Chemical Equation Balancer: 5 Free Modes, Redox & Ionic

A chemical equation balancer takes the skeleton equation you type — Fe + O₂ → Fe₂O₃, say — and returns the smallest whole-number coefficients that make every element (and, for ions, the charge) equal on both sides. It does in a fraction of a second what takes a careful student a minute of counting, and it never forgets an oxygen atom. The one above also shows you why the answer is right: the atom-count table, the algebra behind the coefficients, the molar masses and a proof that the total mass of reactants equals the total mass of products.

The free chemical equation balancer on this page works in five modes: a general balancer for molecular equations with an optional amount-to-moles conversion, an ionic balancer that treats charge as one more element, a redox balancer that writes out both half-reactions in acidic or basic solution, a checker that grades an equation you balanced yourself and names the reaction type, and a combustion writer that gives the oxygen demand and air-fuel ratio of any fuel.

This guide explains what balancing means and why it is non-negotiable, walks through the inspection method and the algebraic method, works the classic examples in full, covers ionic and redox equations (including the basic-solution trick everybody forgets), and ends with a 30-equation reference table, ten practice problems, an exam checklist and the questions students ask most.

What Is a Chemical Equation Balancer?

A chemical equation is a recipe written in formulas: reactants on the left, products on the right, an arrow between them. A balanced chemical equation is one in which the number of atoms of every element is the same on both sides, because atoms are neither created nor destroyed in a chemical change. A chemical equation balancer is a tool that finds the coefficients — the numbers in front of each formula — that make this true.

The need arises because formulas are fixed by nature but proportions are not. Water is always H₂O; you cannot write H₂O₂ to make oxygen come out even, because that is a different compound. What you can change is how many molecules of each substance take part, and that is all a coefficient says: 2H₂ + O₂ → 2H₂O means two molecules (or moles) of hydrogen react with one of oxygen to give two of water.

A good chemical equation balancer therefore does three things. It reads formulas correctly, including parentheses such as Ca₃(PO₄)₂ and hydrates such as CuSO₄·5H₂O. It solves for coefficients that balance every element simultaneously and reduces them to the smallest whole numbers. And it proves the result, by counting atoms and by showing that the total mass on each side is identical.

How to Use the Chemical Equation Balancer

Using the chemical equation balancer takes about ten seconds:

1. Pick a mode. Most homework equations belong in Balance Any Equation. Use Ionic Equation if your species carry charges, Redox if you have been told to use half-reactions, Check & Classify to grade your own attempt, and Combustion when a fuel burns in oxygen.
2. Type the skeleton equation. Use -> or = for the arrow and + between species. Subscripts are plain digits (Fe2O3). State symbols such as (s), (aq) are ignored. Charges are written Fe3+, Fe^3+, SO4^2- or NO3-.
3. Optionally add an amount. In mode 1 you can type, for example, Fe2O3 100 g, and the tool converts that into moles and grams of every other species — a stoichiometry answer in the same click.
4. Read the result. The balanced equation appears in blue, followed by the coefficients, the atom-count table, the algebra steps and the mass check. A bar chart shows the atoms of each element on each side.
5. Copy, download or share. The toolbar exports the working as text or CSV, prints a report, or shares it. The last ten results stay in the history box; each mode has its own Reset.

The example chips under every input are pre-loaded equations — the KMnO₄ + HCl redox, the phosphorus furnace, dichromate and iodide in acid — that show the chemical equation balancer handling the awkward cases you meet in exams.

The Five Modes Explained

All five modes share the same engine: exact-fraction Gaussian elimination over one equation per element. That is why the chemical equation balancer never returns a “close enough” answer — the coefficients are integers or the equation is reported as unbalanceable, with a reason.

The Rules of Balancing

Every method, by hand or by chemical equation balancer, obeys the same four rules.

The chemical equation balancer enforces rule 4 automatically, dividing the coefficients by their greatest common divisor, and mode 4 will tell you when your own answer shares a common factor.

Worked Example: Fe + O₂ → Fe₂O₃ Step by Step

Rusting, written as a skeleton: Fe + O₂ → Fe₂O₃. Here is what the chemical equation balancer does, in the order a person would.

Notice the loop: fixing oxygen disturbed iron, which had to be revisited. That is normal. The algebraic method the chemical equation balancer uses avoids the loop by solving all the constraints at once, which is the next topic after the inspection method.

Balancing by Inspection: A Reliable Order

“Inspection” is the trial-and-error method taught first, and with the right order it is not really trial and error at all. Work through the elements in this sequence and most equations fall into place:

1. Metals that appear in only one compound on each side (Fe, Al, Ca …).
2. Non-metals other than H and O (S, P, Cl, N …); treat a polyatomic ion that stays intact (SO₄, PO₄, NO₃) as a single unit.
3. Hydrogen.
4. Oxygen last, because it usually appears in the most places and O₂ as a free element gives you a coefficient that can absorb any even number.
5. If you end up with an odd number of oxygen atoms facing O₂, double everything and finish.

Example: Al + H₂SO₄ → Al₂(SO₄)₃ + H₂. Aluminium: 2Al. Sulfate as a unit: three on the right, so 3H₂SO₄. Hydrogen: 6 on the left, so 3H₂. Done: 2Al + 3H₂SO₄ → Al₂(SO₄)₃ + 3H₂. The chemical equation balancer reports exactly this, and mode 4 will confirm your inspection answer in one click.

Inspection breaks down when an element appears in three or more species on one side, or when two elements change together in a redox reaction (Cu + HNO₃, KMnO₄ + HCl). For those, use the algebraic method or the half-reaction method.

The Algebraic (Matrix) Method the Balancer Uses

Give each species an unknown coefficient and write one equation per element. For a·Fe + b·O₂ → c·Fe₂O₃:

In matrix language the element-by-species table is a matrix whose null space contains the coefficient vector. The chemical equation balancer builds that matrix (with products entered as negatives), row-reduces it with exact fractions so nothing is lost to rounding, reads off the free variable, scales to integers with a least common multiple and divides by the greatest common divisor. Charge, when present, is simply one more row.

Three outcomes are possible, and the chemical equation balancer reports each honestly:

• One free variable — a unique balanced equation. The normal case.
• No free variable — the only solution is all zeros. The formulas are inconsistent (for example a product containing an element no reactant has), and the tool says so.
• Two or more free variables — the “equation” is really two independent reactions added together (H₂ + O₂ → H₂O + H₂O₂; the aspirin synthesis with acetic acid as by-product). There is no unique answer, so the balancer asks you to supply coefficients, which it then verifies, or to split the reaction.

This is why the algebraic method is the one professionals trust: it cannot get stuck in a loop and it tells you when the question itself is ill-posed.

More Worked Examples

Four equations of increasing difficulty, each verified with the chemical equation balancer.

Other results from the chemical equation balancer that appear in the reference table below: 4NH₃ + 5O₂ → 4NO + 6H₂O (the Ostwald process), 4FeS₂ + 11O₂ → 2Fe₂O₃ + 8SO₂ (pyrite roasting) and C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O (respiration).

Ionic Equations and Charge Balance

In solution, many reactions are best written with only the ions that change. A net ionic equation must balance atoms and charge, and the chemical equation balancer treats charge as one more conservation law — one more row in the matrix.

Take permanganate oxidising iron(II) in acid: MnO₄⁻ + Fe²⁺ + H⁺ → Mn²⁺ + Fe³⁺ + H₂O. Atoms alone give Mn 1 = 1, O 4 = 4H₂O, H 8 = 8, but the iron coefficient is not fixed by atoms — any number of Fe²⁺ becoming the same number of Fe³⁺ balances iron. Charge fixes it: left = −1 + 2n + 8, right = +2 + 3n; equal when n = 5. Result: MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O, net charge +17 on each side.

The last row shows that electrons can be typed as a species (e-). The chemical equation balancer then balances a half-reaction directly and reports how many electrons are gained or lost, which is the number you need for the equivalent weight of an oxidising agent or the normality of its solution. If you are unsure of an oxidation state, the oxidation number calculator will assign it.

Redox: The Half-Reaction Method

Examiners often insist on the half-reaction (ion-electron) method for redox equations, and mode 3 of the chemical equation balancer reproduces it line by line. The procedure in acidic solution:

1. Split the skeleton into an oxidation half and a reduction half.
2. In each half, balance the element other than H and O.
3. Balance oxygen by adding H₂O.
4. Balance hydrogen by adding H⁺.
5. Balance charge by adding electrons (e⁻) to the more positive side.
6. Multiply the halves so the electrons are equal, add them, cancel anything common to both sides.

Hydrogen peroxide and permanganate in acid, H₂O₂ + MnO₄⁻ → O₂ + Mn²⁺, as the chemical equation balancer writes it:

The tool also names the oxidising agent (the species reduced, MnO₄⁻) and the reducing agent (H₂O₂), and reports the electrons transferred per mole of reaction — the number that converts a molarity into a normality and fixes the mole ratio in any redox titration. Other acidic examples verified with the chemical equation balancer: Cu + 2NO₃⁻ + 4H⁺ → Cu²⁺ + 2NO₂ + 2H₂O; 4Zn + NO₃⁻ + 10H⁺ → 4Zn²⁺ + NH₄⁺ + 3H₂O; IO₃⁻ + 5I⁻ + 6H⁺ → 3I₂ + 3H₂O.

Balancing in Basic Solution

In basic solution there is no free H⁺, so after balancing as if in acid you add enough OH⁻ to both sides to neutralise every H⁺, combine H⁺ + OH⁻ into H₂O, and cancel water that now appears on both sides. Selecting Basic in mode 3 makes the chemical equation balancer do this automatically and show the extra line.

Permanganate oxidising iodide in base, MnO₄⁻ + I⁻ → MnO₂ + I₂: the reduction half in acid is MnO₄⁻ + 4H⁺ + 3e⁻ → MnO₂ + 2H₂O; add 4OH⁻ to each side and cancel two waters to get MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻. Combine with 2I⁻ → I₂ + 2e⁻ (electrons 6): 2MnO₄⁻ + 6I⁻ + 4H₂O → 2MnO₂ + 3I₂ + 8OH⁻.

Disproportionation (the same species oxidised and reduced, as with Cl₂) is handled by the chemical equation balancer by splitting the reactant into two half-reactions, one to each product.

Reference Table: 30 Common Equations Balanced

Every equation below was produced by the chemical equation balancer. Use the table to check homework quickly or to build practice sets.

Combustion Equations and Air-Fuel Ratio

Combustion equations have a fixed pattern — fuel + O₂ → CO₂ + H₂O (+ N₂ or SO₂ if the fuel contains N or S) — so mode 5 of the chemical equation balancer only asks for the fuel formula. For a hydrocarbon C_xH_yO_z the oxygen coefficient is x + y/4 − z/2; if that is not a whole number the equation is doubled.

Air is taken as 23.2 % oxygen by mass, so the air-fuel ratio is the oxygen mass divided by 0.232. The chemical equation balancer prints both figures, along with the CO₂ emitted per kilogram of fuel, which is why the same mode is useful for a carbon-footprint estimate. For the reverse problem — deducing a formula from combustion products — use the combustion analysis calculator.

Classifying the Reaction

Once an equation is balanced, mode 4 of the chemical equation balancer names the reaction type using the standard school scheme:

The categories overlap — every combustion and single displacement is also a redox reaction — so the chemical equation balancer reports the most specific label that fits and notes when a reaction is also redox. Rusting, for example, is a synthesis that is also an oxidation of iron.

From Balanced Equation to Stoichiometry

The reason balancing matters is that the coefficients are mole ratios. Once 4Fe + 3O₂ → 2Fe₂O₃ is in hand, “how much oxygen does 100 g of iron need?” is three lines: 100 g ÷ 55.845 g/mol = 1.791 mol Fe; × 3/4 = 1.343 mol O₂; × 31.998 g/mol = 42.98 g O₂. Type Fe 100 g in mode 1 and the chemical equation balancer prints that, plus the 142.97 g of Fe₂O₃ produced, in the same table.

For fuller treatment — limiting reagents, percent yield, excess reactant — the balanced equation feeds straight into the stoichiometry calculator, the limiting reactant calculator, the theoretical yield calculator and the percent yield calculator. The molar masses the chemical equation balancer uses come from the same IUPAC 2021 table as the molecular weight calculator on the home page.

Who Uses a Chemical Equation Balancer

• Students from grade 9 to first-year university, for whom balancing is the gateway to stoichiometry and the single most-tested skill in introductory chemistry.
• Teachers and tutors who build worksheets and need a trustworthy answer key with the working shown.
• Analytical chemists writing redox titration equations, where the electron count fixes the mole ratio between titrant and analyte.
• Process and combustion engineers who need oxygen demand, air-fuel ratios and flue-gas composition from a fuel formula.
• Environmental scientists computing CO₂ per kilogram of fuel or the stoichiometric oxygen demand of a waste stream.
• Anyone writing a report who wants an equation checked before it is printed.

For all of these, the chemical equation balancer removes the counting error and leaves the chemistry.

Full Walkthrough: A Homework Problem

“Balance the equation for the reaction of potassium dichromate with iodide ions in acidic solution, identify the oxidising and reducing agents, and state how many moles of iodine form per mole of dichromate.”

Typing the skeleton into mode 3 of the chemical equation balancer with Acidic selected reproduces every line above, and the “6 e⁻” is also the n-factor you would use in a normality calculation for dichromate.

A Short History of the Balanced Equation

Balancing rests on the law of conservation of mass, established by Antoine Lavoisier in the 1780s with carefully weighed sealed-vessel experiments. Dalton’s atomic theory (1803–1808) explained why mass is conserved — atoms are rearranged, not made or lost — and Berzelius introduced the letter symbols and subscripts we still use around 1813. Once formulas were fixed, the equation with coefficients followed naturally, and by the mid-nineteenth century the arrow notation and the practice of balancing were standard in textbooks.

The algebraic method dates to at least the 1870s, and the matrix formulation was worked out fully in the twentieth century; it became the obvious approach once computers could row-reduce a matrix instantly. That is the lineage of every chemical equation balancer online today, including this one.

Limits: When an Equation Cannot Be Balanced

A chemical equation balancer is only as good as the skeleton it is given. It will return an error, rather than a wrong answer, in these cases:

• An element on one side only. Na + H₂O → NaOH (hydrogen has nowhere to go). Add the missing product, H₂.
• Wrong formula. Mg + O₂ → MgO₂ balances trivially but MgO₂ is not magnesium oxide. A balancer cannot know your chemistry; check formulas with the formula weight calculator first.
• Two independent reactions written as one. The null space has two dimensions and there is no unique answer. The chemical equation balancer asks for your coefficients and verifies them.
• Charges that do not add up. An ionic skeleton that cannot be charge-balanced with the species given usually needs H⁺, OH⁻ or H₂O added — which is exactly what mode 3 does for you.
• Nuclear equations. Balancing mass and atomic numbers is a different problem; this tool is for chemical reactions.

Practice Problems With Answers

Try each by hand, then check with the chemical equation balancer. Answers are hidden below the question.

Tips for Accurate Results

• Write the formulas first, then balance. Ninety percent of “impossible” equations are formula errors, not balancing errors.
• Keep polyatomic ions whole when they appear unchanged on both sides — count SO₄, not S and O separately.
• Leave free elements (O₂, H₂, Cl₂) for last. Their coefficient can be anything without disturbing another element.
• For redox, count electrons. The number of electrons lost must equal the number gained; if your overall equation balances atoms but not charge, the electrons are wrong.
• Reduce. Divide by any common factor. The chemical equation balancer does this automatically and mode 4 warns you if you did not.
• Check mass. Total molar mass left = total molar mass right. It takes twenty seconds and catches everything.

Common Mistakes

Mode 4 of the chemical equation balancer catches the first four automatically, telling you which element or the charge is off and by how much.

How This Chemical Equation Balancer Is Different

The chemical equation balancer is one of a family of free tools on this site. The concentration set covers the molarity calculator, molality calculator, normality calculator, mole fraction calculator and ppm to ppb converter. For formulas and masses there are the atomic mass calculator, grams to moles calculator, exact mass calculator, monoisotopic mass calculator, isotopic mass calculator, average vs monoisotopic mass, molar mass of hydrates calculator, empirical formula calculator, molecular formula calculator, percent composition calculator, degree of unsaturation calculator, formal charge calculator and atom economy calculator. Physical-chemistry tools include the freezing point depression, boiling point elevation, osmotic pressure, vapor density, molar mass from gas density and van der Waals equation calculators, and for polymers the average molecular weight of a mixture, number average, weight average, polydispersity index and viscosity molecular weight tools.

Where the Numbers Come From

The chemical equation balancer uses exact rational arithmetic for the coefficients, so there is no rounding at all in the balancing step. Molar masses for the mass check and the amount conversions come from the IUPAC 2021 standard atomic weights (conventional values for elements with an interval). Definitions and methods follow the standard references:

• IUPAC Gold Book — stoichiometric number: the formal definition of the coefficients in a balanced equation.
• OpenStax Chemistry via LibreTexts — Writing and Balancing Chemical Equations: the inspection method, ionic equations and the half-reaction method.
• CIAAW — Standard Atomic Weights: the atomic weights behind every molar mass on this site.
• Wikipedia — Chemical equation: notation, history and the matrix method of balancing.

Found an error? Our corrections policy explains how we handle reports; contact us or read about the site.

Exam Checklist

Frequently Asked Questions

10 Facts Worth Knowing

1. Lavoisier’s balance experiments in the 1780s established that mass is conserved — the physical law every balanced equation obeys.
2. The seven diatomic elements — H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂ — cause more balancing errors than anything else.
3. The octane equation 2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O consumes 3.5 kg of oxygen, about 15 kg of air, per kilogram of fuel.
4. The permanganate–HCl equation has coefficients summing to 35; it is the most-searched redox equation online.
5. In the matrix method, a unique balanced equation corresponds to a one-dimensional null space.
6. Photosynthesis and respiration are the same balanced equation read in opposite directions.
7. A balanced ionic equation conserves charge as well as atoms; both are stated in every result the chemical equation balancer gives.
8. The half-reaction method was popularised in the 1920s and remains the examiners’ preferred way to show redox working.
9. Doubling every coefficient never breaks a balanced equation; dividing by a common factor is what makes it conventional.
10. Every combustion of a C_xH_y hydrocarbon needs exactly x + y/4 moles of O₂ per mole of fuel.

Final Thoughts

Balancing an equation is the first place chemistry insists on being quantitative, and it stays with you through every stoichiometry, titration and yield problem afterwards. Learn the inspection order, understand why the algebraic method always works, and practise the half-reaction method until the basic-solution step is automatic.

Then use the chemical equation balancer above the way a professional uses any calculator: to check, to speed up and to see the working laid out when a question turns awkward. Type a skeleton equation, press Balance, and read the atom table and the mass proof — that is what a balanced equation looks like.