Calculate average atomic mass from isotope masses and abundances, or solve for a missing isotope mass or abundance, using percent or decimal inputs.

Use isotope masses and abundances for one elemental sample. This tool does not parse molecular formulas or calculate monoisotopic molecular mass.

Changing scale reinterprets abundance entries. For 25%, enter 25 or fraction 0.25.

Optional settings

Isotope Mixture Formula

The calculator above uses A = Σ(mifi): isotope mass mi multiplied by sample fraction fi, summed across two to five isotopes. Percentages are divided by 100. Select the missing mass or abundance explicitly; all shares must total one. Normalization is available only for the average-mass calculation.

The molecular formulas and examples below are separate background calculations. This calculator does not accept chemical formulas or compute molecular monoisotopic masses or isotopic distributions.

Mₘₒₙₒ = Σᵢ nᵢ mi,mono\ Mavg = Σᵢ nᵢ mᵢ
  • Where Mmono is the monoisotopic (exact) mass (u or Da)
  • Mavg is the average mass based on natural isotopic abundances (u or Da)
  • ni is the number of atoms of element i in the formula
  • mi,mono is the exact mass of the most abundant isotope of element i (e.g., 12C, 1H, 16O)
  • mÌ„i is the average atomic mass of element i (weighted by natural abundances)

To calculate a monoisotopic mass, multiply each element’s atom count by that element’s monoisotopic isotope mass and sum the results. To calculate an average mass, do the same using the element’s average atomic mass. The isotopic distribution is built by combining (convolving) the isotope distributions of each element in the formula.

Molecular Mass Examples (Separate Calculations)

The following example problems outline how to calculate monoisotopic (exact) mass from a chemical formula.

Example Problem #1:

  1. First, determine the chemical formula.
    • The formula is given as: C6H12O6.
  2. Next, identify the monoisotopic isotope masses to use (most abundant isotope of each element).
    • 12C = 12.00000000000 u, 1H = 1.00782503223 u, 16O = 15.99491461957 u
  3. Finally, calculate the monoisotopic (exact) mass using the equation above.

Mmono = Σ ni·mi,mono

The values given above are inserted into the equation below and the solution is calculated:

Mmono = 6(12.00000000000) + 12(1.00782503223) + 6(15.99491461957) = 180.063388 (u)

Example Problem #2: 

For this problem, the variables needed are provided below:

chemical formula = H2O

Find the monoisotopic (exact) mass (u) and the abundance (%) of the monoisotopic isotopic composition.

This molecular example requires a separate formula-based calculation using hydrogen and oxygen isotope data. The isotope-mixture calculator above cannot check molecular composition or its abundance.

Mmono = Σ ni·mi,mono = ?