Electric Dipole Moment Calculator (p = qd in C·m and debye, torque and energy in a field)

Understanding the electric dipole moment calculator — concept and principle

Two equal and opposite charges a small distance apart form an electric dipole. This calculator finds its dipole moment in C·m and debye, and the torque and potential energy it experiences in a uniform electric field.

One elementary charge pair 1 Å apart makes 4.8 debye; real bonds share charge only partly, so they are smaller.

How it is calculated

Dipole moment p = q × d, pointing from the negative to the positive charge.
1 debye = 10⁻²¹ ÷ c C·m ≈ 3.33564 × 10⁻³⁰ C·m.
Torque in a uniform field: τ = pE sin θ.
Potential energy: U = −pE cos θ (lowest when aligned, θ = 0°).
e = 1.602176634 × 10⁻¹⁹ C (exact, 2019 SI).

The principle

A dipole has no net charge, but because its charges are separated, a uniform field pushes them in opposite directions, creating a torque that turns the dipole towards the field. The dipole moment combines both factors that matter: charge size and separation. Molecules with uneven electron distribution, such as water, have permanent dipoles, which explains their alignment in fields, their high dielectric constants and many intermolecular forces.

Worked example

Default inputs: q = 1 e, d = 100 pm, E = 10⁶ V/m, θ = 90°.

p = 1.602 × 10⁻¹⁹ C × 100 × 10⁻¹² m ≈ 1.602 × 10⁻²⁹ C·m.
In debye: 1.602 × 10⁻²⁹ ÷ 3.33564 × 10⁻³⁰ ≈ 4.803 D.
Torque = 1.602 × 10⁻²⁹ × 10⁶ × sin 90° ≈ 1.602 × 10⁻²³ N·m.
Potential energy = −pE cos 90° = 0 J (0 eV).

How to read the result

Real molecular dipoles are smaller than this full-charge example because charges are only partly separated: water's dipole is about 1.85 D, while 4.8 D would mean a full electron transferred over 100 pm. Comparing a measured dipole with q × d gives the "percent ionic character" of a bond.

Common mistakes

Using the full charge e for bonds with only partial charges.
Mixing picometres and ångströms (1 Å = 100 pm).
Confusing torque (maximum at 90°) with energy (zero at 90°).
Getting the sign of U wrong.

Keep in mind: The point-dipole model is an approximation for molecules. Use quantum chemistry or measured values for precise work.

Frequently asked questions

What is a debye?

A unit of dipole moment, about 3.336 × 10⁻³⁰ C·m.

What is the dipole moment of water?

About 1.85 D in the gas phase.

When is the torque on a dipole largest?

When the dipole is perpendicular to the field (θ = 90°).

Sources: Griffiths, D. J., Introduction to Electrodynamics, 4th ed. Cambridge University Press (dipoles) · CRC Handbook of Chemistry and Physics, Dipole moments of molecules

Checked 9 Nov 2026. Electric dipole moment p = qd, torque τ = p × E and energy U = −p·E — standard results of electrostatics. Debye unit 10⁻²¹/c C·m (standard definition); e exact (2019 SI).

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