# What is the dipole moment?

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.

- Page: https://www.acalculator.org/chemistry/dipole-moment-calculator
- JSON spec: https://www.acalculator.org/chemistry/dipole-moment-calculator.json
- Version: 2360bfe24a49

## Default answer

Example with the default inputs (Find Dipole moment, Charge Q 1, Charge unit e, Distance r 100, Distance unit pm): μ = 4.8032 D (1.60218 × 10⁻²⁹ C·m).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | The dipole moment from charge and distance, the charge from μ and distance, or the distance. |
| mu | Dipole moment μ | The measured dipole moment, in the unit chosen below. |
| mu_u | Dipole moment unit | Debyes or coulomb meters. |
| q | Charge Q | The size of the partial charges at each end, in the unit chosen below. |
| q_u | Charge unit | Elementary charges (e) or coulombs. |
| d | Distance r | The distance between the charges: the bond length for a bond dipole. |
| d_u | Distance unit | Picometers, ångströms or nanometers. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The dipole moment, the charge with the percent ionic character, or the distance. |
| muD | Dipole moment (D) | μ in debyes. |
| muCm | Dipole moment (C·m) | μ in coulomb meters. |
| qE | Charge (e) | Q in elementary charges. |
| qC | Charge (C) | Q in coulombs. |
| rPm | Distance (pm) | r in picometers. |
| rA | Distance (Å) | r in ångströms. |
| ionic | Percent ionic character (%) | Q ÷ e × 100: the dipole moment as a percent of the one a full electron charge would give. |

## 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.

## Worked examples

1. find = mu, q = 1, q_u = e, d = 100, d_u = pm gives muCm = 1.60218 × 10⁻²⁹, muD = 4.8032, 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.
2. find = q, mu = 1.109, mu_u = D, d = 127.5, d_u = pm gives qE = 0.181088, ionic = 18.1088. 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.
3. find = q, mu = 9.001, mu_u = D, d = 236.1, d_u = pm gives ionic = 79.3713. 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.
4. find = q, mu = 6.08, mu_u = D, d = 228.1, d_u = pm gives ionic = 55.4941. 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%.
5. find = d, mu = 0, mu_u = Cm, q = 0, q_u = C gives 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.

## FAQ

### How do I calculate a dipole moment?

Multiply the charge by the distance between the charges: μ = Q × r. A full electron charge (1.602 × 10⁻¹⁹ C) 100 pm from its opposite gives 1.602 × 10⁻¹⁹ × 1 × 10⁻¹⁰ = 1.602 × 10⁻²⁹ C·m, which is 4.80 D.

### What is a debye?

The usual unit of dipole moment for molecules: 1 D = 3.335 641 × 10⁻³⁰ C·m (NIST). Molecular dipole moments are a few debyes; HCl’s is 1.109 D.

### How do I calculate percent ionic character?

Divide the measured dipole moment by the one a full electron charge at the bond length would give, and multiply by 100. That is the same as the charge Q = μ ÷ r in units of e, times 100. HCl: 1.109 D at 127.5 pm gives Q = 0.181 e, so the bond is about 18% ionic.

### Why does my percent ionic character differ from the textbook?

Textbooks round along the way. For NaCl (9.001 D, 236.1 pm), Averill and Eldredge round Q to 1.272 × 10⁻¹⁹ C and get 79.39%; without rounding, the page gives 79.3713%. They also use 1 D = 3.3356 × 10⁻³⁰ C·m and e = 1.6022 × 10⁻¹⁹ C.

### Is a molecule’s dipole moment the same as its bond dipole?

Only for a two-atom molecule. A bigger molecule’s dipole moment is the vector sum of its bond dipoles, so symmetric molecules such as CO₂ have polar bonds but no overall dipole (OpenStax §7.6). This page works with one pair of charges.

### What sets the size of the partial charges?

The electronegativity difference between the two atoms: the larger it is, the larger the partial charges and the dipole moment. HF has a larger dipole moment than CO, because the difference is larger (OpenStax §7.6).

## 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)