Chemical Equation Balancer with Whole-Number Coefficients
Balance a supported chemical reaction with the smallest positive whole-number coefficient ratio, or check coefficients you already entered. The result includes a species table and an element-by-element conservation check.
- Exact integer arithmetic
- Nested groups and hydrates
- Ions, charge and electrons
- Coefficient verification mode
Online Chemical Equation Balancer
Enter known reactants and products. The tool changes coefficients only. It never changes formula subscripts, invents products or decides whether a reaction occurs.
The balanced equation, coefficients, conservation totals and calculation steps will appear here.
Species Coefficients
A coefficient multiplies the complete formula unit that follows it.
| Side | Species | Coefficient |
|---|---|---|
| Waiting | — | — |
Conservation Check
Every element count must match. Net charge must also match when ionic charge or electrons are entered.
| Row | Reactants | Products | Status |
|---|---|---|---|
| Waiting | — | — | — |
Calculation Steps
- Enter reactants, one equation separator and products.
- Select balance or coefficient-check mode, then calculate.
How to Use This Chemical Equation Balancer
A standard equation usually takes less than two minutes to enter, balance and review.
- Write the reactants. Separate complete chemical formulas with plus signs.
- Add one equation separator. Use ->, =>, = or a supported Unicode arrow.
- Write the products. Keep every formula subscript unchanged.
- Mark ions clearly. Use caret notation such as Fe^3+, SO4^2- or e^- and spaces around separator plus signs.
- Choose a mode. Balance a skeleton equation or check coefficients already present.
- Calculate and inspect the tables. Review every species coefficient, element total and charge total.
- Confirm the chemistry. Check the species, states, reaction conditions and safety against your course or laboratory source.
What a Balanced Chemical Equation Means
A balanced chemical equation uses stoichiometric coefficients so the amount of every chemical element is the same on both sides. In an ionic equation, total electric charge must also be equal. These conditions reflect conservation of atoms and charge in the written reaction.
Coefficients multiply entire species. Subscripts belong to the chemical formula and identify its composition. Changing H2O to H2O2 does not balance water. It changes water into hydrogen peroxide. A valid balancing method changes the number placed before a formula, never the formula itself.
In this expression, each matrix column represents a species. Each row represents one conserved element, with an extra row for charge when needed. A reactant column uses the opposite sign from a product column. A nonzero vector in the matrix nullspace gives a coefficient ratio that makes every row sum to zero.
How the Exact Balancing Method Works
The calculator first parses each formula into exact element counts. It expands parentheses, square brackets, braces and whole-number hydrate components. It then constructs a conservation matrix from the written reactants and products.
Exact rational row reduction finds the matrix nullspace. When the nullspace has one independent direction, the calculator clears all denominators, makes the coefficient signs positive and divides every coefficient by their greatest common divisor. The result is the primitive whole-number ratio.
JavaScript decimal arithmetic is not used for the matrix. Atom counts, charges, numerators, denominators and final coefficients stay as integers through BigInt-backed rational operations. The tool verifies the final vector against the original matrix before displaying it.
Supported Chemical Formula and Equation Syntax
| Input feature | Example | Rule |
|---|---|---|
| Element symbols and subscripts | Al2O3 | Symbols are case-sensitive. ASCII or Unicode subscript digits are accepted. |
| Nested groups | K4[Fe(CN)6] | Round, square and curly brackets must match and contain a valid formula. |
| Hydrates and adducts | CuSO4·5H2O | Use a middle dot between components. A period is accepted as an ASCII input substitute and displayed as a middle dot. The component multiplier must be a positive whole number. |
| Ionic charge | Cr2O7^2- | Use a terminal caret charge. A bare final + or - means a charge magnitude of one. |
| Electrons | e^- | An electron contributes charge -1 and no element count. |
| State labels | H2O(l) | (s), (l), (g) and (aq) are preserved but do not alter atom counts. |
| Leading coefficients | 2H2 + O2 -> 2H2O | Balance mode recomputes them. Check mode uses positive whole numbers as entered. |
A leading number before a dotted formula is ambiguous. Write a reaction coefficient with a space, as in 2 CuSO4·5H2O. Encode a first-component multiplier with grouping, as in (CdSO4)3·8H2O. The unspaced form 3CdSO4·8H2O is rejected instead of being guessed.
The parser recognizes all 118 current element symbols. It does not interpret names such as water, isotope labels such as D and T, structural bonds, oxidation-state annotations, fractional formula subscripts or variables such as n. Write an explicit molecular or ionic formula.
The arrow separates the two sides but does not affect coefficient arithmetic. Choose its chemical meaning carefully. IUPAC distinguishes = for a stoichiometric relation, → for a net forward reaction, ⇆ for reaction in both directions and ⇌ for equilibrium. The balancer preserves those symbols and the general ↔ symbol.
Worked Chemical Equation Balancing Examples
Example 1: Iron and oxygen
Start with Fe + O2 → Fe2O3. The smallest coefficient vector is 4, 3, 2. The balanced equation is 4Fe + 3O2 → 2Fe2O3. Both sides contain four iron atoms and six oxygen atoms.
Example 2: Ethane combustion
For C2H6 + O2 → CO2 + H2O, carbon and hydrogen establish the product coefficients first. The exact primitive ratio is 2, 7, 4, 6. This gives four carbon atoms, twelve hydrogen atoms and fourteen oxygen atoms on each side.
Example 3: Hydrated copper sulfate
For CuSO4·5H2O → CuSO4 + H2O, the hydrate formula already contains five water units. The smallest ratio is 1, 1, 5. The dot component is part of one reactant formula, not a separate reaction species.
Balancing Ionic and Redox Equations
An ionic reaction needs both atom balance and charge balance. Enter each ionic charge explicitly. For example, the acidic redox equation Fe^2+ + Cr2O7^2- + H+ → Fe^3+ + Cr^3+ + H2O balances with coefficients 6, 1, 14, 6, 2, 7. The total charge is +24 on each side.
The calculator balances only the species you supply. It does not add H2O, H+, OH- or electrons automatically. For a half-reaction, write the required electron explicitly as e^-. The equation Fe^2+ → Fe^3+ + e^- then balances 1:1:1.
Use spaces around separator plus signs in ionic input. For example, write H^+ + OH^- -> H2O. Caret notation prevents a charge sign from being confused with the plus sign that separates two species.
Balance Mode Versus Coefficient Check Mode
Balance mode treats a leading whole number as an old or provisional coefficient. It removes that number from the matrix and calculates a new primitive ratio. This means 4H2 + 2O2 → 4H2O returns 2, 1, 2.
Coefficient check mode keeps the entered values. A species without a leading number receives coefficient 1. The table then compares every reactant total with its product total. If a balanced vector has a common factor, the page shows the reduced form of that entered ratio. If the entered values are unbalanced and the skeleton has one unique solution, the page supplies a balanced suggestion.
This distinction helps when checking homework, a laboratory procedure or a published reaction. A coefficient set can conserve atoms while still being nonprimitive. Both describe the same stoichiometric proportion, but classroom convention normally reports the smallest whole-number ratio.
Why an Equation May Not Balance
- An element appears on only one side. Check for a missing reactant, product or formula symbol.
- A formula is mistyped. Capitalization matters. CO is carbon monoxide, while Co is cobalt.
- Brackets do not match. Every opening group needs the correct closing bracket and a positive multiplier when one is written.
- Charge is missing. Ionic species with omitted charges may pass atom balance while representing the wrong equation.
- The equation is underdetermined. Duplicate, spectator or optional species can create more than one independent coefficient family.
- A species would need a zero or negative coefficient. The written species list does not form one positive reaction balance.
- The input describes separate reactions. Split independent transformations and balance each equation on its own.
A mathematical balance does not prove chemical validity. The tool cannot decide whether the stated products form, whether the arrow should be reversible, or which catalyst, solvent, temperature, pressure or electrochemical conditions are required.
Using Balanced Coefficients in Stoichiometry
Balanced coefficients give mole ratios between written species. In 2H2 + O2 → 2H2O, two moles of hydrogen correspond stoichiometrically to one mole of oxygen and two moles of water. The same 2:1:2 ratio applies to molecule counts for a molecular interpretation.
Coefficients do not directly give mass ratios. Convert each amount to moles with a suitable molar mass, apply the coefficient ratio, then convert to the desired unit. A real yield may be lower because of incomplete conversion, side reactions, transfer loss, purity, equilibrium or measurement uncertainty.
State labels and reaction conditions matter in practice even though they do not change element counts. Keep the complete sourced equation when using a balanced ratio for limiting-reactant, theoretical-yield or concentration work.
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Chemical Equation Balancer FAQs
How do you balance a chemical equation?
Choose coefficients that make the count of every element equal on both sides. For ionic equations, make total charge equal too. Reduce the final coefficients to their smallest positive whole-number ratio.
Can I change subscripts to balance an equation?
No. A subscript is part of a substance’s formula. Changing it changes the substance. Change only the coefficient placed before the complete formula.
Why are coefficients normally written as whole numbers?
Fractional coefficients can express the same stoichiometric relation. Multiplying every term by a common denominator gives the conventional whole-number form, which the calculator then reduces by the common gcd.
Does the calculator balance ionic charge?
Yes, when you enter terminal charges explicitly. Use forms such as H^+, Fe^3+, SO4^2- and e^-. The conservation table then includes a net-charge row.
Does it add water, hydrogen ions or electrons automatically?
No. The solver balances only the species you write. Add the chemically appropriate H2O, H+, OH- or e^- terms before calculating a redox or half-reaction.
Are parentheses, brackets and hydrates supported?
Yes. Matched round, square and curly groups are expanded exactly. Use a middle dot between hydrate components; a period is accepted as an ASCII input substitute and displayed as a middle dot.
What happens to state symbols such as (aq) and (s)?
The calculator preserves (aq), (s), (l) and (g) in the displayed equation. State labels do not change atom counts or coefficients.
Why does the calculator report an underdetermined equation?
The written species allow more than one independent coefficient ratio. Remove duplicate, spectator or optional species, or split the input into separate reactions.
Can I verify coefficients without rebalancing?
Yes. Select coefficient check mode. Enter a positive whole-number coefficient before each species, or omit it to use 1, then review every conservation row.
Does a balanced equation prove the reaction will occur?
No. Balance confirms only conservation for the written species. It does not establish products, rate, equilibrium direction, mechanism, energy change, conditions or laboratory safety.
Chemical Equation References
- OpenStax Chemistry 2e, Writing and Balancing Chemical Equations, coefficient, subscript and atom-conservation guidance.
- OpenStax Chemistry 2e, Review of Redox Chemistry, half-reaction and electron-balance guidance.
- IUPAC Gold Book, chemical reaction equation, reaction-equation and stoichiometric-coefficient terminology.
- IUPAC Red Book, Nomenclature of Inorganic Chemistry, authoritative formula and ionic-charge notation guidance.
- IUPAC Periodic Table of the Elements, current element names and symbols.
Disclaimer: This educational calculator balances supported formulas entered by the user. It does not identify products, validate reaction feasibility, choose reaction conditions, assess hazards, replace laboratory procedures or substitute for qualified chemistry review.