Chemical Equation Balancer
Balance any chemical equation with the smallest whole-number coefficients. It solves the atom balance exactly, handles ions and electrons, and tells you when an equation can’t be balanced or has more than one answer.
How to Use
- Type the equation with
=or->between the two sides, for exampleFe + O2 = Fe2O3. Element symbols are case-sensitive: Co is cobalt, CO is carbon monoxide. - Write charges after the formula:
Fe3+,SO4^2-,MnO4-, and electrons ase-. Hydrates take a dot:CuSO4.5H2O. - Keep Balance selected to get the smallest whole-number coefficients, or choose Check to test coefficients you have written yourself.
- Read the balanced equation and the coefficients; the picture shows the atoms of each element on each side.
- Show Work gives the balance equation for every element, the exact solution and a before-and-after atom table.
Fe3+ SO4^2- MnO4- · electrons: e- · hydrates: CuSO4.5H2O · put spaces round the + between ions: Fe3+ + e-Worked Example
Iron rusting: Fe + O2 → Fe2O3. Call the coefficients a, b and c. Iron: a = 2c. Oxygen: 2b = 3c. Put c = 1, so a = 2 and b = 3/2, then multiply everything by 2 to clear the fraction: 4Fe + 3O2 → 2Fe2O3. Check: 4 iron and 6 oxygen atoms on each side, and 319.37 g on each side for these mole amounts.
Chlorine from permanganate: KMnO4 + HCl → KCl + MnCl2 + H2O + Cl2. Five elements give five equations in six unknowns: K: a = c, Mn: a = d, O: 4a = e, H: b = 2e, Cl: b = c + 2d + 2f. With f = 1 the exact solution is a = 2/5, b = 16/5, c = 2/5, d = 2/5, e = 8/5; multiplying by 5 gives 2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2, with 16 chlorine atoms on each side.
The common mistake: balancing with subscripts. H2 + O2 → H2O has 2 oxygen atoms on the left and 1 on the right. Changing the product to H2O2 makes the count 2 = 2, but that is hydrogen peroxide. The right fix changes coefficients only: 2H2 + O2 → 2H2O, with 4 hydrogen and 2 oxygen atoms on each side.
Show Work
Formulas
From Lavoisier’s Scales to Linear Algebra
Balancing rests on the conservation of mass, which Antoine Lavoisier set out in his Traité élémentaire de chimie of 1789 after careful weighing of reactions in closed vessels. John Dalton’s atomic theory, published in A New System of Chemical Philosophy from 1808, explained why: atoms are neither created nor destroyed, only rearranged, so every element must count the same on both sides.
The letter symbols we use come from Jöns Jacob Berzelius, who proposed them in 1813. He wrote the counts as superscripts (H²O); the subscripts used today came later. Balancing by inspection works for small equations, but an equation is just a set of linear equations in the coefficients, and treating it that way, as this tool does, also proves when no balance or more than one balance exists.
About This Tool
This balancer writes one equation per element, plus one for charge when ions or electrons are present, and solves them exactly with whole-number fractions, so there is no rounding at any point. A unique answer is scaled to the smallest whole numbers. When no positive answer exists it says why, and when several independent answers exist it lists them and the smallest valid mixes instead of picking one at random.
Check mode tests coefficients you have written yourself and tells you whether they are balanced and whether they reduce. Everything runs in your browser; nothing is sent anywhere.
Related tools: Stoichiometry & Limiting Reagent Calculator, Molar Mass Calculator, and Ideal Gas Law Calculator.
Frequently Asked Questions
How do you balance a chemical equation?
Give each formula an unknown coefficient and require every element to have the same count on both sides. For a Fe + b O2 → c Fe2O3, iron gives a = 2c and oxygen gives 2b = 3c. Setting c = 1 gives a = 2 and b = 3/2; multiplying by 2 clears the fraction: 4Fe + 3O2 → 2Fe2O3.
Why can’t I change the subscripts to balance it?
Subscripts say what the substance is. Changing H2 + O2 → H2O into H2 + O2 → H2O2 makes the atoms match, but H2O2 is hydrogen peroxide, not water. Only the coefficients in front may change: 2H2 + O2 → 2H2O.
How do I balance an ionic or redox equation?
Type the charges and the tool adds a charge balance to the atom balances. MnO4- + Fe2+ + H+ = Mn2+ + Fe3+ + H2O balances to MnO4- + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O, with a total charge of +17 on each side. Electrons are written e-: Cu2+ + 2e- → Cu.
What does “no unique answer” mean?
The atoms can be balanced in more than one independent way, so the equation is really two reactions added together. H2 + O2 = H2O + H2O2 hides 2H2 + O2 → 2H2O and H2 + O2 → H2O2; any mix of the two, such as 3H2 + 2O2 → 2H2O + H2O2, balances. The chemistry, not the algebra, decides which happens.
Why does it say my equation can’t be balanced?
Because no positive coefficients work. For H2O = H2O2, hydrogen needs 2a = 2b and oxygen needs a = 2b, which only a = b = 0 satisfies. An element on one side only, such as nitrogen in H2 + O2 = H2O + N2, can never balance either. Check the formulas and look for a missing species.
How do I use the Chemical Equation Balancer?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Combustion
Propane burns as C3H8 + 5O2 → 3CO2 + 4H2O: 44.10 g of propane takes 159.99 g of oxygen and gives 132.03 g of CO2.
Rusting iron
4Fe + 3O2 → 2Fe2O3: four iron atoms take three O2 molecules, and 223.38 g of iron becomes 319.37 g of rust.
Making chlorine
2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2: two moles of permanganate free five moles of chlorine.
Redox titrations
In MnO4- + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O one permanganate ion oxidises five iron(II) ions, the 1 : 5 ratio a titration uses.
Copper in nitric acid
3Cu + 8HNO3 → 3Cu(NO3)2 + 2NO + 4H2O: only 2 of the 8 nitric acid molecules are reduced to NO.
Photosynthesis
6CO2 + 6H2O → C6H12O6 + 6O2: one glucose molecule for every six carbon dioxide molecules.
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