Atomic Mass Calculator

Calculate average atomic mass from isotope masses and natural abundances. Find percent abundance of an unknown isotope. Convert between mass in amu and grams per mole.

⚗️ Atomic Structure📐 M̄ = Σ(fi × mi)🧪 Chemistry
Isotope 1 mass (amu)
Abundance of isotope 1 (%)
Isotope 2 mass (amu)
Abundance of isotope 2 (%)
Isotope 3 mass (amu, optional)
Abundance 3 (%)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Atomic Mass Calculator—M̄ = Σ(fi × mi)g/mol

Step-by-Step Examples

Example 1
Carbon

C-12: 12.000 amu, 98.93%. C-13: 13.003 amu, 1.07%.

  • M = 12.000 x 0.9893 + 13.003 x 0.0107
  • = 11.872 + 0.139 = 12.011 amu
✓ Average atomic mass of C = 12.011 amu
Example 2
Silicon (3 isotopes)

Si-28: 27.977 (92.23%), Si-29: 28.977 (4.67%), Si-30: 29.974 (3.10%).

  • M = 27.977x0.9223+28.977x0.0467+29.974x0.0310
  • = 25.794+1.353+0.929 = 28.076 amu
✓ M(Si) = 28.076 amu
Example 3
Unknown Isotope

Two isotopes of X: m1=62.930 amu, m2=64.928 amu. Average mass=63.546. Find abundances.

  • Let x = fraction of isotope 1
  • 62.930x + 64.928(1-x) = 63.546
  • 1.998x = 1.382; x = 0.6918 = 69.18%
  • Isotope 2: 30.82%
✓ Isotope 1: 69.18%, Isotope 2: 30.82% (this is copper!)

Real-World Applications

⚗️
Periodic Table
All atomic masses in the periodic table are weighted averages of isotope masses.
🧪
Mass Spectrometry
MS directly measures isotope masses and abundances. Used to verify element identity.
☢️
Geochemistry
Isotope ratios reveal geological age, temperature of formation, and biological fractionation.
💡
Nuclear Fuel
Uranium enrichment: increase U-235 (natural 0.72%) to 3-5% for nuclear reactor fuel.

Common Mistakes to Avoid

⚠️
Percent abundances sum to 100

All isotopes account for all atoms. Sum must be 100%. Check before calculating.

⚠️
1 amu = 1 g/mol exactly

Average atomic mass in amu equals molar mass in g/mol by definition of Avogadro constant.

⚠️
C-12 is exact mass 12.000

The amu is defined as 1/12 of C-12 mass. C-12 has exact integer mass by definition.

Frequently Asked Questions

What is the atomic mass unit? ▾
1 amu (or Dalton, Da) = 1/12 the mass of one C-12 atom = 1.66054x10^-27 kg. Convenient unit for atomic and molecular masses.
Why are atomic masses not integers? ▾
Isotopes have masses close to (but not exactly) integer due to nuclear binding energy (mass defect). Also, most elements have multiple isotopes with non-integer average.
What is the mass defect? ▾
Actual nuclear mass < sum of separate proton and neutron masses. Difference = binding energy/c^2. C-12 nucleons sum = 12.099 but C-12 mass = 12.000 (0.099 mass defect = 7.68 MeV/nucleon).
How are isotope abundances measured? ▾
Mass spectrometry measures relative peak heights. Isotope ratio mass spectrometry (IRMS) for high-precision measurements. Abundances are very stable geologically.
What is the most abundant isotope of each element? ▾
H: H-1 (99.98%). C: C-12 (98.93%). O: O-16 (99.76%). Fe: Fe-56 (91.75%). Most stable elements have one dominant isotope.

Related Chemistry Calculators

☢️ Isotope Abundance☢️ Nuclear Symbol⚗️ Molar Mass⚗️ Electron Config☢️ Nuclear Equation

Formula Explorer connections

Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.

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