Atom Calculator
Convert between mass, moles, and particles for any chemical formula, count how many atoms of one specific element are in a sample, split those atoms across their natural or custom isotopes, or compare two substances head-to-head to see which one packs in more atoms. Every mode shows a distinct diagram, full step-by-step reasoning, and a callout explaining what the result means.
Background
Chemists rarely count atoms one at a time — instead they weigh a sample and use its molar mass (M, in g/mol) to convert that mass into moles (n), then use Avogadro's number (NA = 6.022×1023) to convert moles into an actual particle count (N). Multiply by how many atoms are packed into one formula unit and you get the total atom count — the same three-step bridge (mass → moles → particles → atoms) underlies every calculation below.
How to use this calculator
- Choose Convert Units to turn a mass, mole, or particle count into the other two, plus the total atom count.
- Choose Count One Element to find how many atoms of a specific element are hiding inside a compound.
- Choose Isotopic Split to divide an element's atoms across its naturally occurring (or your own custom) isotopes.
- Choose Compare Substances to see which of two formulas packs more atoms into the same mass or mole amount.
- Click Calculate to see the diagram, the full step-by-step reasoning, and a callout explaining what the result means.
How the Conversions Work
Molar mass (M) is the mass of one mole of a substance, in grams. For a formula, it's the sum of every element's atomic weight times its subscript.
Moles (n) bridge mass and particle count: n = m / M. A mole is just a very large, fixed-size "bag" of particles — exactly 6.022×1023 of them.
Avogadro's number (NA = 6.022×1023 mol−1) converts moles into an actual particle count: N = n · NA.
Atoms per formula unit is the sum of all the subscripts in the formula — H₂O has 3 (2 H + 1 O); Ca(OH)₂ has 5 (1 Ca + 2 O + 2 H).
To count atoms of one specific element, multiply the particle count N by that element's subscript, not by the total atoms per formula unit.
An isotope is a version of an element with a different number of neutrons. Natural abundance gives the average percentage of atoms that are each isotope — multiplying that percentage by the atom count gives the expected number of each, not a literal integer count in one exact sample.
Comparing two substances at the same mass almost always gives a different atom count, because they have different molar masses and different atoms per formula unit — lighter formula units pack more particles (and often more atoms) into the same number of grams.
Formulas & Equations Used
Moles from mass: n = m / M
Particles from moles: N = n · NA, where NA = 6.022×1023 mol−1
Total atoms: atoms = N × (atoms per formula unit)
Atoms of one element: atoms(X) = N × subscript(X)
Isotopic split: atoms(isotope i) = atoms(X) × (abundancei / 100)
Example Problems & Step-by-Step Solutions
Example 1 — Convert mass to particles
2.30 g of sodium (Na). Find the number of atoms.
Step: n = m / M = 2.30 / 22.99 = 0.100 mol; N = n · NA = 0.100 × 6.022×1023.
Result: N ≈ 6.02×10²² atoms.
Example 2 — Count one element
18.0 g of water (H₂O). Find the number of H atoms.
Step: M ≈ 18.015 g/mol; n ≈ 0.999 mol; N ≈ 6.02×10²³ molecules; H's subscript is 2.
Result: Atoms of H ≈ 1.20×10²⁴.
Example 3 — Isotopic split
0.250 mol of Cl₂. Split the chlorine atoms into ³⁵Cl and ³⁷Cl.
Step: N = 0.250 × 6.022×1023; atoms of Cl = N × 2; multiply by 75.78% and 24.22%.
Result: ≈ 2.28×10²³ atoms of ³⁵Cl and ≈ 7.29×10²² atoms of ³⁷Cl.
Example 4 — Compare substances
10 g of NaCl vs. 10 g of H₂O. Which has more atoms?
Step: Lighter molar mass and more atoms per formula unit both push the atom count up — compute both totals and compare directly.
Result: 10 g of water contains more total atoms than 10 g of salt, since water's molar mass is lower and it packs 3 atoms per unit.
Frequently Asked Questions
What counts as "particles"?
Formula units, molecules, or atoms of the substance as a whole — whatever one unit of your formula represents. Multiplying by subscripts converts that into a count of individual atoms.
Do I need to know density?
No. This calculator works from mass, moles, or particle count directly. Density only matters if you're converting from a volume first.
When can I split into isotopes?
Either the formula is a single element (e.g. Cl₂ splits into isotopes of Cl), or you name a specific element to split within a compound (e.g. H within H₂O).
Are isotope counts exact?
They're expected values based on average natural abundance — a statistical prediction, not a literal atom-by-atom count in one particular sample.
Why don't equal masses give equal atom counts?
Molar mass differs by substance, so the same number of grams corresponds to a different number of moles — and therefore a different number of particles and atoms — for each one.
What formulas can I type in?
Any standard chemical formula with optional parentheses and subscripts, e.g. Na, Cl2, H2O, Ca(OH)2, Al2(SO4)3, C6H12O6.
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