What balancing actually means
A chemical equation is a sentence written in formulas: reactants on the left, an arrow, and products on the right. Balancing it means choosing the numbers in front of each formula (the coefficients) so that every element appears the same number of times on both sides. The tool above lets you set those coefficients with − and + steppers and watch a live atom tally check your work, element by element. It is free to embed on your own site or LMS.
Why it has to balance: conservation of mass
Atoms are not created or destroyed in an ordinary chemical reaction; they are only rearranged into new combinations. This is the law of conservation of mass. If you start with two hydrogen atoms and one oxygen atom, you must end with exactly two hydrogen atoms and one oxygen atom; they have simply been reassembled into a water molecule. So when the count of an element differs between the two sides, the equation is describing an impossible reaction. The atom tally turns this rule into something you can see: each element gets a row, and a row that doesn’t match is flagged until you fix it.
Coefficients vs. subscripts
This is the distinction students trip on most. A subscript is part of the formula itself: the 2 in water (H₂O) says each molecule has two hydrogen atoms. You must never change it to balance an equation, because H₂O₂ is hydrogen peroxide, a different substance entirely. A coefficient is the number in front, and it multiplies the whole formula: 2 H₂O means two water molecules, or four H atoms and two O atoms in total. You balance an equation by adjusting coefficients only.
A worked example: burning methane
Take the combustion of methane, CH₄ + O₂ → CO₂ + H₂O. Start every coefficient at 1 and the tally is off: the left has 4 hydrogen atoms but the right has only 2, and oxygen doesn’t match either. Balance carbon first: one C on each side, so CH₄ and CO₂ are fine. Next hydrogen: 4 on the left, so put a 2 in front of water to get 2 H₂O, giving 4 H atoms on the right. Now count oxygen on the right: 2 from CO₂ plus 2 from 2 H₂O is 4, so put a 2 in front of O₂. The balanced equation is CH₄ + 2 O₂ → CO₂ + 2 H₂O: carbon, hydrogen, and oxygen all match. Try it in the tool, or hit Show me to reveal the answer for any reaction.
How to balance by inspection
For anything you will meet in a school course, this order works:
- Start with an element that appears in only one substance on each side. Carbon and hydrogen in a combustion reaction are usually the ones.
- Balance it by changing a coefficient, never a subscript.
- Move on to the next element, and expect earlier ones to go out of step. Fix them and keep going; it settles.
- Leave free elements until last. O₂, H₂, Cl₂ and the like appear on their own, so they can absorb whatever is left over without disturbing anything.
- Scale down at the end. If every coefficient shares a factor, divide it out: 4, 2, 4 is the same equation as 2, 1, 2, and the smaller set is the answer.
Take C₃H₈ + O₂ → CO₂ + H₂O. Carbon first: three on the left, so 3 CO₂. Hydrogen next: eight on the left, so 4 H₂O. That fixes the oxygen on the right at 6 + 4 = 10, and O₂ carries two atoms each, so 5 O₂. The answer is C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O.
Balance your own equation
Pick Type your own equation in the menu above and write it the way you would
on paper, like C3H8 + O2 -> CO2 + H2O. Any of ->, =, → will do as the
arrow, coefficients are optional, and spaces do not matter.
The atom tally then works on your equation exactly as it does on the stored ones, so you can still balance it yourself with the steppers. Show me solves it, using linear algebra rather than trial and error: each element gives one equation and each substance is one unknown, so the coefficients are the smallest whole numbers that make every element cancel at once. That method does not care how awkward the equation is, which is why it handles 2 KMnO₄ + 16 HCl → 2 KCl + 2 MnCl₂ + 8 H₂O + 5 Cl₂ as easily as water.
One thing it will not do is guess at capital letters. co could be Co,
cobalt, or CO, carbon monoxide, and those balance to different answers, so
when a formula is ambiguous it asks instead of picking. When there is only one
sensible reading it offers it back to you as a suggestion.
Balanced equations for 13 common reactions
The widget starts every coefficient at 1 on purpose, because working it out is the point. Here are the answers for when you want to check one.
| Reaction | Balanced equation | Type |
|---|---|---|
| Formation of water | 2 H₂ + O₂ → 2 H₂O | Synthesis |
| Haber process (ammonia) | N₂ + 3 H₂ → 2 NH₃ | Synthesis |
| Formation of table salt | 2 Na + Cl₂ → 2 NaCl | Synthesis |
| Burning magnesium | 2 Mg + O₂ → 2 MgO | Synthesis |
| Electrolysis of water | 2 H₂O → 2 H₂ + O₂ | Decomposition |
| Decomposition of limestone | CaCO₃ → CaO + CO₂ | Decomposition |
| Decomposition of hydrogen peroxide | 2 H₂O₂ → 2 H₂O + O₂ | Decomposition |
| Zinc in hydrochloric acid | Zn + 2 HCl → ZnCl₂ + H₂ | Single replacement |
| Iron in copper(II) sulfate | Fe + CuSO₄ → FeSO₄ + Cu | Single replacement |
| Silver nitrate + sodium chloride | AgNO₃ + NaCl → AgCl + NaNO₃ | Double replacement |
| Acid–base neutralization | HCl + NaOH → NaCl + H₂O | Double replacement |
| Burning methane | CH₄ + 2 O₂ → CO₂ + 2 H₂O | Combustion |
| Burning propane | C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O | Combustion |
Where balancing leads next
Once an equation is balanced, the coefficients become a recipe in moles: they tell you the ratio in which substances react and form. That ratio is the foundation of stoichiometry, where balanced equations let you predict how much product a reaction makes. The shape of the equation also reveals its category (synthesis, decomposition, replacement, or combustion) which you can explore in reaction types. And if you want to see the molecules behind the formulas, build them atom by atom in the Molecule Builder.