Why this calculation pays for itself

Percent composition is the bridge between a formula on paper and what comes out of a furnace, a fertilizer bag, or an elemental analyzer. When a mining company decides whether magnetite (Fe₃O₄, 72.4% Fe) is worth digging instead of hematite (Fe₂O₃, 69.9% Fe), that 2.5-percentage-point gap drives multimillion-dollar decisions. When a farmer reads “21-0-0” on a sack of ammonium sulfate, that first number is the percent nitrogen by mass — calculated exactly the way you’re about to learn.

In the lab, percent composition is the round-trip check on synthesis. You make a compound, send it to combustion analysis, and compare the measured C/H/N percentages against the theoretical values. A 0.3% deviation usually means clean product. A 5% deviation means you made something else.

The formula

For any element in a compound:

% mass = (atoms × atomic mass) / (molar mass of compound) × 100%

Sum the percentages and you should land within 0.01% of 100. If you don’t, the arithmetic is wrong.

Method, end-to-end

Get the formula right first. Iron(III) oxide is Fe₂O₃, not FeO. Aluminum sulfate is Al₂(SO₄)₃, not AlSO₄. A miscount of subscripts cascades through everything downstream.

Compute the molar mass by multiplying each element’s atomic mass by its count and summing. Use IUPAC standard atomic weights (the values printed on a modern periodic table — H = 1.008, C = 12.011, O = 15.999, etc.).

For each element, multiply atomic mass × count → that’s the element’s contribution. Divide by molar mass × 100% → percentage.

Add the percentages. They should sum to 100.00 ± 0.01%.

Five worked examples

Water (H₂O)

Molar mass: 2(1.008) + 15.999 = 18.015 g/mol

H: 2.016 / 18.015 × 100% = 11.19%
O: 15.999 / 18.015 × 100% = 88.81%

Sum: 100.00%. Hydrogen is light — even with two atoms it carries only an eighth of the mass.

Sulfuric acid (H₂SO₄)

Molar mass: 2(1.008) + 32.065 + 4(15.999) = 98.079 g/mol

H: 2.06%
S: 32.69%
O: 65.25%

Two-thirds of concentrated H₂SO₄’s mass is oxygen. That’s why dehydration reactions with H₂SO₄ work so dramatically — there’s a huge oxygen reservoir hungry to grab water.

Glucose (C₆H₁₂O₆)

Molar mass: 6(12.011) + 12(1.008) + 6(15.999) = 180.156 g/mol

C: 72.066 / 180.156 = 40.00%
H: 6.71%
O: 53.29%

Notice the 40/53/7 split: every “carbohydrate” with the empirical formula CH₂O lands at exactly these percentages, because the ratio doesn’t change when you scale the formula.

Ammonium nitrate (NH₄NO₃)

This one trips students up because nitrogen appears in two distinct chemical environments — as ammonium and as nitrate. Doesn’t matter for percent composition: count all N atoms together.

Atoms: 2 N, 4 H, 3 O. Molar mass: 80.043 g/mol.

N: 35.00%
H: 5.04%
O: 59.96%

That 35.00% N is exactly what makes NH₄NO₃ such a potent (and tightly regulated) fertilizer.

Calcium phosphate (Ca₃(PO₄)₂) — the parentheses test

Atoms: 3 Ca, 2 P, 8 O. The 8 oxygens come from 4 × 2 — the subscript 2 outside the parentheses multiplies everything inside, including the implicit 4 on oxygen. Miscount this and your answer falls apart.

Molar mass: 3(40.078) + 2(30.974) + 8(15.999) = 310.174 g/mol

Ca: 38.76%
P: 19.97%
O: 41.27%

Where this shows up in real work

Ore grading. Hematite (Fe₂O₃) is 69.9% Fe; magnetite (Fe₃O₄) is 72.4% Fe. A smelter will pay more per ton for magnetite because each ton yields more iron — even though magnetite is harder to process.

Fertilizer N-P-K ratings. The first number on every fertilizer bag is %N by mass, calculated the way you just did it. NH₄NO₃ is 35.0% N; (NH₄)₂SO₄ is 21.2% N. Per gram of fertilizer, ammonium nitrate delivers 65% more nitrogen.

Combustion analysis. Burn a milligram of unknown organic, capture the CO₂ and H₂O, weigh them. The masses convert directly to %C and %H — and if those match your target compound’s calculated percentages, you’ve confirmed the formula.

Common ways to get this wrong

Miscounting through parentheses. Ca₃(PO₄)₂ has 8 oxygens, not 4. Always distribute the outer subscript before counting.

Atomic number vs. atomic mass. Nitrogen’s atomic number is 7; its atomic mass is 14.007. Plug 7 into a percent composition calculation and your nitrogen percentage halves. The number you want lives below the symbol on the periodic table, not above it.

Skipping the × 100. The fraction 0.4000 is not “40 percent” until you multiply. It’s a recurring source of one-decimal-off answers.

Premature rounding. Carry full precision through the calculation; round only at the final step. Round each intermediate to two decimals and you’ll routinely accumulate 0.5% error.

Not summing. If your percentages add to 87% or 112%, something is wrong — recount atoms or recheck atomic masses. The correct total is always within 0.01% of 100.

The Percent Composition Calculator takes any formula and returns the full element-by-element breakdown with mass contributions and percentages — useful for spot-checking lab calculations or stress-testing a synthesis target.

How to Calculate Percent Composition