Balance Chemical Equations Calculator instantly finds smallest integer coefficients, checks atom counts, and previews steps with helpful notes for students.
->, =, or →. Parentheses like Al2(SO4)3 and nested groups are supported.A Balance Chemical Equations Calculator automatically finds the smallest whole-number coefficients to make a chemical reaction obey the law of conservation of atoms and charge. Each element appears with the same count on both sides of the reaction arrow, ensuring total matter conservation.
The calculator accepts unbalanced formulas, optionally with physical states, analyzes all atomic elements, and computes integer coefficients to satisfy stoichiometric balance. For oxidation-reduction (redox) reactions, it applies the half-reaction method under acidic or basic conditions to balance both mass and electrons. Visual previews show how coefficients distribute across molecules, ions, and charges, emphasizing that subscripts never change — only coefficients do.
Mathematically, balancing is a homogeneous linear system. The element–species matrix \(A\) contains atom counts for each species: reactants negative, products positive. A non-trivial solution \( \mathbf{x}\neq \mathbf{0} \) to \(A\mathbf{x}=\mathbf{0}\) gives the coefficients. Dividing by the greatest common divisor (gcd) yields the smallest integers.
For ionic equations, an extra row represents net charge. In redox reactions, the half-reaction method separates oxidation and reduction steps, balances non-oxygen and non-hydrogen atoms, then adds \( \mathrm{H_2O} \), \( \mathrm{H^+} \) (acidic) or \( \mathrm{OH^-} \) (basic), and electrons \( e^- \) to enforce mass and charge conservation. Electrons are canceled when combining half-reactions.
The calculator also supports polyatomic ion shortcuts (treat groups as units) and fractional oxygen tactics for combustion, followed by scaling to clear fractions.
C3H8 + O2 → CO2 + H2O). Including states is optional but recommended.Unbalanced: \( \mathrm{C_3H_8 + O_2 \rightarrow CO_2 + H_2O} \). Balance carbon first: \(3\,\mathrm{CO_2}\), hydrogen next: \(4\,\mathrm{H_2O}\), then oxygen: \(5\,\mathrm{O_2}\). Final equation: \( \mathrm{C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O} \).
\( \mathrm{Fe^{2+} + MnO_4^- \rightarrow Fe^{3+} + Mn^{2+}} \) in acidic solution. Balanced equation: \( \mathrm{5Fe^{2+} + MnO_4^- + 8H^+ \rightarrow 5Fe^{3+} + Mn^{2+} + 4H_2O} \).
\( \mathrm{Cl_2 + OH^- \rightarrow Cl^- + ClO^- + H_2O} \). Balanced equation: \( \mathrm{Cl_2 + 2OH^- \rightarrow Cl^- + ClO^- + H_2O} \).
\( \mathrm{Na_3PO_4 + CaCl_2 \rightarrow NaCl + Ca_3(PO_4)_2} \). Balanced equation: \( \mathrm{2Na_3PO_4 + 3CaCl_2 \rightarrow 6NaCl + Ca_3(PO_4)_2} \).
Balance carbon and hydrogen first, then oxygen. Fractional \( \mathrm{O_2} \) can be used temporarily, then multiply all coefficients to clear fractions.
Yes, intermediate fractional coefficients are fine. Final balanced equations should use the smallest whole numbers by dividing by the gcd.
Coefficients scale entire species; subscripts define molecular composition and must never be changed.
Use the half-reaction method to balance atoms and charge. Add \( \mathrm{H^+} \), \( \mathrm{OH^-} \), and \( \mathrm{H_2O} \) depending on the medium.
No, but including them communicates reaction conditions accurately.
Use acidic when \( \mathrm{H^+} \) is present; basic when \( \mathrm{OH^-} \) dominates. The medium determines which species appear.
The matrix nullspace gives proportional values. Divide by the gcd to get the smallest integers.
Yes, if the same ion appears unchanged on both sides. This simplifies balancing and saves time.
Count atoms of each element and check net charge equality. Both must match exactly.
Some inputs may produce multiple basis vectors. Any positive integer multiple maintaining the ratios is valid.