Empirical Formula Calculator - Mass to Integer Subscripts

The empirical formula calculator turns the measured masses of elements in a compound into the smallest whole-number subscripts of the empirical formula. Use it for homework problems, lab-report conversions, and percent-composition reverse calculations.

• • General chemistry homework: Solve textbook problems where you are given element masses and asked for the simplest whole-number ratio.
• • Combustion analysis follow-up: Convert CO2 and H2O masses from a CHN burn into the empirical formula before extending to the molecular formula.
• • Percent composition reverse: Take percent-by-mass data, treat it as grams in a 100 g sample, and recover the empirical subscripts the same way.
• • Quick ratio sanity checks: Verify that a guessed empirical formula matches the measured element masses.

The calculator divides each mass by its IUPAC atomic weight to get moles, then divides every element's mole count by the smallest non-zero count to recover the empirical subscripts. The result is the simplest whole-number ratio, written in Hill system order.

For percent composition data, divide each percent by its atomic weight and follow the same divisor step. The empirical formula is the gateway to the molecular formula with a separately measured molar mass.

If your raw data came from a CHN burn rather than direct element masses, Combustion Analysis Calculator recovers the empirical formula from CO2 and H2O masses using the same IUPAC atomic weights.

The calculator applies standard chemistry steps: convert each element's mass to moles using IUPAC atomic weights, divide every mole count by the smallest non-zero value, and scale the ratios to whole numbers.

• massC, massH, massO, massN, massS: Measured masses of carbon, hydrogen, oxygen, nitrogen, and sulfur in grams. Enter 0 for any absent element.
• atomic weights: IUPAC 2023 standard atomic weights: H 1.008, C 12.011, N 14.007, O 15.999, S 32.06 g/mol.
• smallestMoles: The smallest non-zero mole count, used as the divisor for the empirical ratio step.
• k: Smallest integer from 1 to 9 that makes every ratio an integer within 0.05.

When you enter element masses, the calculator treats any zero value as an absent element and excludes it from the divisor step. The smallest-mole divisor step converts raw mole counts into the simplest integer ratio and is the heart of the calculation.

The calculator checks scaled ratios (k from 1 to 9) and uses the smallest k within 0.05 of an integer. That k scales every ratio, then each rounds to the nearest integer for the empirical subscript. This handles a 1.5 ratio without forcing you to multiply by 2.

According to IUPAC Standard Atomic Weights 2023, the standard atomic weights used to convert element masses to moles are H 1.008, C 12.011, N 14.007, O 15.999, and S 32.06 g/mol.

According to Wikipedia Empirical Formula, the empirical formula of a compound is the simplest whole-number ratio of atoms it contains, illustrated by methyl acetate which converts from 48.64% C / 8.16% H / 43.20% O to the empirical formula C3H6O2.

When you need a refresher on how atomic weights turn grams into moles, Mole & Molar Mass Calculator walks through the gram-to-mole conversion for any element on the periodic table.

Four ideas show up in every empirical-formula calculation. Once you understand them, the calculator's outputs map onto the steps you would write on a worksheet.

These four ideas are the same steps you would write out by hand on a worksheet. Glucose C6H12O6 and formaldehyde CH2O share the empirical formula CH2O because both reduce to the same 1:2:1 ratio.

The gram-to-mole conversion is the first step of every empirical formula, so Grams to Moles Calculator is a good place to double-check the arithmetic for any single element.

Enter the masses you measured for each element, leave unused ones at zero, and let the calculator do the moles, division, and rounding.

1. 1 Enter the mass of carbon: Type the grams of carbon, or leave at 0 to skip carbon from the empirical formula.
2. 2 Enter the mass of hydrogen: Type the grams of hydrogen; most organic compounds have hydrogen, so this value is rarely 0.
3. 3 Enter the mass of oxygen: Type the grams of oxygen, or 0 if the compound contains no oxygen.
4. 4 Enter nitrogen and sulfur if present: Set the grams of nitrogen and sulfur if your compound contains them; otherwise leave both at 0.
5. 5 Read the empirical formula: Use the formula for the homework answer or as input to a molecular-formula calculation.
6. 6 Check the empirical formula mass: Divide the measured molar mass by this value to get n, then multiply every subscript by n for the molecular formula.

For 1.000 g of a compound containing 0.400 g C, 0.067 g H, and 0.533 g O, enter 0.4, 0.067, 0.533, 0, 0. The calculator reports CH2O with empirical formula mass 30.026 g/mol, smallest mole count 1.0000 mol, and 3 elements present.

Once you have the empirical formula in hand, Chemical Equation Balancer Calculator uses those subscripts to balance the full chemical equation for a combustion or synthesis reaction.

The empirical formula calculator handles the mole math and smallest-mole division so you can focus on the chemistry decision after you have the formula.

• • Skip the moles-by-hand step: Enter element masses and the calculator divides each by its IUPAC atomic weight, removing the most common arithmetic slips.
• • Apply the smallest-mole rule automatically: No need to identify the smallest non-zero mole count yourself; the calculator reports it as its own output so you can verify the divisor.
• • Use Hill system ordering: The empirical formula is written with carbon first, hydrogen second, then remaining elements alphabetically, matching the convention in textbooks.
• • Cover five common elements: Carbon, hydrogen, oxygen, nitrogen, and sulfur are the five elements most often seen in organic empirical-formula problems.
• • Pair with a molecular formula step: Feed the empirical formula mass into a molar-mass ratio to recover the molecular formula without re-entering the masses.
• • Mobile-friendly in lab or library: Real-time recalculation lets you try different masses on a phone while reading a sample off the balance.

Use the empirical formula output to answer the first half of the worksheet, then move to the molecular formula only when the problem gives a molar mass. If the elements-present count does not match what you expected, double-check the input fields; a stray zero in the wrong row silently drops an element from the formula.

The empirical formula is also the starting point for reaction stoichiometry, and Stoichiometry Reaction Calculator converts those subscripts into theoretical product yields for a balanced reaction.

The arithmetic is exact, but your inputs and assumptions about the compound affect the results.

• • Empirical formula only: this calculator does not produce a molecular formula unless you multiply every empirical subscript by an integer n that matches a separately measured molar mass.
• • Borderline rounding: a 1.49 ratio rounds down to 1 and a 1.51 rounds up to 2; if your data sits between, double-check with a more precise measurement.
• • Hill system assumption: when carbon is absent, the calculator sorts elements alphabetically, which differs from the strict Hill system requirement that forces alphabetical order whenever no C is present.

Treat the calculator's outputs as a starting point and confirm them against your lab report. The empirical formula and percent composition must round-trip through the same atomic weights.

If the smallest mole count is below 1e-6 mol, check the input masses; the displayed moles may need a sanity check against your balance's readability.

According to LibreTexts Determining Empirical Formulas, an empirical formula is found by assuming a 100 g sample, converting grams of each element to moles, dividing every mole count by the smallest, and rounding to whole-number subscripts.

When the empirical-formula math leads to a percent-composition question on the same homework set, Alligation Calculator handles the mixture-style mass-percent problems that show up alongside it.