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Balance Equation Calculator — Chemical Equation Balancer

Balance any neutral molecular chemical equation instantly using the algebraic method. See the coefficients plus a step-by-step element-count check.

Updated

Separate compounds with +, separate reactants from products with -> or =. Enter plain formulas — no coefficients needed, this tool solves for them. Parentheses like Ca(OH)2 and Al2(SO4)3 are supported.

Balanced Equation
CH4 + 2O2 → CO2 + 2H2O
ElementReactant AtomsProduct AtomsMatch
C11✓
H44✓
O44✓

Uses the algebraic method: every compound gets an unknown coefficient, one linear equation is written per element (atoms in = atoms out), and the resulting system is solved with exact fraction arithmetic (Gauss-Jordan elimination — no floating point) before scaling to the smallest whole-number ratio. Scope: neutral molecular equations only — no ionic charges or redox half-reactions. Always double-check unusual or advanced equations against a textbook answer.
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Reference Values

Last verified:
Category Range What It Means Status
Input syntax ★ formula + formula -> formula + formula Separate compounds with + and use -> (or =) as the arrow. Type plain formulas only — no coefficients needed, since the calculator solves for them. Example: CH4 + O2 -> CO2 + H2O. ★ Best
Parentheses / groups Ca(OH)2, Al2(SO4)3 A number right after a closing parenthesis multiplies every element inside that group. Al2(SO4)3 means 2 Al, 3×(1 S + 4 O) = 3 S and 12 O. Good
Implicit subscript of 1 NaOH, H2O An element symbol with no number after it means exactly 1 atom. NaOH = 1 Na, 1 O, 1 H. Good
The algebraic method ★ System of linear equations Assigns an unknown coefficient to every compound, writes one equation per element (atoms in = atoms out), then solves the resulting linear system for the smallest whole-number ratio. This is the same method used by professional chemistry software — it always finds the correct answer for a valid equation, unlike trial-and-error inspection. ★ Best
Balancing by inspection Trial and error The manual classroom method: adjust coefficients one element at a time, starting with the most complex compound, until every element matches. Works fine for simple equations but gets error-prone and slow once an equation has 4+ compounds or several polyatomic groups. Okay
Scope: neutral molecular equations Supported Whole neutral compounds only — no charges, no ions, no half-reactions. Covers the vast majority of general-chemistry textbook equations (synthesis, decomposition, single/double displacement, combustion). Good
Scope: ionic / redox equations Not supported Equations with charged species (Fe3+, SO4^2-) or oxidation-state half-reactions need charge-balancing or electron-transfer rules this tool doesn't apply. Balance the neutral overall equation here, or use a dedicated redox/ionic method for those cases. Poor
Element/term safety cap ≤15 unique elements, ≤12 compounds Equations above this size are rejected with an error rather than risking a slow or unreliable solve — real textbook and lab equations are almost always well under this cap. Okay
Common element symbols H, C, N, O, Na, Mg, Al, Si, P, S, Cl, K, Ca, Fe, Cu, Zn, Ag, Ba, Pb The most frequently used symbols in general-chemistry equations. Remember: only the first letter of an element symbol is capitalized (Co = cobalt, one atom; CO = carbon monoxide, two atoms). Good

Source: Algebraic balancing method per LibreTexts Chemistry, "Balancing Chemical Equations" (chem.libretexts.org) and standard IUPAC element symbol conventions (iupac.org). Method logic cross-checked against the open-source approach described by Project Nayuki's Chemical Equation Balancer methodology writeup.

Worked Examples

Simple 2-Element Equation

Unbalanced equation
H2 + O2 -> H2O
2H2 + O2 -> 2H2O

Hydrogen: 2x1 = 2x3. Oxygen: 2x2 = x3. Solving gives x1:x2:x3 = 2:1:2 — the smallest whole-number ratio that balances both elements.

Compound With a Parenthetical Group

Unbalanced equation
Ca(OH)2 + HCl -> CaCl2 + H2O
Ca(OH)2 + 2HCl -> CaCl2 + 2H2O

Ca(OH)2 expands to 1 Ca, 2 O, 2 H. Four element equations (Ca, O, H, Cl) resolve to x1:x2:x3:x4 = 1:2:1:2, matching the classic acid-base neutralization ratio.

3-Element Combustion Reaction

Unbalanced equation
CH4 + O2 -> CO2 + H2O
CH4 + 2O2 -> CO2 + 2H2O

Methane combustion. Carbon: x1 = x3. Hydrogen: 4x1 = 2x4. Oxygen: 2x2 = 2x3 + x4. Solving gives 1:2:1:2 — the textbook-standard ratio for burning methane completely.

Larger Combustion Reaction (Bigger Coefficients)

Unbalanced equation
C3H8 + O2 -> CO2 + H2O
C3H8 + 5O2 -> 3CO2 + 4H2O

Propane combustion needs larger coefficients than methane because each propane molecule carries 3 carbons and 8 hydrogens. Carbon: 3x1 = x3. Hydrogen: 8x1 = 2x4. Oxygen: 2x2 = 2x3 + x4. Solving gives 1:5:3:4.

5-Element Double Displacement With Two Parenthetical Groups

Unbalanced equation
Al2(SO4)3 + BaCl2 -> AlCl3 + BaSO4
Al2(SO4)3 + 3BaCl2 -> 2AlCl3 + 3BaSO4

Al2(SO4)3 expands to 2 Al, 3 S, 12 O; BaSO4 expands to 1 Ba, 1 S, 4 O. Five element equations (Al, S, O, Ba, Cl) reduce to a single free variable once redundant rows (O and Cl both restate the S and Al relationships) are eliminated, giving 1:3:2:3 — this is the equation type balancing-by-inspection struggles with most.

How to Use This Calculator

  1. 1

    Write your unbalanced equation

    Use plain formulas, a + between compounds, and -> or = between reactants and products. No coefficients needed — e.g., Fe + O2 -> Fe2O3.

  2. 2

    Check the parentheses

    For compounds with polyatomic groups, use standard notation like Ca(OH)2 or Al2(SO4)3 — the calculator expands nested groups correctly.

  3. 3

    Read the balanced equation

    The result updates instantly, showing each compound with its correct whole-number coefficient (a coefficient of 1 is omitted, matching standard chemistry notation).

  4. 4

    Confirm with the verification table

    Each row shows one element's total atom count on the reactant side vs. the product side — they should match exactly, which is how you know the equation is truly balanced.

  5. 5

    Double-check unusual results

    For advanced or unfamiliar equations, compare the answer against your textbook or instructor's key before submitting it as coursework.

What Each Value Means

Coefficient (whole number)
The whole number placed in front of a compound in a balanced equation, showing how many molecules (or moles) of it react or form. A coefficient of 1 is conventionally left off.
Subscript (atoms per molecule)
The small number written after an element symbol inside a formula, showing how many atoms of that element are in one molecule of the compound — fixed by the compound's identity, never changed while balancing.
Reactant
A starting substance consumed in a chemical reaction, written on the left side of the equation's arrow.
Product
A substance formed by a chemical reaction, written on the right side of the equation's arrow.

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Frequently Asked Questions

How does this calculator balance equations — is it the same as balancing by inspection?
No. Balancing by inspection is the manual classroom method: you adjust coefficients one element at a time by trial and error until everything matches, usually starting with the most complex compound. This calculator instead uses the algebraic method — it assigns an unknown coefficient to every compound, writes one linear equation per element (atoms in must equal atoms out), and solves the entire system at once using exact fraction arithmetic. The algebraic method always finds the correct answer for a valid equation, while inspection can get slow or error-prone once an equation has four or more compounds or several polyatomic groups like sulfate or phosphate.
What input syntax does this calculator expect?
Type each compound's plain chemical formula, separated by a plus sign (+), with an arrow separating reactants from products. The arrow can be written as -> or =. Do not include coefficients — this calculator computes them for you, and any leading number you do type is simply ignored. Example: CH4 + O2 -> CO2 + H2O. Parentheses for polyatomic groups are supported, so Ca(OH)2 and Al2(SO4)3 parse correctly.
Does this tool handle ionic equations or redox reactions?
No — it's scoped to neutral molecular equations only. It does not accept charges (like Fe3+ or SO4^2-) and does not apply oxidation-state or electron-transfer rules needed for redox half-reactions. That covers the large majority of general-chemistry textbook equations — synthesis, decomposition, single and double displacement, and combustion reactions — but if your equation involves ions or a redox half-reaction, you'll need a dedicated ionic or redox balancing method instead.
Can every chemical equation be balanced this way?
Every chemically valid neutral molecular equation with a unique balanced solution can be solved with this method. The calculator will show an error instead of a guessed answer in three situations: if a formula can't be parsed (a typo or unknown element symbol), if the linear system has no non-trivial solution (the equation as written isn't chemically consistent), or if the system has more than one independent solution (rare, but it means the equation as entered doesn't represent one specific reaction). In every case, it tells you what went wrong rather than showing a wrong or fabricated result.
Why do some balanced equations need such large coefficients?
Coefficient size depends on how many atoms of each element the compounds carry and how those numbers interact across the whole system. Propane combustion (C3H8 + 5O2 -> 3CO2 + 4H2O) needs a coefficient of 5 on oxygen simply because propane's 3 carbons and 8 hydrogens both need matching oxygen on the product side, and 5 is the smallest whole number that satisfies both element balances at once. This is exactly the kind of equation where the algebraic method has a clear advantage over inspection — the correct ratio falls out of the linear system automatically instead of requiring several rounds of guess-and-check.

References & Sources

  1. [1]
    OpenStax Chemistry 2e - Writing and Balancing Chemical Equations (opens in new tab)

    Supports: Conservation of atoms, chemical-equation notation, and the balancing procedure.

    Verified

  2. [2]
    IUPAC - Periodic Table of Elements (opens in new tab)

    Supports: Official element names, symbols, atomic numbers, and periodic-table conventions.

    Verified

  3. [3]
    NIST Chemistry WebBook (opens in new tab)

    Supports: Authoritative chemical species, formula, and thermochemical reference data.

    Verified