Chemical Equation Balancer & Stoichiometry

Balance chemical equations using Gaussian elimination, compute stoichiometric quantities, find limiting reagents, calculate percent yield, and identify reaction types. Also: Periodic Table | Molar Mass.

Enter a chemical equation using = as the separator (e.g., Fe + O2 = Fe2O3, H2 + O2 = H2O, C3H8 + O2 = CO2 + H2O).

How it works: The equation balancer counts atoms on each side, builds a coefficient matrix, and solves using Gaussian elimination to find the smallest integer coefficients. The stoichiometry calculator uses molar masses of all species to convert between mass and moles.
What is a balanced chemical equation?

A chemical equation is a recipe written in atoms. The law of conservation of mass says atoms are neither created nor destroyed in a reaction, so the left side and the right side must account for exactly the same atoms — and balancing is the bookkeeping that enforces it. The big numbers in front of each formula (the coefficients) are the dials you turn until every element's count matches: rusting iron needs 4 Fe + 3 O2 = 2 Fe2O3, not 1 + 1 = 1. Balancing is pure algebra, which is why this page can do it by Gaussian elimination and then re-count every element to show Left = Right. Fractional coefficients are legitimate in thermochemistry (per mole of reaction); lab recipes clear denominators by multiplying through.

The one rule to remember: coefficients count moles, not individual molecules. 2H2 + O2 = 2H2O reads “2 mol of hydrogen plus 1 mol of oxygen give 2 mol of water” — which is also why 10 g of H2 and 32 g of O2 are not the same amount of reaction.
Stoichiometry: the mole bridge

You cannot weigh moles; you weigh grams. Every stoichiometry problem is the same three-step crossing: grams → moles (divide by molar mass), moles of one species → moles of another (multiply by the coefficient ratio), moles → grams (multiply by the other molar mass). The middle step is where the balanced equation does its work. For the sample above, 10 g of H2 is 4.960 mol; the equation 2H2 + O2 = 2H2O then gives 2.480 mol of O2 (79.4 g) consumed alongside, and up to 4.960 mol of H2O (89.4 g) formed. Molar masses come straight from the periodic table — the Molar Mass page is the tool dedicated to that step.

Limiting reagent: sandwich logic

With two reactants, one of them runs out first and the reaction stops there — the limiting reagent decides everything, and the other is in excess. The comparison is moles divided by coefficients: whichever quotient is smaller runs out first. The sample makes the counterintuitive point: 32 g of O2 is three times heavier than 10 g of H2, yet O2 is the limiting reagent (1.000 mol ÷ 1 beats 4.960 mol ÷ 2), so the theoretical yield is only 36.03 g of H2O and 2.96 mol of H2 survives unused. Mass alone never settles the question — the equation's coefficients must be in the comparison.

Theoretical, actual, and percent yield

The theoretical yield is what the limiting reagent permits if every molecule cooperates; the actual yield is what you actually isolate; percent yield = actual/theoretical × 100%. The sample's 85 g out of 100 g rates “Good/Fair” — real syntheses lose yield to side reactions, incomplete separation, product left on glassware, and equilibrium that refuses to finish. Percent yield above 100% is a red flag for wet or contaminated product, not a miracle.

Reaction types at a glance

The classifier panel reads a balanced equation's shape: two things becoming one is synthesis, one thing splitting is decomposition, an element swapping into a compound is single displacement, two compounds trading partners is double displacement. Burning anything with O2 to make CO2 and H2O is combustion, and any reaction that moves electrons between species is additionally redox — categories overlap (the sample 2H2 + O2 = 2H2O is synthesis, combustion and redox all at once). Redox bookkeeping has its own page: Redox & Electrochem.

Common misconceptions
  • Balancing by changing subscripts. H2O and H2O2 are different substances; only the coefficients in front are yours to adjust.
  • The smaller mass is the limiting reagent. The sample is the disproof: 32 g of O2 outweighs 10 g of H2 and still limits. Compare moles per coefficient, never raw grams.
  • A balanced equation means the reaction happens. Balancing says nothing about speed (kinetics) or how far it goes (equilibrium) — see Chemical Equilibrium.
  • Yield above 100% means more product than possible. It means the measured product carries water or impurities; the reaction did not break any law.

Related tools: Molar Mass (the grams–moles bridge this page depends on), Chemical Equilibrium (how far reactions actually go), and Redox & Electrochem (electron-transfer reactions).