shows the atom counts before and after, and writes out the algebra it used.

It opens on propane burning. Type your own equation, or build it from element and compound tiles underneath the box.

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Equation Balancer

Balance chemical and ionic equations with the working shown

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How to use the chemical equation balancer

1. Type the unbalanced equation in the Equation box, with + between species and -> or = for the arrow, such as Al + O2 -> Al2O3. Or press Build it with tiles to pick elements and compounds.
2. Write charges after the formula, such as Fe3+ or SO4^2-, and e- for an electron. Brackets and hydrates such as CuSO4.5H2O work too.
3. Read the balanced equation, with the smallest whole numbers.
4. Check the atom count table, which lists each element (and the charge, for ions) on the left and right, before and after balancing.
5. Follow the working: each species gets an unknown, each element gives one equation, and the equations are solved together.

Starting points in the sidebar include the Haber process, the blast furnace and a manganate(VII) ionic equation. If an equation cannot balance, the calculator says why, such as an element that appears on one side only. Practice and help sets random equations to balance.

How to balance a chemical equation by hand

Atoms are not made or destroyed in a reaction, so each element must have the same count on both sides. You may only change the numbers in front of formulas, never the small numbers inside them: changing H₂O to H₂O₂ makes a different substance.

1. Write the unbalanced equation with correct formulas.
2. Count the atoms of each element on each side.
3. Balance one element at a time, starting with one that appears in only one species on each side. Leave hydrogen, oxygen and lone elements, such as O₂ or Fe, until last.
4. Recount everything. If you end with a fraction, multiply every number through to clear it.
5. Check the numbers are the smallest whole-number set.

Worked examples you can check in the balancer

Example 1: burning ethane

Balance C₂H₆ + O₂ → CO₂ + H₂O. Carbon first: 2 C on the left, so 2CO₂. Hydrogen next: 6 H, so 3H₂O. Now the right has 2 × 2 + 3 = 7 O, which needs 3½ O₂. Double everything to clear the half:

Type C2H6 + O2 -> CO2 + H2O. The balancer gives 2, 7, 4 and 6, and its atom table matches the one above.

Example 2: the algebra method the balancer uses

For the same equation, give each species an unknown: aC₂H₆ + bO₂ → cCO₂ + dH₂O. Each element gives one equation:

Set d = 1, solve, and you get a = 1/3, b = 7/6 and c = 2/3. Multiply by 6 to clear the fractions: a = 2, b = 7, c = 4, d = 6. These are the steps the balancer shows in its working. The method always works, even for equations that are hard to balance by inspection.

Example 3: brackets

Balance Al₂(SO₄)₃ + NaOH → Al(OH)₃ + Na₂SO₄. Treat the sulfate group as one unit: 3 SO₄ on the left needs 3Na₂SO₄, so 6 Na, so 6NaOH, and the 2 Al need 2Al(OH)₃:

The balancer gives 1, 6, 2 and 3. It reads the brackets, so you do not need to expand them.

Try one:

Ionic equations and half equations

For an ionic equation, the charge must balance as well as the atoms. The balancer adds charge as one more row in its table. The manganate(VII) and iron(II) reaction in acid balances as:

Check the charge: 1− + 10+ + 8+ = 17+ on the left, and 2+ + 15+ = 17+ on the right. Half equations work the same way, with e- for electrons. Type Cr2O72- + H+ + e- -> Cr3+ + H2O and the balancer gives Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O, with 6 electrons taking the charge from 12+ to 6+.

When an equation will not balance

The last case is really two reactions added together, so atom counts alone cannot pick one answer. The balancer gives the smallest set, 3H₂ + 2O₂ → H₂O₂ + 2H₂O, and says that for a redox reaction you need oxidation numbers or half equations to decide.

Oxidation numbers

The balancer does not work out oxidation numbers. Find them by hand with a few rules: an element on its own is 0, oxygen is usually −2, hydrogen is usually +1, and the numbers in a compound add up to its charge. In MnO₄⁻, 4 × (−2) = −8, so Mn must be +7 for the total to be −1. Our oxidation numbers guide covers every rule with worked examples.

What the balancer does not do

• It does not predict products. You need to type both sides. It balances the equation you give it, so a wrong product gives a balanced but wrong equation.
• Formulas only. A word equation such as sodium + water has to be turned into formulas first: Na + H2O -> NaOH + H2.
• It does not add state symbols. Type them, as in Mg(s) + HCl(aq), and it keeps them in the answer.

Common mistakes

• Changing the small numbers. Only change the numbers in front. H₂O and H₂O₂ are different substances.
• Leaving a fraction. 3½O₂ is fine as a step, but a final answer needs whole numbers.
• Forgetting the charge in ionic equations. Atoms can balance while the charge does not.
• Not simplifying. 4H₂ + 2O₂ → 4H₂O balances, but the answer is 2H₂ + O₂ → 2H₂O.
• Miscounting brackets. In Ca(OH)₂ there are 2 O and 2 H, and in Ca₃(PO₄)₂ there are 8 O.

Practise balancing equations in a short timed paper

Balanced symbol equations come up in High School Chemistry practice, and ionic and redox equations in Honors Chemistry. In the UK they appear in GCSE Chemistry Higher and A-level Chemistry: Year 1. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. To work out masses from a balanced equation, use the Stoichiometry Calculator.

Read next

Chemistry · Reactions and electrolysisIonic equations: how to write them, with examplesWhat an ionic equation is, how to write one in four steps by removing spectator ions, and examples for neutralisation, precipitation and displacement.