Chemical equation

Tip: Use plain numbers for subscripts (H2O) and + or - signs at the end for ions (Fe+3, SO4-2). You can also paste Unicode subscripts (H₂O) or leading coefficients (2H2O): they are rebalanced automatically

Typical equations

Is this an ionic redox reaction in acidic or basic medium? Solve it by half-reactions

Your equation in chemical notation (unbalanced)

\text{H}_{2} + \text{O}_{2} \rightarrow \text{H}_{2}\text{O}

Elements in equation

Explore Elements1 / 118

Nonmetal

Hydrogen

1.0080 u

Results

Balanced equation

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Stoichiometric coefficients

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Molar masses

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Reactant Masses

Enter masses to calculate the limiting reagent

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Limiting reagent—

Excess reagents

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Theoretical yield

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Fundamentals & Explanation

What does stoichiometry calculate?

In a chemical reaction atoms are neither created nor destroyed: they rearrange. That is the Law of Conservation of Mass (Lavoisier, 1789), and everything else follows from it: if every element must have the same number of atoms on both sides, the coefficients of the equation are not free — they form a system of equations with a unique minimal integer solution. That is exactly what the balancer does: it solves the system and returns the canonical coefficients.

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

In ionic equations, electric charge is conserved as well: the electrons lost by the species being oxidized are exactly those gained by the one being reduced. The balancer verifies both conservations before returning a result.

The mole as a bridge: grams → moles → grams

A balance measures grams, but the chemical equation speaks in particles (in proportions set by the coefficients). The bridge between the two worlds is the mole, via the molar mass $M$ :

n = \frac{m}{M} \qquad \xrightarrow{\;\text{ratio } \nu\;} \qquad m_{\text{product}} = n_{\text{product}} \cdot M_{\text{product}}

Every stoichiometric calculation is this three-leg journey: convert the entered masses to moles, move from one substance to another using the coefficient ratio $\nu$ , and convert back to grams. The calculator performs all three legs and shows you the intermediate quantities so you can audit them.

The n/ν ratio decides what limits

With real reactant amounts, you almost never have the exact proportion of the equation. To find which reactant runs out first, compute for each one the ratio between its available moles and its coefficient:

\text{Limiting reagent} = \min_i\left(\frac{n_i}{\nu_i}\right)

The ratio $n/\nu$ is "how many times the reaction can run" on that reactant. The smallest one rules, and there are three possible outcomes:

Single limiting reagent: one reactant has the minimum ratio; the rest are in excess.
Codeterminant reagents: two or more share the minimum and run out together, while others remain.
Stoichiometric mixture: all of them share the minimum — exact proportion, nothing left over.

A surprising detail: mixing 4.0 g of H₂ with 32.0 g of O₂ looks like the exact proportion of $2\text{H}_2 + \text{O}_2$ , but the real molar masses (2.016 and 31.998 g/mol) make the ratios differ by ~0.8%: H₂ limits. The calculator displays both ratios so the difference is visible, not a mystery.

Excess and theoretical yield

Once the minimum $r = \min(n_i/\nu_i)$ is identified, each product forms in proportion to its coefficient, and whatever was not consumed remains of each leftover reactant:

m_{\text{product}} = \nu_{\text{product}} \cdot r \cdot M_{\text{product}}

m_{\text{excess}} = \left(n_i - \nu_i \cdot r\right) M_i

The theoretical yield assumes a complete reaction (100%). In the lab the actual yield is always lower — losses, side reactions, equilibrium — and is reported as a percentage of the theoretical value this tool calculates.

Ions, hydrates and phases: how to write them

The engine accepts the full chemistry, with a syntax designed to be unambiguous:

Charges greater than 1: sign before the magnitude — Fe+2, Fe+3, SO4-2.
Unit charges: trailing sign — NH4+, MnO4-, OH-, H+.
Hydrates: middle dot or double dot — CuSO4·5H2O or CuSO4..5H2O.
Phases: in parentheses — AgCl(s), H2O(l), CO2(g), NaCl(aq).
Coefficients: you can paste them (2H2O) — they are discarded and the equation is rebalanced canonically.

The method, step by step

Write the equation with $+$ separated by spaces and $\to$ (or =).
Balance: the engine returns the minimal integer coefficients.
Enter the mass of each reactant; it is converted to moles with $M$ .
Look at each reactant's $n/\nu$ ratio.
The minimum marks the limiting reagent (or the exact mixture).
Read the theoretical yield per product and the excess per reactant.

Common mistakes

Fe3+ is ambiguous (Fe₃ with charge +?): write Fe+3.
CuSO4.5H2O with a single dot would be read as a decimal subscript (O: 5.5): use · or ...
The same species repeated on one side (H2 + H2) does not add up: write it once.
H2+O2 without spaces is not split: the + between substances needs spaces.

Related calculators

Stoichiometry tells you how much product forms if the reaction goes to completion; when it is reversible, the final state is set by equilibrium — that is solved in ICE Table. For electrolytes in water there is Ionic Dissociation, for moles ↔ gas volume the Gas Simulator, and for preparing solutions, Advanced Solutions.

Academic References

[1] Chang, R. & Goldsby, K. A. (2015). Chemistry (12th ed.). McGraw-Hill. (Stoichiometry, limiting reagent, yield.)
[2] Brown, T. L., et al. (2017). Chemistry: The Central Science (14th ed.). Pearson. (Mole relationships and formula calculations.)
[3] Flowers, P., et al. (2019). Chemistry 2e. OpenStax. (Balancing equations and reaction stoichiometry; open access.)

Stoichiometric Calculator

Results

Fundamentals & Explanation

What does stoichiometry calculate?

The mole as a bridge: grams → moles → grams

The n/ν ratio decides what limits

Excess and theoretical yield

Ions, hydrates and phases: how to write them

The method, step by step

Academic References

What does stoichiometry calculate?

The mole as a bridge: grams → moles → grams

The n/ν ratio decides what limits

Excess and theoretical yield

Ions, hydrates and phases: how to write them

The method, step by step

Academic References