Deducing Empirical Formula

General Chemistry • Chemical Compounds

Written by STEM Calculators Team Published October 16, 2025 Updated February 24, 2026

Enter each element with its mass (g) or mass percent (%). The tool converts to moles, divides by the smallest to get a ratio, and scales to whole-number subscript.

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Format: Element then value (mass or percent). Header rows are ignored.

Composition

Provide at least two elements.

Molar mass (optional, for molecular formula)

g/mol

If provided, the tool computes the molecular formula using \(k = \dfrac{M_\text{molecular}}{M_\text{empirical}}\).

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Empirical formula from composition

The empirical formula gives the simplest whole-number ratio of elements in a compound. An empirical formula calculator converts masses or percent composition into mole ratios and returns the reduced subscripts (a simplest ratio, not necessarily the true molecular formula).

Core definitions and essential equations

\[ \begin{aligned} n_i &= \frac{m_i}{M_i} \\ r_i &= \frac{n_i}{\min(n)} \end{aligned} \]

\(m_i\) is the mass of element \(i\) in the sample (or percent mass treated as grams in a 100 g basis), \(M_i\) is its molar mass in \(\mathrm{g\cdot mol^{-1}}\), \(n_i\) is moles, and \(r_i\) is the normalized mole ratio after dividing by the smallest mole amount. The empirical subscripts are obtained by scaling all \(r_i\) values by a small whole number until they are close to integers, then rounding and reducing by any common factor.

How to interpret results

Larger subscripts mean that element is present in a larger mole ratio relative to the others. Because the result is a ratio, the absolute sample size does not matter; a 10 g or 100 g basis gives the same empirical formula as long as the composition is the same. If the calculator outputs intermediate moles and normalized ratios, those values show how the integer subscripts were built from molar masses and composition data. To move from empirical to molecular formula, compare the compound’s molar mass with the empirical formula mass and multiply all subscripts by the resulting integer factor.

Common pitfalls

Not using a 100 g basis for percent composition (treating percent as grams simplifies \(n_i=\frac{m_i}{M_i}\)).
Rounding ratios too early before checking for simple fractions such as 0.5, 0.33, 0.25, 0.20.
Dividing by the wrong “smallest” value (use the smallest nonzero \(n_i\)).
Forgetting to reduce after scaling (e.g., 2:4:2 should become 1:2:1).

Micro example

\[ \begin{aligned} \text{Assume }100\ \mathrm{g:}\quad m_\mathrm{C}&=40.0,\ m_\mathrm{H}=6.7 \\ n_\mathrm{C}&=\frac{40.0}{12.011}=3.33,\quad n_\mathrm{H}=\frac{6.7}{1.008}=6.65 \\ r_\mathrm{H}&=\frac{6.65}{3.33}\approx 2.00\ \Rightarrow\ \text{CH}_2 \end{aligned} \]

Use this tool when composition data (mass, percent mass, or elemental analysis) is available and a simplest ratio is needed for identification or stoichiometry. It is not appropriate for mixtures or samples with water of hydration not accounted for; a next-step concept for more complex cases is molecular formula determination using molar mass and additional structural/analytical data.

Frequently Asked Questions

How do I find an empirical formula from mass percent composition?

Treat the percentages as grams in a 100 g sample, convert each to moles with n = m/M, then divide all mole values by the smallest to get ratios. If ratios are not close to integers, multiply all ratios by a small whole number until they are.

Why do you divide by the smallest number of moles when finding an empirical formula?

Dividing by the smallest mole amount converts the mole counts into relative ratios compared to 1. These ratios represent the simplest proportional relationship among the elements before scaling to integers.

What should I do if I get a ratio like 1.5 or 2.33 instead of an integer?

Multiply every ratio by a small whole number to eliminate the fractional part (for example, 1.5 suggests multiplying by 2; 2.33 suggests multiplying by 3). The goal is a set of whole-number subscripts that preserve the ratios.

Is the empirical formula the same as the molecular formula?

Not always. The empirical formula is the simplest ratio, while the molecular formula can be a whole-number multiple of it if the compound molar mass is larger than the empirical formula mass.

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