Chemical Equation Balancer
Enter an unbalanced chemical equation and get balanced coefficients instantly.
Use -> or = to separate reactants and products. Use + between compounds.
Example Equations
How to Balance Chemical Equations
A balanced chemical equation has equal numbers of each type of atom on both sides of the reaction arrow, satisfying the Law of Conservation of Mass. This law, established by Antoine Lavoisier in 1789, states that atoms are neither created nor destroyed during a chemical reaction — they are only rearranged.
Step-by-Step Manual Balancing
- Write the unbalanced equation. Identify all reactants and products with correct chemical formulas. For example: Fe + O₂ → Fe₂O₃
- Count atoms on each side. Left: 1 Fe, 2 O. Right: 2 Fe, 3 O. The equation is unbalanced.
- Balance one element at a time. Start with elements that appear in only one reactant and one product. Balance metals before nonmetals, and save hydrogen and oxygen for last.
- Adjust coefficients, not subscripts. Place numbers in front of formulas to change how many molecules participate. Never alter subscripts — that changes the compound itself.
- Verify the result. Count every atom on both sides to confirm they match. The balanced equation: 4Fe + 3O₂ → 2Fe₂O₃
How This Tool Works
This balancer uses Gaussian elimination on the stoichiometry matrix — a systematic algebraic method rather than trial and error. Each element contributes one equation (atoms in = atoms out), and the unknowns are the coefficients. The algorithm solves this system of linear equations and converts the result to the smallest set of whole-number coefficients.
This approach handles reactions of any complexity, including multi-step redox reactions, organic combustion, and equations with polyatomic ions, where manual balancing by inspection would be tedious.
Types of Chemical Reactions
- Synthesis — Two or more simple substances combine to form a more complex product: 2Na + Cl₂ → 2NaCl
- Decomposition — A compound breaks down into simpler substances: 2H₂O → 2H₂ + O₂
- Single replacement — One element displaces another from a compound: Zn + 2HCl → ZnCl₂ + H₂
- Double replacement — Two compounds exchange ions: AgNO₃ + NaCl → AgCl + NaNO₃
- Combustion — A substance reacts with O₂, typically producing CO₂ and H₂O: CH₄ + 2O₂ → CO₂ + 2H₂O
Input Format Tips
- Use standard chemical notation:
H2O,Ca(OH)2,Fe2O3 - Separate reactants and products with
->or= - Separate compounds with
+ - Parentheses for polyatomic groups:
Ca3(PO4)2
After balancing, use the stoichiometry calculator to compute exact masses and moles for your reaction, or the molar mass calculator to find the molecular weight of any compound.
Frequently Asked Questions
Why do chemical equations need to be balanced?
Chemical equations must be balanced to satisfy the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. Every atom present in the reactants must also appear in the products.
An unbalanced equation like H2 + O2 -> H2O implies that an oxygen atom disappears during the reaction, which violates this fundamental law. The balanced form, 2H2 + O2 -> 2H2O, correctly shows that all four hydrogen atoms and both oxygen atoms are conserved.
Balanced equations are essential for stoichiometric calculations — determining how much of each reactant is needed and how much product will be formed.
What is the difference between coefficients and subscripts?
Coefficients and subscripts serve different roles in a chemical equation:
- Coefficients — Numbers placed before a chemical formula (e.g., the 2 in 2H2O). They indicate how many molecules or moles of that substance participate in the reaction. You adjust coefficients when balancing equations.
- Subscripts — Numbers placed after an element symbol within a formula (e.g., the 2 in H2O). They indicate how many atoms of that element are in one molecule. You never change subscripts when balancing — doing so would change the substance itself.
For example, 2H2O means two molecules of water (4 hydrogen atoms and 2 oxygen atoms total), while H2O2 is hydrogen peroxide, a completely different compound.
How do you balance equations with polyatomic ions?
When a polyatomic ion appears unchanged on both sides of an equation, you can treat it as a single unit rather than balancing each element individually. This simplifies the process significantly.
For example, in the reaction Ca(OH)2 + H3PO4 -> Ca3(PO4)2 + H2O:
- Identify polyatomic ions that appear intact on both sides — here, PO4 appears in both H3PO4 and Ca3(PO4)2.
- Balance the polyatomic ion as a group: 2 PO4 on the right means you need 2 H3PO4 on the left.
- Balance other elements: 3 Ca on the right needs 3 Ca(OH)2 on the left.
- Balance remaining atoms (H and O from OH and H2O) last.
The balanced equation is 3Ca(OH)2 + 2H3PO4 -> Ca3(PO4)2 + 6H2O.
What types of chemical reactions can this tool balance?
This equation balancer handles all types of chemical reactions that can be balanced algebraically:
- Synthesis reactions — Two or more substances combine to form a product (e.g., 2Na + Cl2 -> 2NaCl).
- Decomposition reactions — A compound breaks down into simpler substances (e.g., 2H2O -> 2H2 + O2).
- Single replacement — One element replaces another in a compound (e.g., Zn + 2HCl -> ZnCl2 + H2).
- Double replacement — Two compounds exchange ions (e.g., AgNO3 + NaCl -> AgCl + NaNO3).
- Combustion reactions — A substance reacts with oxygen, producing CO2 and H2O (e.g., CH4 + 2O2 -> CO2 + 2H2O).
- Redox reactions — Reactions involving electron transfer, including complex reactions like KMnO4 + HCl -> KCl + MnCl2 + H2O + Cl2.
The tool uses Gaussian elimination on a stoichiometry matrix, which is a general algebraic method that works regardless of reaction type.
What is the law of conservation of mass?
The Law of Conservation of Mass, established by Antoine Lavoisier in 1789, states that the total mass of substances does not change during a chemical reaction. The atoms are rearranged into new combinations, but no atoms are created or destroyed.
This law has practical consequences:
- Mass balance — If you start with 10 grams of reactants, you will end with 10 grams of products (assuming a complete reaction with no side products).
- Atom counting — The number of each type of atom must be identical on both sides of a balanced equation.
- Stoichiometry — Balanced equations provide the mole ratios needed to calculate how much of each substance is involved in a reaction.
Note that the law applies to chemical reactions under normal conditions. In nuclear reactions, a tiny amount of mass is converted to energy according to Einstein's E=mc2, but this is negligible in chemistry.