Empirical Formula Calculator

The Simplest Ratio: A Guide to the Empirical Formula Calculator

In chemistry, a compound's formula can be represented in different ways. The molecular formula tells you the exact number of atoms of each element in a single molecule (e.g., the molecular formula for glucose is C₆H₁₂O₆). The empirical formula, on the other hand, represents the simplest whole-number ratio of atoms in a compound. It is the most reduced or simplified version of the molecular formula.

For example, while the molecular formula for glucose is C₆H₁₂O₆, all the subscripts (6, 12, and 6) can be divided by 6. This gives the simplest ratio of 1:2:1, so the empirical formula for glucose is CH₂O. For some molecules, like water (H₂O), the empirical and molecular formulas are the same because the ratio of atoms is already in its simplest form. Determining the empirical formula is a fundamental first step in chemical analysis. When a new compound is discovered, chemists first determine its elemental composition (the percentage of each element by mass) through experimental analysis. From this data, they can calculate the empirical formula. This calculator automates that crucial calculation, allowing you to convert either mass data or percent composition into the simplest whole-number ratio of atoms, providing the empirical formula.

How to Calculate the Empirical Formula

The process involves converting the mass of each element into moles and then finding the simplest whole-number ratio of those moles.

1. Assume 100g Sample (for percentages): If you are given percent composition, assume you have a 100-gram sample of the compound. This makes the calculation easy, as each percentage simply converts directly to grams (e.g., 40.0% Carbon becomes 40.0 grams of Carbon). If you are given mass data already, you can skip this step.
2. Convert Mass to Moles: For each element, divide its mass in grams by its molar mass (atomic weight from the periodic table) to find the number of moles of that element.
3. Find the Smallest Mole Ratio: Look at the mole values you just calculated and find the smallest one. Then, divide all the mole values by this smallest value. This will give you a set of ratios.
4. Convert to Whole Numbers: The ratios you calculated may not be perfect whole numbers.
   • If the numbers are very close to whole numbers (e.g., 2.01 or 3.99), you can round them to the nearest whole number.
   • If the numbers are not close to whole numbers (e.g., 1.5, 2.33, 1.25), you must multiply *all* the ratios by a small integer (usually 2, 3, or 4) to get whole numbers. For example, if you have a ratio of 1:1.5, you would multiply both by 2 to get a whole-number ratio of 2:3.
5. Write the Formula: The resulting whole numbers are the subscripts for each element in the empirical formula.

From Empirical to Molecular Formula

The empirical formula gives the simplest ratio, but not the actual number of atoms in a molecule. To find the molecular formula, you need one more piece of information: the molar mass of the entire compound. The molecular formula will always be a whole-number multiple of the empirical formula. The formula is:

Molecular Formula = n × (Empirical Formula)

Where n = (Molar Mass of Compound) / (Molar Mass of Empirical Formula).

For example, if a compound has an empirical formula of CH₂O and a molar mass of 180 g/mol: The molar mass of the empirical formula (CH₂O) is about 30 g/mol. The ratio 'n' is 180 / 30 = 6. Therefore, the molecular formula is 6 × (CH₂O) = C₆H₁₂O₆.