Input Mode
Symbol Amount (%)
Empirical Formula
Add elements above to begin
Common Decimal Multipliers - Cheat Sheet

After dividing moles by the smallest mole value, you may see ratios with decimal remainders. This table shows the exact multiplier to apply to convert them to whole numbers. This calculator applies these automatically.

Ratio Decimal Multiply All By Fraction It Represents Example
.5 ×2 1/2 1.5 and 1.0 become 3 and 2
.33 or .67 ×3 1/3 or 2/3 1.33 and 1.0 become 4 and 3
.25 or .75 ×4 1/4 or 3/4 1.25 and 1.0 become 5 and 4
.2, .4, .6, or .8 ×5 1/5 through 4/5 1.4 and 1.0 become 7 and 5
.167 or .833 ×6 1/6 or 5/6 1.167 and 1.0 become 7 and 6
.143 or .857 ×7 1/7 or 6/7 1.143 and 1.0 become 8 and 7
Pro tip: If ratios still don't resolve cleanly after multiplying by 2-7, double-check your input values. Small rounding errors in experimental data are the most common cause.
Key Terms Explained
Empirical Formula
The simplest whole-number ratio of elements in a compound. It does not tell you how many atoms are in one molecule, only the ratio between them.
Molecular Formula
The actual count of each atom in one molecule of a compound. It is always a whole-number multiple of the empirical formula.
Mole
The SI unit for amount of substance. One mole equals 6.022 x 10^23 particles. It is the chemist's "dozen" for counting atoms.
Molar Mass
The mass of one mole of a substance in grams per mole (g/mol). For elements, it equals the atomic weight shown on the periodic table.
Atomic Weight
The weighted average mass of all naturally occurring isotopes of an element, expressed in atomic mass units (amu) or g/mol.
Percent Composition
The mass of each element expressed as a percentage of the total compound mass. The values must sum to 100%.
Subscript
The small number written below and after an element symbol in a chemical formula that indicates the number of atoms of that element (e.g., the 2 in H2O).
Mole Ratio
The relative number of moles of each element in a compound. Dividing all mole values by the smallest produces the initial ratio used to find the empirical formula.
Stoichiometry
The branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions, rooted in mole ratios.
Whole Number Multiplier
The integer (2, 3, 4, or 5) applied to all initial ratios when decimals like .5 or .33 appear, converting fractional ratios into whole numbers.

The Complete Guide to Finding the Empirical Formula

Finding an empirical formula is one of the most fundamental skills in general chemistry. Whether you are working from lab data on a new compound or studying for the AP Chemistry exam, the four-step process below is universal. This calculator automates every step - but understanding the math underneath is what makes the difference on a test.

How to Use This Calculator

Select your input mode at the top: "Mass (%)" if you have percent composition data, or "Mass (g)" if you have direct gram measurements. Add one row per element by entering the element symbol (e.g., C, H, O, N, Fe) and its corresponding value. The formula and step-by-step table update instantly with every keystroke - no button to press.

In percentage mode, the calculator warns you if your values do not sum within 1% of 100%, which catches common data-entry errors. You can use up to any number of elements - just click "Add Element" for each additional one.

The Four Steps - Explained

STEP 1Convert to Grams. If you have percent composition, assume a 100-gram sample. This converts every percentage directly to grams (34% oxygen = 34 grams oxygen). If you already have grams, skip this step.

STEP 2Convert Grams to Moles. Divide each element's gram amount by its molar mass (atomic weight). This gives you raw mole counts for each element. The mole values at this stage are not yet a clean ratio.

STEP 3Divide by the Smallest Mole Value. Find the element with the fewest moles, then divide all mole counts by that number. The element with the smallest value becomes 1.00. This produces the initial ratio. If all ratios are already whole numbers (or within 0.05 of one), you are done.

STEP 4Apply a Multiplier if Needed. If any ratio contains a recognizable fraction (.5, .33, .25, .2), multiply all ratios by the appropriate integer to clear the decimals. See the cheat sheet above for the correct multiplier for each fraction. The resulting integers are the subscripts in the empirical formula.

Worked Example: Ethylene (C2H4)

Suppose a compound contains 85.63% carbon and 14.37% hydrogen. Assume 100 g: 85.63 g C and 14.37 g H. Divide by atomic masses: 85.63 / 12.011 = 7.130 mol C, and 14.37 / 1.008 = 14.256 mol H. Divide both by 7.130 (the smaller): C = 1.00, H = 2.000. Both are whole numbers, so the empirical formula is CH2. (The molecular formula, found separately using molar mass data, happens to be C2H4.)

Frequently Asked Questions

An empirical formula gives the simplest whole-number ratio of elements in a compound. A molecular formula gives the actual number of each atom in one molecule. For example, glucose has the molecular formula C6H12O6, but its empirical formula is CH2O because all subscripts share the common factor 6. Sometimes they are the same - water (H2O) cannot be simplified further, so its empirical and molecular formulas are identical.
Dividing every element's mole count by the smallest mole value converts the raw numbers into a ratio relative to the element present in the least quantity. That ratio tells you the proportional relationship between elements. The element with the smallest moles becomes 1.00, and every other element is expressed as a multiple of that. This is the same operation as simplifying a fraction - you are reducing all values to the smallest common denominator before rounding to whole numbers.
A ratio ending in .5 means multiply all ratios by 2. A ratio ending in .33 or .67 means multiply all by 3. A ratio ending in .25 or .75 means multiply all by 4. A ratio ending in .2, .4, .6, or .8 means multiply all by 5. This calculator detects these common fractions automatically and applies the correct multiplier so you never need to do this step by hand. The cheat sheet above the glossary covers all common cases, including 1/6 and 1/7 fractions.
Yes. When the subscripts in a molecular formula are already in their lowest whole-number ratio, the two formulas are identical. Water (H2O), carbon dioxide (CO2), and ammonia (NH3) are common examples. The ratio 2:1 in H2O cannot be reduced further, so H2O is both the empirical and molecular formula for water. To determine which case applies, you need additional information - specifically the compound's molar mass - which is not part of this calculator's scope.
Percent by mass means grams per 100 grams of compound. Assuming exactly 100 grams means each percent value converts directly to grams with no arithmetic - 34.0% oxygen becomes 34.0 grams of oxygen. The final mole ratios depend only on the relative amounts, not the actual sample size, so the 100-gram assumption always gives the correct empirical formula regardless of how large the real sample is. It is a mathematical shortcut, not an approximation.