Empirical Formula Calculator
The empirical formula of a compound is the simplest whole-number ratio of the atoms of each element present. It is derived from percent composition data using the mole ratio method, which converts mass percentages into mole amounts and then simplifies the ratios to the smallest possible integers. For example, if a compound contains 40% carbon, 6.7% hydrogen and 53.3% oxygen by mass, dividing each percentage by the element's molar mass gives the number of moles per 100 grams, then dividing by the smallest mole value produces a ratio of approximately 1:2:1, which corresponds to the empirical formula CH2O. The molecular formula may be a whole-number multiple of the empirical formula, but you need the compound's actual molar mass to determine that. This calculator accepts up to five elements. For each you enter the element symbol (for display), the percentage by mass from an elemental analysis, and the element's molar mass. The mole ratio method is applied automatically: divide each percentage by the molar mass to get moles per 100 g, divide all values by the minimum, then round to the nearest integer (or multiply through by 2, 3 or 4 if fractions remain). The calculator shows the intermediate mole values and the final ratio alongside the empirical formula string. Common molar masses: H = 1.008, C = 12.011, N = 14.007, O = 15.999, S = 32.06, Cl = 35.45. Use this tool in conjunction with the molar mass calculator to determine whether your empirical formula matches the molecular formula.
Enter up to 5 elements (symbol, % by mass, molar mass g/mol). Percentages should sum to 100%.
| Element | % by mass | Moles per 100 g | Divide by min | Integer ratio |
|---|
If the ratio step gives 0.5 or 1.5 values, the calculator multiplies through by 2. For 0.33 or 0.67, it multiplies by 3. Results may vary slightly from published values due to rounding.
How it works
The mole ratio method has three steps. Step 1: divide each percentage by the element's molar mass to get moles per 100 g (assume a 100 g sample). Step 2: divide all mole values by the smallest mole value to get the raw ratio. Step 3: round to the nearest whole number. If any value is near 0.5, multiply all ratios by 2; if near 0.33 or 0.67, multiply by 3. The empirical formula string is built from the element symbols and their integer subscripts (subscript 1 is omitted by convention).
Worked example
A compound contains C: 40%, H: 6.7%, O: 53.3%. Moles per 100 g: C = 40 / 12.011 = 3.330; H = 6.7 / 1.008 = 6.646; O = 53.3 / 15.999 = 3.332. Divide by minimum (3.330): C = 1.00; H = 1.996 = 2; O = 1.001 = 1. Empirical formula: CH2O. These match the default values pre-filled above.
Related calculators
- Percent Composition Calculator: find the percentage by mass of each element in a known compound.
- Molar Mass Calculator: find the molar mass of a compound to test if the empirical and molecular formulas match.
- Stoichiometry Calculator: convert masses of reactants and products in balanced equations.
- Percent Error Calculator: compare experimental elemental percentages with theoretical values.