Example data table
| Atoms (N) | Molar mass (g/mol) | Mass (g) |
|---|---|---|
| 6.022e23 | 12.011 (Carbon) | 12.011 |
| 3.011e23 | 18.015 (Water) | 9.008 |
| 1.000e20 | 63.546 (Copper) | 0.01055 |
Values are rounded for readability. Your settings control rounding and style.
Formula used
This calculator converts atoms to mass using Avogadro’s constant:
- n = N / Nₐ (moles from atoms)
- m = n × M (mass in grams)
Where N is atoms, Nₐ = 6.02214076×10²³ mol⁻¹, and M is molar mass in g/mol. The final mass is converted to your selected unit.
How to use this calculator
- Enter the number of atoms (N). Scientific notation is allowed.
- Pick an element to auto-fill molar mass, or type your own value.
- Choose an output unit (g, kg, mg, or µg).
- Select rounding mode and number style for your preferred display.
- Press Calculate Mass to view the result above the form.
- Use the download buttons to export CSV or a PDF report.
Atoms to Mass Guide
1) What this calculator converts
This tool converts a counted number of atoms into an actual mass. You provide atoms N and a molar mass M in g/mol, then it returns mass in g, kg, mg, or µg. It is useful when particle counts come from microscopy, simulations, or stoichiometry problems.
2) Key constant: Avogadro’s number
The bridge between microscopic counts and macroscopic amounts is Avogadro’s constant: Nₐ = 6.02214076×10²³ mol⁻¹. One mole of any substance contains exactly this many entities. If you enter 6.02214076e23 atoms of carbon, you should get about 12.011 g.
3) Converting atoms to moles
Moles are computed with n = N / Nₐ. For example, 3.011×10²³ atoms equals roughly 0.500 mol because it is half of Nₐ. This step is unit‑free and only depends on the atom count and the constant value.
4) Converting moles to grams
Mass in grams follows m = n × M. If n = 0.500 mol and M = 18.015 g/mol (water), then m ≈ 9.008 g. The calculator also shows the intermediate grams value, which helps verify unit conversions and rounding choices.
5) Picking the correct molar mass
For pure elements, use the atomic molar mass (for example, Fe ≈ 55.845 g/mol, Cu ≈ 63.546 g/mol). For molecules, add the atom contributions: water is 2×1.008 + 15.999 = 18.015 g/mol. Even a small molar‑mass error scales the final mass by the same percentage.
6) Unit conversions you can trust
The core formula yields grams. From there, conversions are simple multipliers: 1 g = 10³ mg, 1 g = 10⁶ µg, and 1 kg = 10³ g. For tiny atom counts, micrograms can display cleanly; for huge counts, kilograms reduce long strings of zeros.
7) Rounding and scientific notation
Scientific notation is ideal when results span many orders of magnitude. For example, 1×10²⁰ atoms of copper is only about 1.055×10⁻² g. Use significant figures to match measurement precision, or fixed decimals when you need consistent formatting for reports and spreadsheets.
8) Practical uses in labs and industry
Converting atoms to mass appears in nanoparticle mass estimates, thin‑film deposition, tracer studies, and reaction‑yield checks. If a simulation outputs 2.0×10²² atoms of silicon (28.085 g/mol), the mass is about 0.933 g. Exporting CSV helps document runs, while PDF is handy for audits and lab notebooks.
FAQs
1) Can I enter scientific notation like 4.2e21?
Yes. The calculator accepts scientific notation and large comma-separated numbers, then converts them into moles and mass using the same formulas.
2) What molar mass should I use for compounds?
Use the molecular molar mass: sum each element’s atomic molar mass multiplied by its count in the formula, such as H₂O = 2×1.008 + 15.999.
3) Why does the result change when I switch units?
The underlying mass in grams is the same. Unit selection only scales the displayed value, for example grams to milligrams multiplies by 1000.
4) How accurate is Avogadro’s constant here?
The calculator uses 6.02214076×10²³ mol⁻¹, which is the defined value in modern SI. Any remaining uncertainty mainly comes from your input molar mass and atom count.
5) When should I use significant figures?
Use significant figures when your inputs have measurement limits. For example, if atoms are known to three significant figures, reporting mass with three significant figures keeps precision consistent.
6) What if I have molecules, not atoms?
Enter the number of molecules as “atoms” in the count field, and enter the compound’s molar mass. The same conversion works because Avogadro’s constant counts entities per mole.
7) Why is my result extremely small or extremely large?
Atom counts often span many orders of magnitude. Switch to scientific notation, and choose mg or µg for tiny masses, or kg for huge masses, to keep the display readable.