{
  "id": "percent-abundance",
  "version": "b128a245df6e",
  "status": "published",
  "name": "Percent Abundance Calculator",
  "question": "What is the percent abundance?",
  "summary": "Finds the percent abundance of each of an element’s two isotopes from their masses and the average atomic mass, or the average or an isotope’s mass from the others.",
  "category": "chemistry",
  "subcategory": "stoichiometry",
  "url": "https://www.acalculator.org/chemistry/percent-abundance-calculator",
  "markdown": "https://www.acalculator.org/chemistry/percent-abundance-calculator.md",
  "kind": "formulas",
  "method": "M = m₁ × p₁ ÷ 100 + m₂ × p₂ ÷ 100 with p₂ = 100 − p₁, so p₁ = (M − m₂) ÷ (m₁ − m₂) × 100; m₁ = m₂ + (M − m₂) × 100 ÷ p₁; m₂ = m₁ + (M − m₁) × 100 ÷ p₂.",
  "assumptions": [
    "The element has exactly two isotopes, and the abundances are percents of atoms (amount fractions).",
    "Masses are in unified atomic mass units (u, also called amu or Da); the molar mass in g/mol has the same number.",
    "An abundance is from 0% to 100%, so the average must lie between the two isotope masses."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "avg": {
        "title": "Average atomic mass (u)",
        "description": "The element’s average atomic mass, in unified atomic mass units.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 300
      },
      "m1": {
        "title": "Isotope 1 mass (u)",
        "description": "The mass of the first isotope, in unified atomic mass units.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 300
      },
      "m2": {
        "title": "Isotope 2 mass (u)",
        "description": "The mass of the second isotope, in unified atomic mass units.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 300
      },
      "p1": {
        "title": "Isotope 1 abundance",
        "description": "The percent of the element’s atoms that are isotope 1.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "avg",
      "m1",
      "m2",
      "p1"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "avg": {
      "label": "Average atomic mass (u)",
      "description": "m₁ × p₁ ÷ 100 + m₂ × p₂ ÷ 100.",
      "format": "number"
    },
    "m1": {
      "label": "Isotope 1 mass (u)",
      "description": "m₂ + (M − m₂) × 100 ÷ p₁.",
      "format": "number"
    },
    "m2": {
      "label": "Isotope 2 mass (u)",
      "description": "m₁ + (M − m₁) × 100 ÷ (100 − p₁).",
      "format": "number"
    },
    "p1": {
      "label": "Isotope 1 abundance",
      "description": "(M − m₂) ÷ (m₁ − m₂) × 100: the percent of atoms that are isotope 1.",
      "format": "percent"
    },
    "p2": {
      "label": "Isotope 2 abundance",
      "description": "100% − isotope 1’s abundance.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "avg": 35.453,
      "m1": 34.96885,
      "m2": 36.9659
    },
    "outputs": {
      "p1": 75.75674119326005,
      "p2": 24.24325880673994
    },
    "text": "With isotope masses 34.96885 u and 36.9659 u and an average of 35.453 u, isotope 1 is 75.7567% and isotope 2 is 24.2433%."
  },
  "examples": [
    {
      "given": {
        "avg": 35.453,
        "m1": 34.96885,
        "m2": 36.9659
      },
      "expect": {
        "p1": 75.75674119326005,
        "p2": 24.24325880673994
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average mass = Σ(fractional abundance × isotopic mass); Example 2.5: 35Cl 34.96885 amu, 37Cl 36.96590 amu, average 35.453 amu give 75.76% and 24.24%; Check Your Learning: 63Cu 62.9296, 65Cu 64.9278, average 63.546 give 69.15% and 30.85%), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-18); hand calculation in content.mdx: (35.453 − 36.96590) ÷ (34.96885 − 36.96590) = 1.51290 ÷ 1.99705"
    },
    {
      "given": {
        "avg": 63.546,
        "m1": 62.9296,
        "m2": 64.9278
      },
      "expect": {
        "p1": 69.15223701331198,
        "p2": 30.847762986688018
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average mass = Σ(fractional abundance × isotopic mass); Example 2.5: 35Cl 34.96885 amu, 37Cl 36.96590 amu, average 35.453 amu give 75.76% and 24.24%; Check Your Learning: 63Cu 62.9296, 65Cu 64.9278, average 63.546 give 69.15% and 30.85%), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-18); hand calculation in content.mdx: (63.546 − 64.9278) ÷ (62.9296 − 64.9278) = 1.3818 ÷ 1.9982"
    },
    {
      "given": {
        "m1": 10.0129,
        "m2": 11.0093,
        "p1": 19.9
      },
      "expect": {
        "avg": 10.8110164,
        "p2": 80.1
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average mass = Σ(fractional abundance × isotopic mass); Example 2.5: 35Cl 34.96885 amu, 37Cl 36.96590 amu, average 35.453 amu give 75.76% and 24.24%; Check Your Learning: 63Cu 62.9296, 65Cu 64.9278, average 63.546 give 69.15% and 30.85%), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-18) (boron, about 10.81 amu); hand calculation in content.mdx: 10.0129 × 0.199 + 11.0093 × 0.801"
    },
    {
      "given": {
        "avg": 63.546,
        "m1": 62.9296,
        "p1": 69.15
      },
      "expect": {
        "m2": 64.92765510534846,
        "p2": 30.85
      },
      "source": "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average mass = Σ(fractional abundance × isotopic mass); Example 2.5: 35Cl 34.96885 amu, 37Cl 36.96590 amu, average 35.453 amu give 75.76% and 24.24%; Check Your Learning: 63Cu 62.9296, 65Cu 64.9278, average 63.546 give 69.15% and 30.85%), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-18); hand calculation in content.mdx: 62.9296 + (63.546 − 62.9296) × 100 ÷ (100 − 69.15)"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism: average mass = Σ(fractional abundance × isotopic mass); Example 2.5, Calculation of Percent Abundance (chlorine, 75.76% 35Cl and 24.24% 37Cl); Check Your Learning (copper, 69.15% Cu-63 and 30.85% Cu-65). https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-18)"
  ],
  "related": [
    "atomic-mass",
    "molar-mass",
    "mole"
  ],
  "changelog": []
}