{
  "id": "dipole-moment",
  "version": "2360bfe24a49",
  "status": "published",
  "name": "Dipole Moment Calculator",
  "question": "What is the dipole moment?",
  "summary": "Finds a bond’s dipole moment μ = Q × r in debyes and coulomb meters from the partial charge and the distance between the charges, or the charge (with the percent ionic character) or the distance from the other two.",
  "category": "chemistry",
  "subcategory": "atoms",
  "url": "https://www.acalculator.org/chemistry/dipole-moment-calculator",
  "markdown": "https://www.acalculator.org/chemistry/dipole-moment-calculator.md",
  "kind": "function",
  "method": "μ = Q × r; 1 D = 3.335641 × 10⁻³⁰ C·m; e = 1.602176634 × 10⁻¹⁹ C; percent ionic character = Q ÷ e × 100.",
  "assumptions": [
    "A bond dipole: two equal and opposite point charges a distance r apart. A molecule’s dipole moment is the vector sum of its bond dipoles.",
    "Percent ionic character compares a measured dipole moment with the one a full electron charge at the bond length would give."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "The dipole moment from charge and distance, the charge from μ and distance, or the distance.",
        "type": "string",
        "enum": [
          "mu",
          "q",
          "d"
        ]
      },
      "mu": {
        "title": "Dipole moment μ",
        "description": "The measured dipole moment, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-40,
        "maximum": 1000000
      },
      "mu_u": {
        "title": "Dipole moment unit",
        "description": "Debyes or coulomb meters.",
        "type": "string",
        "enum": [
          "D",
          "Cm"
        ]
      },
      "q": {
        "title": "Charge Q",
        "description": "The size of the partial charges at each end, in the unit chosen below.",
        "type": "number",
        "minimum": 1e-30,
        "maximum": 1000000
      },
      "q_u": {
        "title": "Charge unit",
        "description": "Elementary charges (e) or coulombs.",
        "type": "string",
        "enum": [
          "e",
          "C"
        ]
      },
      "d": {
        "title": "Distance r",
        "description": "The distance between the charges: the bond length for a bond dipole.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000000000
      },
      "d_u": {
        "title": "Distance unit",
        "description": "Picometers, ångströms or nanometers.",
        "type": "string",
        "enum": [
          "pm",
          "A",
          "nm"
        ]
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The dipole moment, the charge with the percent ionic character, or the distance.",
      "format": "text"
    },
    "muD": {
      "label": "Dipole moment (D)",
      "description": "μ in debyes.",
      "format": "number"
    },
    "muCm": {
      "label": "Dipole moment (C·m)",
      "description": "μ in coulomb meters.",
      "format": "number"
    },
    "qE": {
      "label": "Charge (e)",
      "description": "Q in elementary charges.",
      "format": "number"
    },
    "qC": {
      "label": "Charge (C)",
      "description": "Q in coulombs.",
      "format": "number"
    },
    "rPm": {
      "label": "Distance (pm)",
      "description": "r in picometers.",
      "format": "number"
    },
    "rA": {
      "label": "Distance (Å)",
      "description": "r in ångströms.",
      "format": "number"
    },
    "ionic": {
      "label": "Percent ionic character (%)",
      "description": "Q ÷ e × 100: the dipole moment as a percent of the one a full electron charge would give.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "mu",
      "mu": 1.109,
      "mu_u": "D",
      "q": 1,
      "q_u": "e",
      "d": 100,
      "d_u": "pm"
    },
    "outputs": {
      "result": "μ = 4.8032 D (1.60218 × 10⁻²⁹ C·m)",
      "muD": 4.803204643425357,
      "muCm": 1.602176634e-29,
      "qE": 1,
      "qC": 1.602176634e-19,
      "rPm": 100,
      "rA": 1,
      "ionic": 100
    },
    "text": "μ = 4.8032 D (1.60218 × 10⁻²⁹ C·m)."
  },
  "examples": [
    {
      "given": {
        "find": "mu",
        "q": 1,
        "q_u": "e",
        "d": 100,
        "d_u": "pm"
      },
      "expect": {
        "muCm": 1.602176634e-29,
        "muD": 4.803204643425357,
        "result": "μ = 4.8032 D (1.60218 × 10⁻²⁹ C·m)"
      },
      "source": "OpenStax, Chemistry 2e, §7.6 Molecular Structure and Polarity (μ = Qr), https://openstax.org/books/chemistry-2e/pages/7-6-molecular-structure-and-polarity; NIST SP 811, Appendix B.8 (debye = 3.335 641 × 10⁻³⁰ C·m), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8; hand calculation in content.mdx; Python 3"
    },
    {
      "given": {
        "find": "q",
        "mu": 1.109,
        "mu_u": "D",
        "d": 127.5,
        "d_u": "pm"
      },
      "expect": {
        "qE": 0.18108824964583137,
        "ionic": 18.10882496458314
      },
      "source": "Averill and Eldredge, General Chemistry: Principles, Patterns, and Applications, §8.9 Polar Covalent Bonds (percent ionic character), https://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s12-09-polar-covalent-bonds.html: Q = 0.1811 e, about 18% ionic; Python 3",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "q",
        "mu": 9.001,
        "mu_u": "D",
        "d": 236.1,
        "d_u": "pm"
      },
      "expect": {
        "ionic": 79.37133484513384
      },
      "source": "Averill and Eldredge, General Chemistry: Principles, Patterns, and Applications, §8.9 Polar Covalent Bonds (percent ionic character), https://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s12-09-polar-covalent-bonds.html, Example 11: 79.39% after rounding Q to 1.272 × 10⁻¹⁹ C (see content.mdx); Python 3",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "q",
        "mu": 6.08,
        "mu_u": "D",
        "d": 228.1,
        "d_u": "pm"
      },
      "expect": {
        "ionic": 55.49414998224976
      },
      "source": "Averill and Eldredge, General Chemistry: Principles, Patterns, and Applications, §8.9 Polar Covalent Bonds (percent ionic character), https://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s12-09-polar-covalent-bonds.html, Exercise: 55.5%; Python 3",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "d",
        "mu": 1.60218e-29,
        "mu_u": "Cm",
        "q": 1.60218e-19,
        "q_u": "C"
      },
      "expect": {
        "rPm": 100,
        "rA": 1,
        "result": "r = 100 pm (1 Å)"
      },
      "source": "OpenStax, Chemistry 2e, §7.6 Molecular Structure and Polarity (μ = Qr), https://openstax.org/books/chemistry-2e/pages/7-6-molecular-structure-and-polarity: r = μ ÷ Q; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, §7.6 Molecular Structure and Polarity: the bond dipole moment μ = Qr, partial charges from the electronegativity difference, the molecular dipole as the vector sum of bond dipoles. https://openstax.org/books/chemistry-2e/pages/7-6-molecular-structure-and-polarity (retrieved 2026-10-19)",
    "NIST, Special Publication 811, Appendix B.8: debye (D) = 3.335 641 × 10⁻³⁰ C·m; ångström = 1 × 10⁻¹⁰ m. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19)",
    "NIST, CODATA value: elementary charge e = 1.602 176 634 × 10⁻¹⁹ C (exact). https://physics.nist.gov/cgi-bin/cuu/Value?e (retrieved 2026-10-19)",
    "Averill and Eldredge, General Chemistry: Principles, Patterns, and Applications (Saylor Academy), §8.9 Polar Covalent Bonds: HCl (1.109 D, 127.5 pm, 0.1811 e, about 18% ionic), Example 11 NaCl (9.001 D, 236.1 pm, 79.39%), AgCl exercise (6.08 D, 228.1 pm, 55.5%). https://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s12-09-polar-covalent-bonds.html (retrieved 2026-10-19)"
  ],
  "related": [
    "electronegativity",
    "formal-charge",
    "bond-order",
    "effective-nuclear-charge"
  ],
  "changelog": []
}