Stoichiometry Calculator

About the Stoichiometry Calculator

Stoichiometry is the arithmetic of chemical reactions. It answers practical questions such as how much oxygen a fuel burns, how much product a reaction can make, and how much of each reagent to order.

Every such problem has the same two stages: balance the equation so atoms are conserved, then use the coefficients as mole ratios. This calculator does both. Balancing is done exactly, by solving the atom-balance equations with fractions rather than trial and error, so even redox equations with many species come out right.

What is stoichiometry?

Stoichiometry is the study of the quantitative relationships between reactants and products. Its foundation is the law of conservation of mass: atoms are rearranged in a reaction, never created or destroyed, so every element must have the same number of atoms on both sides.

The coefficients of a balanced equation give the ratio in which particles, and therefore moles, react. In 2H₂ + O₂ → 2H₂O, two moles of hydrogen react with one mole of oxygen to give two moles of water. The ratio is in moles, not grams, which is why masses must be converted first.

How to use the Stoichiometry Calculator

Type the equation with an arrow (->, → or =) between the sides.
Separate species with +; state labels like (aq) or (g) are ignored.
To convert amounts, enter a known species and its mass in grams.
Optionally name the one species you want to find.
Press Balance and calculate and follow the mole-ratio steps.

Formulas

Moles from mass

n = \frac{m}{M}

Mole ratio

n_B = n_A \cdot \frac{c_B}{c_A}

Mass from moles

m_B = n_B \cdot M_B

Conservation of mass

\sum m_{\text{reactants}} = \sum m_{\text{products}}

Percent yield

\%\ \text{yield} = \frac{\text{actual}}{\text{theoretical}} \times 100

Worked example: Balance H₂ + O₂ → H₂O

How much iron(III) oxide forms when 10 g of iron rusts? Balancing Fe + O₂ → Fe₂O₃ gives $4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3$ .

Moles of iron: $\frac{10}{55.845} \approx 0.17907$ mol. The ratio of Fe₂O₃ to Fe is 2 : 4, so $n = 0.089534$ mol and $m = 0.089534 \times 159.687 \approx 14.30$ g. The extra 4.30 g is the oxygen taken from the air.

The solution below is generated by the same engine that powers the calculator above.

Final answer

2\mathrm{H_{2}} + \mathrm{O_{2}} \rightarrow 2\mathrm{H_{2}O}

How we read your problem

Balance atoms of every element, then use the coefficients as mole ratios.

2\mathrm{H_{2}} + \mathrm{O_{2}} \rightarrow 2\mathrm{H_{2}O}

Step-by-step solution

Write an atom balance for each element
Give each species an unknown coefficient; atoms of every element must be equal on both sides.
$\text{H}: 2c_{1} = 2c_{3} \\ \text{O}: 2c_{2} = 1c_{3}$
Solve the linear system with the smallest whole numbers
Exact elimination leaves one free coefficient; scaling by the least common denominator gives integers.
$c_{1} = 2,\ c_{2} = 1,\ c_{3} = 2$
Balanced equation
$2\mathrm{H_{2}} + \mathrm{O_{2}} \rightarrow 2\mathrm{H_{2}O}$

Formulas used

Moles from mass
$n = \frac{m}{M}$
Mole ratio
$n_B = n_A \cdot \frac{c_B}{c_A}$

Coefficients in a balanced equation count particles (moles), not grams. Convert grams to moles, apply the mole ratio, then convert back to grams with the other species' molar mass. Assumes the reaction goes to completion with the known species fully consumed (or formed).

Verification

H: 4 = 4, O: 2 = 2 ✓

Detailed explanation

How the balancing works

Each species gets an unknown coefficient. For every element, the atoms on the left must equal the atoms on the right, which gives one linear equation per element. Solving this system exactly leaves one free coefficient; setting it and clearing fractions gives the smallest whole-number set.

For KMnO₄ + HCl → KCl + MnCl₂ + H₂O + Cl₂ the method gives 2, 16, 2, 2, 8 and 5, a result that takes many attempts by inspection. The check line lists the atom count of each element on both sides so you can verify it.

When an equation cannot be balanced

If an element appears on only one side, no coefficients can fix it, which usually means a formula is mistyped or a product is missing. The calculator names the element so you can find the error quickly.

Some equations can be balanced in more than one independent way because they really describe two reactions at once, for example hydrogen and oxygen forming both water and hydrogen peroxide. There is then no single answer; split the process into separate reactions.

From theoretical to actual yield

The mass this calculator gives is the theoretical yield: what forms if the known reactant is used up completely and nothing is lost. Real reactions fall short because of side reactions, incomplete conversion and losses during filtering or transfer.

If a synthesis predicted 14.3 g of product but you collected 12.0 g, the percent yield is 12.0/14.3 × 100 ≈ 84%. When two reactants are both limited, run the calculation from each one; the reactant giving less product is the limiting reagent.

Common mistakes

Changing subscripts to balance an equation instead of coefficients.
Using mass ratios instead of mole ratios.
Forgetting that oxygen, hydrogen and chlorine gases are diatomic.
Using the molar mass of a single atom for a polyatomic species.
Assuming the theoretical yield is what you will actually collect.

Tips

Write O2, H2, N2 and Cl2 for elemental gases.
Brackets work: Ca3(PO4)2 and Al2(SO4)3 are parsed correctly.
Leave the target empty to see every other species at once.
Compare reactant and product masses to check conservation.
Use the molarity calculator for reactions in solution.

Frequently asked questions

How do I balance a chemical equation?

Give each species a coefficient and make the atom count of every element equal on both sides. This calculator solves those conditions exactly and returns the smallest whole numbers.

How do I convert grams of one substance to grams of another?

Convert grams to moles with the molar mass, multiply by the ratio of coefficients, then convert moles back to grams with the second molar mass.

Why do I need moles and not grams?

Coefficients count particles. Equal masses of different substances contain different numbers of particles, so ratios only work in moles.

Can it balance redox equations?

Yes, for neutral molecular equations such as KMnO₄ with HCl. Ionic equations with charges are not supported.

Does it find the limiting reagent?

Not automatically. Run the calculation from each reactant's mass; the one that gives the smaller amount of product is limiting.

What do (aq), (s), (l) and (g) mean?

They are state symbols: aqueous, solid, liquid and gas. They do not affect the balancing and are ignored.

Why does the total mass stay the same?

Atoms are conserved in a chemical reaction, so the mass of the reactants used equals the mass of the products formed.

Balance an equation

Type the reaction above and optionally a known mass to convert.

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