Empirical Formula Calculator
Find an empirical formula from masses (grams) or percent composition. We convert each element to moles, divide by the smallest, then scale to whole-number ratios. Supports the full standard periodic table, and an optional hydrate term like · x H₂O.
Background
The empirical formula is the simplest whole-number ratio of atoms in a compound. Example: glucose C₆H₁₂O₆ has empirical formula CH₂O.
How to use this calculator
- Pick Mass (g) or Percent mode.
- Add each element (symbol) and its value — any element on the periodic table works.
- Click Calculate to get the empirical formula, a mole-ratio visual, and a mole-ratio table.
- If needed, we scale ratios to the nearest whole numbers (like ×2 for 1.5).
How this calculator works
- Convert each entry to moles: moles = grams / atomic mass.
- Divide all moles by the smallest mole value to get ratios.
- Find a small multiplier (×1..×12) that turns ratios into near integers.
- Format the formula with subscripts (e.g., C₆H₁₂O₆).
Formula & Equation Used
Moles: n = m / M
Ratio: rᵢ = nᵢ / min(n)
Scale: find integer k such that k·rᵢ ≈ integers
Example Problems & Step-by-Step Solutions
Example 1 — Percent composition of glucose
- Assume 100 g: C=40.00 g, H=6.71 g, O=53.29 g.
- Convert to moles: C≈3.33, H≈6.66, O≈3.33.
- Divide by smallest (3.33): C=1, H=2, O=1 → CH₂O.
Example 2 — Percent composition of carbon dioxide
- Assume 100 g: C=27.29 g, O=72.71 g.
- Convert to moles: C≈2.27, O≈4.54.
- Divide by smallest (2.27): C=1, O=2 → CO₂.
Example 3 — Mass data (iron oxide)
- Given masses: Fe=111.69 g, O=48.00 g.
- Convert to moles: Fe≈2.00, O≈3.00.
- Divide by smallest (2.00): Fe=1, O=1.5 → multiply by 2 → Fe=2, O=3.
- Empirical formula: Fe₂O₃.
Example 4 — Mass data (arsenic trioxide)
- Given masses: As=149.84 g, O=48.00 g.
- Convert to moles: As≈2.00, O≈3.00.
- Divide by smallest (2.00): As=1, O=1.5 → multiply by 2 → As=2, O=3.
- Empirical formula: As₂O₃.
Frequently Asked Questions
What if I get ratios like 1.5 or 2.33?
We multiply by a small number (like ×2 or ×3) to make them whole numbers.
Can I use percent composition?
Yes — percent mode treats each percent as grams in a 100 g sample.
Is empirical formula always the same as molecular formula?
Not always. Molecular formula can be a multiple of the empirical formula (like C₆H₁₂O₆ vs CH₂O).
Which elements are supported?
The full set of standard atomic masses used in general chemistry, including less common ones like arsenic (As), antimony (Sb), and bismuth (Bi).
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