{
  "id": "atomic-mass",
  "version": "a41ad0f9ebcb",
  "status": "published",
  "name": "Atomic Mass Calculator",
  "question": "What is the average atomic mass?",
  "summary": "Finds the average atomic mass of an element from its isotopes’ masses and abundances, Σ(mass × abundance), or the abundance of each of two isotopes from the average.",
  "category": "chemistry",
  "subcategory": "stoichiometry",
  "url": "https://www.acalculator.org/chemistry/atomic-mass-calculator",
  "markdown": "https://www.acalculator.org/chemistry/atomic-mass-calculator.md",
  "kind": "function",
  "method": "Average atomic mass = Σ(mass × abundance) ÷ Σ(abundance). For two isotopes and an average A: abundance 1 = (A − m₂) ÷ (m₁ − m₂) × 100%, abundance 2 = 100% − abundance 1.",
  "assumptions": [
    "Abundances are percents of atoms (amount fractions), and must add to 100% within 0.5 points; the average divides by their sum.",
    "Element presets use NIST’s representative isotopic compositions; natural samples vary a little, which is why IUPAC gives some atomic weights as ranges.",
    "The molar mass in g/mol has the same number as the average atomic mass in u."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "The average atomic mass from isotopes, or the abundances of two isotopes from the average.",
        "type": "string",
        "enum": [
          "average",
          "abundance"
        ]
      },
      "el": {
        "title": "Element",
        "description": "An element to fill in its stable isotopes, or your own isotopes.",
        "type": "string",
        "enum": [
          "custom",
          "B",
          "C",
          "Mg",
          "Cl",
          "Cu",
          "Br",
          "Ag"
        ]
      },
      "isotopes": {
        "title": "Isotopes",
        "description": "Each isotope’s mass in u and its natural abundance in percent.",
        "type": "array",
        "items": {
          "type": "object",
          "properties": {
            "m": {
              "title": "Isotope mass (u)",
              "description": "The isotope’s mass in unified atomic mass units.",
              "type": "number",
              "exclusiveMinimum": 0,
              "maximum": 300
            },
            "a": {
              "title": "Abundance",
              "description": "The share of atoms that are this isotope.",
              "type": "number",
              "x-unit": "percent",
              "minimum": 0,
              "maximum": 100
            }
          }
        }
      },
      "ma": {
        "title": "Isotope 1 mass",
        "description": "Isotope 1 mass in unified atomic mass units (u, also Da).",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 300
      },
      "mb": {
        "title": "Isotope 2 mass",
        "description": "Isotope 2 mass in unified atomic mass units (u, also Da).",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 300
      },
      "avg": {
        "title": "Average atomic mass",
        "description": "Average atomic mass in unified atomic mass units (u, also Da).",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 300
      }
    }
  },
  "outputs": {
    "mass": {
      "label": "Average atomic mass (u)",
      "description": "Σ(isotope mass × abundance) ÷ Σ(abundance).",
      "format": "number"
    },
    "share1": {
      "label": "Isotope 1 abundance",
      "description": "(average − mass 2) ÷ (mass 1 − mass 2) × 100.",
      "format": "percent"
    },
    "share2": {
      "label": "Isotope 2 abundance",
      "description": "100% minus isotope 1’s abundance.",
      "format": "percent"
    },
    "total": {
      "label": "Abundances add to",
      "description": "The sum of the abundances used; the average divides by it.",
      "format": "percent"
    },
    "molar": {
      "label": "Molar mass (g/mol)",
      "description": "The same number in grams per mole.",
      "format": "number"
    },
    "working": {
      "label": "Working",
      "description": "Each isotope’s part of the average.",
      "format": "text"
    },
    "summary": {
      "label": "Answer",
      "description": "The answer in one sentence.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "average",
      "el": "custom",
      "isotopes": [
        {
          "mass": 34.969,
          "abundance": 75.78
        },
        {
          "mass": 36.966,
          "abundance": 24.22
        }
      ],
      "ma": 62.9296,
      "mb": 64.9278,
      "avg": 63.546
    },
    "outputs": {
      "mass": 35.4526734,
      "total": 100,
      "molar": 35.4526734,
      "working": "34.969 × 0.7578 + 36.966 × 0.2422",
      "summary": "The average atomic mass is 35.4527 u"
    },
    "text": "The average atomic mass is 35.4527 u."
  },
  "examples": [
    {
      "given": {
        "find": "average",
        "el": "Cl"
      },
      "expect": {
        "mass": 35.452937582608,
        "total": 100
      },
      "source": "NIST, Atomic Weights and Isotopic Compositions for Chlorine (35Cl 34.968852682 u, 0.7576; 37Cl 36.965902602 u, 0.2424), https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Cl (retrieved 2026-10-02); OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02); Python 3: 34.968852682*0.7576 + 36.965902602*0.2424"
    },
    {
      "given": {
        "find": "average",
        "el": "custom",
        "isotopes": [
          {
            "mass": 34.969,
            "abundance": 75.78
          },
          {
            "mass": 36.966,
            "abundance": 24.22
          }
        ]
      },
      "expect": {
        "mass": 35.4526734,
        "summary": "The average atomic mass is 35.4527 u"
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02); hand calculation in content.mdx: 34.969 × 0.7578 + 36.966 × 0.2422; Python 3"
    },
    {
      "given": {
        "find": "average",
        "el": "custom",
        "isotopes": [
          {
            "mass": 10.0129,
            "abundance": 19.9
          },
          {
            "mass": 11.0093,
            "abundance": 80.1
          }
        ]
      },
      "expect": {
        "mass": 10.811016399999998
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02): about 10.81 amu; Python 3: (10.0129*19.9+11.0093*80.1)/100"
    },
    {
      "given": {
        "find": "abundance",
        "ma": 34.96885,
        "mb": 36.9659,
        "avg": 35.453
      },
      "expect": {
        "share1": 75.75674119326001,
        "share2": 24.243258806739988
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02): 75.76% 35Cl and 24.24% 37Cl; Python 3: (35.453-36.96590)/(34.96885-36.96590)*100"
    },
    {
      "given": {
        "find": "abundance",
        "ma": 62.9296,
        "mb": 64.9278,
        "avg": 63.546
      },
      "expect": {
        "share1": 69.15223701331212,
        "share2": 30.847762986687883
      },
      "source": "NIST, Atomic Weights and Isotopic Compositions for Copper (63Cu 62.92959772 u, 0.6915; 65Cu 64.92778970 u, 0.3085; standard atomic weight 63.546), https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Cu (retrieved 2026-10-02); hand calculation in content.mdx: (63.546 − 64.9278) ÷ (62.9296 − 64.9278); Python 3"
    },
    {
      "given": {
        "find": "average",
        "el": "Mg"
      },
      "expect": {
        "mass": 24.3050516198371
      },
      "source": "NIST, Atomic Weights and Isotopic Compositions for Magnesium (standard atomic weight [24.304, 24.307]), https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Mg (retrieved 2026-10-02); Python 3"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average mass = Σ(fractional abundance × isotopic mass); boron, magnesium and neon examples; chlorine abundances 75.76% and 24.24% from the average 35.453 amu). https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02)",
    "NIST Physical Measurement Laboratory, Atomic Weights and Isotopic Compositions for All Elements (relative atomic masses and representative isotopic compositions of B, C, Mg, Cl, Cu, Br and Ag, from IUPAC/CIAAW). https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl (retrieved 2026-10-02)",
    "IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Chlorine (standard atomic weight [35.446, 35.457]; isotope amount fractions ³⁵Cl [0.755, 0.761], ³⁷Cl [0.239, 0.245]). https://www.ciaaw.org/chlorine.htm (retrieved 2026-10-02)"
  ],
  "related": [
    "molar-mass",
    "mole",
    "stoichiometry"
  ],
  "changelog": []
}