What percent composition tells you
Percent composition is the fraction of a compound's mass supplied by each element. It answers a practical question: if you buy a tonne of this material, how many kilograms of the element you actually want are in the bag? A 50 kg bag of ammonium sulfate is 21.2% nitrogen, so it delivers 10.6 kg of nitrogen — which is exactly what the 21-0-0 grade printed on the bag means.
The quantity runs in two directions, and both matter. Going forward, from a formula to percentages, is what this page does; it gives you the theoretical composition of a pure substance. Going backward, from measured percentages to a formula, is the job of the empirical formula calculator. Analytical chemists use both in the same afternoon: they measure the composition of a new compound by combustion analysis, derive a candidate formula, then compute that formula's theoretical composition and check that the two agree.
Percent composition is also a purity check. If a sample of what should be calcium carbonate assays 38.1% calcium rather than the theoretical 40.04%, roughly 5% of the mass is something else. That single comparison is the basis of a great deal of quality control in the mineral, cement and fertiliser industries.
The formula, and the denominator people get wrong
Multiply the number of atoms of the element by its standard atomic weight to get the mass that element contributes to one mole of compound. Divide by the molar mass of the whole formula unit. Multiply by 100.
The numerator is straightforward as long as you count every occurrence of the element. In ammonium sulfate, (NH₄)₂SO₄, nitrogen appears inside a bracket with subscript 2, so there are two nitrogen atoms, not one. In sodium hydrogen carbonate, NaHCO₃, hydrogen appears once; in ammonium carbonate, (NH₄)₂CO₃, it appears eight times.
The denominator is where errors hide, and there is one specific trap: water of crystallisation belongs in the denominator. Copper(II) sulfate pentahydrate is 25.45% copper, but the anhydrous salt is 39.81% copper. Both numbers are correct for their own substance. If your reagent bottle says pentahydrate and you use the anhydrous percentage, you will under-deliver copper by more than a third. Whenever a compound can be hydrated, decide which substance you actually have before you compute anything.
Because every element's contribution is divided by the same total, the percentages sum to exactly 100. That is a free arithmetic check — if the table below does not add to 100, something has been mis-parsed.
Worked example: nitrogen in ammonium sulfate
Ammonium sulfate, (NH₄)₂SO₄, is sold as a 21-0-0 nitrogen fertiliser. Verify the grade.
- Count the atoms. The bracket subscript 2 doubles everything inside: 2 nitrogen and 8 hydrogen. Outside it, 1 sulfur and 4 oxygen.
- Nitrogen contribution. 2 × 14.007 = 28.014 g/mol.
- Hydrogen contribution. 8 × 1.008 = 8.064 g/mol.
- Sulfur contribution. 1 × 32.06 = 32.06 g/mol.
- Oxygen contribution. 4 × 15.999 = 63.996 g/mol.
- Molar mass. 28.014 + 8.064 + 32.06 + 63.996 = 132.134 g/mol.
- Percent nitrogen. 100 × 28.014 ÷ 132.134 = 21.20%.
That matches the printed grade, which is rounded down to 21. Now size a real application: to apply 40 kg of nitrogen per hectare you need 40 ÷ 0.2120 = 188.7 kg of ammonium sulfate per hectare. The same arithmetic on urea, CO(NH₂)₂ at 46.65% N, would need only 85.7 kg — which is why urea dominates bulk nitrogen shipping even though ammonium sulfate also supplies 24.26% sulfur that urea does not.
How to read the result
Compare against the theoretical value for the substance you believe you have. In synthetic chemistry the accepted criterion for reporting a new compound is agreement between measured and calculated carbon, hydrogen and nitrogen percentages to within 0.4 percentage points. A carbon result well below the calculated value usually means residual solvent or water; a nitrogen result above it often means a retained ammonium salt.
For minerals, the percentage is the theoretical grade of the pure mineral, not of the ore. Pure hematite, Fe₂O₃, is 69.94% iron; a shipped iron ore assaying 62% Fe is therefore about 89% hematite by mass with the balance silica and alumina. The gap between mineral grade and ore grade is the entire business of beneficiation.
For anything you will dissolve, convert the percentage into what you actually need. Grams of element wanted, divided by the mass fraction, gives grams of compound to weigh. From there the molarity calculator takes you to a solution of known concentration, and the dilution calculator to a working strength.
Theoretical composition of compounds people look up
| Compound | Formula | Element | Molar mass (g/mol) | Mass percent |
|---|---|---|---|---|
| Water | H₂O | O | 18.015 | 88.81% |
| Ammonia | NH₃ | N | 17.031 | 82.24% |
| Urea | CH₄N₂O | N | 60.056 | 46.65% |
| Ammonium nitrate | NH₄NO₃ | N | 80.043 | 35.00% |
| Ammonium sulfate | (NH₄)₂SO₄ | N | 132.134 | 21.20% |
| Carbon dioxide | CO₂ | C | 44.009 | 27.29% |
| Glucose | C₆H₁₂O₆ | C | 180.156 | 40.00% |
| Calcium carbonate | CaCO₃ | Ca | 100.086 | 40.04% |
| Hematite | Fe₂O₃ | Fe | 159.687 | 69.94% |
| Magnetite | Fe₃O₄ | Fe | 231.531 | 72.36% |
| Copper(II) sulfate, anhydrous | CuSO₄ | Cu | 159.602 | 39.81% |
| Copper(II) sulfate pentahydrate | CuSO₄·5H₂O | Cu | 249.677 | 25.45% |
| Sodium chloride | NaCl | Na | 58.440 | 39.34% |
| Potassium chloride | KCl | K | 74.548 | 52.45% |
The two copper sulfate rows show why the hydrate state must be settled before any composition figure is used.
Where percent composition calculations go wrong
- Ignoring the hydrate. The waters count in the denominator, and they can be a third of the mass. Anhydrous and hydrated forms give genuinely different percentages for the same element.
- Missing atoms inside brackets. A subscript outside a bracket multiplies everything within it. (NH₄)₂SO₄ has two nitrogens and eight hydrogens.
- Confusing elemental percent with oxide percent. Fertiliser labels quote phosphorus as P₂O₅ and potassium as K₂O, not as the elements. A 0-46-0 phosphate is 46% P₂O₅, which is only 20.1% elemental phosphorus.
- Comparing a mineral grade to an ore grade. The formula gives the composition of the pure mineral. Real ore is a mixture and always assays lower.
- Using mass percent where mole percent is meant. Gas mixtures and alloy phase diagrams are often quoted in mole or atom percent, which for elements of different atomic weight is a different number entirely.
- Assuming a percentage proves identity. Compounds with the same empirical formula share the same composition: formaldehyde CH₂O, acetic acid C₂H₄O₂ and glucose C₆H₁₂O₆ are all 40.00% carbon.
Related methods and when to use them instead
Percent composition is one leg of a triangle. The second leg is the empirical formula, which converts measured percentages back into an atom ratio. The third is the molar mass, which turns that ratio into a molecular formula once you know how heavy the molecule is. Any two of the three determine the position of the third.
In the laboratory the measurement itself is usually combustion analysis: a milligram of sample is burned in oxygen, the carbon dioxide and water produced are weighed or measured by thermal conductivity, and carbon and hydrogen percentages follow directly. Nitrogen comes from the same instrument; oxygen is normally reported by difference rather than measured, which is why an oxygen percentage from CHN data carries every other element's error.
Two conventions are worth knowing because they look like percent composition and are not. Weight percent in a solution divides solute mass by total solution mass and has nothing to do with a formula. Atom percent counts atoms rather than mass, and for a compound of light and heavy elements the two diverge sharply: water is 88.81% oxygen by mass but only 33.3% oxygen by atom count.
Finally, note what this calculation cannot see. It uses average atomic weights, so an isotopically enriched sample will not match. It assumes the substance is pure and stoichiometric, which many minerals are not — natural olivine, for instance, varies continuously between magnesium and iron end members and has no single percent composition at all.