Empirical Formula Calculator
Turn percent composition or masses into an empirical formula. Add the molar mass and you get the molecular formula too.
Empirical versus molecular formula
An empirical formula gives the simplest whole-number ratio of atoms in a compound. A molecular formula gives the actual number of atoms in one molecule.
| Compound | Empirical | Molecular |
|---|---|---|
| Water | H2O | H2O |
| Hydrogen peroxide | HO | H2O2 |
| Glucose | CH2O | C6H12O6 |
| Benzene | CH | C6H6 |
| Acetic acid | CH2O | C2H4O2 |
Notice that glucose and acetic acid share an empirical formula. Percent composition alone cannot tell them apart, which is exactly why the molar mass is needed for the second half of the problem. For ionic compounds like sodium chloride the empirical formula is the only one that makes sense, because a crystal is a repeating lattice rather than a set of separate molecules.
The method, step by step
- Assume 100 g of compound. This makes each percentage a number of grams. If you were given masses instead, skip this.
- Convert each mass to moles. Divide by that element's atomic mass.
- Divide every result by the smallest one. This sets the smallest ratio to exactly 1.
- Clear any fractions. If a value sits near 1.5, multiply everything by 2. Near 1.33, multiply by 3. Near 1.25, multiply by 4.
- Round and write the formula. The results should now be close to whole numbers.
Worked example
A compound is 40.00% carbon, 6.71% hydrogen, and 53.29% oxygen. Its molar mass is 180.16 g/mol.
Step 1 and 2. Treat the percentages as grams and convert to moles.
C: 40.00 ÷ 12.011 = 3.330 mol
H: 6.71 ÷ 1.008 = 6.657 mol
O: 53.29 ÷ 15.999 = 3.331 mol
Step 3. Divide by the smallest, which is 3.330.
C: 1.000, H: 1.999, O: 1.000
Step 4 and 5. These are already close to whole numbers, giving an empirical formula of CH2O.
Molecular formula. The empirical formula mass is 12.011 + 2(1.008) + 15.999 = 30.03 g/mol. Divide the real molar mass by that:
180.16 ÷ 30.03 = 6.0
Multiply every subscript by 6 to get C6H12O6, which is glucose.
Getting from empirical to molecular
n = molar mass ÷ empirical formula mass
That multiplier should come out very close to a whole number. If it lands on 2.5 or 3.7, something upstream is wrong, usually a rounding error in the percentages or a mistaken empirical formula. Go back rather than forcing the rounding.
Handling awkward ratios
Step 4 is where most mistakes happen. After dividing by the smallest value you will often get numbers that are close to, but not exactly, whole. Small deviations are just experimental error and should be rounded. Genuine fractions need multiplying out.
| If a value is near | Multiply everything by | Example |
|---|---|---|
| 0.5 | 2 | Fe1O1.5 becomes Fe2O3 |
| 0.33 or 0.67 | 3 | C1H2.67 becomes C3H8 |
| 0.25 or 0.75 | 4 | P1O2.5 becomes P2O5 |
A useful rule of thumb: anything within about 0.1 of a whole number is rounding error. Anything further out is a real fraction that needs clearing.
Mistakes worth avoiding
- Rounding to whole numbers too early. Carry four significant figures until the last step.
- Rounding 2.5 down to 2. That is a real fraction, so double everything instead.
- Forgetting an element. If the percentages do not add to 100, the missing share is usually oxygen.
- Dividing by the largest value. Always divide by the smallest.
- Reporting a molecular formula without the molar mass. Percent composition alone can only give the empirical formula.
Frequently asked questions
What is an empirical formula?
An empirical formula shows the simplest whole-number ratio of the atoms in a compound. Hydrogen peroxide is H2O2 as a molecule, but its empirical formula is HO because that is the simplest ratio.
How do I find the empirical formula from percentages?
Assume you have 100 g, so each percentage becomes grams. Divide each mass by that element's atomic mass to get moles, divide every result by the smallest one, then multiply through to clear any fractions.
How do I get the molecular formula?
Divide the compound's real molar mass by the mass of the empirical formula. The answer is a whole number, and multiplying every subscript in the empirical formula by it gives the molecular formula.
What if my percentages do not add up to 100?
A small gap is rounding. A large one usually means an element was not listed, and it is most often oxygen. You can take the missing percentage as that element's share.
What if I get 1.5 after dividing?
That is a genuine fraction, not an error. Multiply every value by 2 to clear it. Values near 0.33 or 0.67 need multiplying by 3, and values near 0.25 or 0.75 need multiplying by 4.
Can two compounds share an empirical formula?
Yes. Glucose and acetic acid both reduce to CH2O, and benzene and ethyne both reduce to CH. That is why you need the molar mass to identify which compound you actually have.
Related terms
Next: check your answer on the molar mass calculator, or go the other way with the percent composition calculator.