Dipole Moment Calculator

Background.

Put a positive and a negative charge of equal size close together and, seen from far away, they almost cancel: the net charge is zero. Almost is the interesting part. The pair still produces an electric field, still twists when placed in an external field, and still tugs on nearby charges, and the single quantity that governs all of that at a distance is the electric dipole moment — the size of either charge multiplied by the distance between them.

In SI units the moment is in coulomb-metres. The default pair here, ±2 µC held 3 cm apart, has a moment of 6 × 10⁻⁸ C·m. Chemistry works in a far smaller unit, the debye, worth about 3.336 × 10⁻³⁰ C·m, because molecular dipoles involve fractions of an electron's charge across fractions of a nanometre; a water molecule's moment is about 1.85 D.

Why the product, rather than the charges alone? Because, seen from a distance, doubling the separation has exactly the same effect as doubling the charge. The far field of a dipole is proportional to p and falls off with the cube of distance, the torque in a uniform field E is pE sin θ, and the potential energy there is −pE cos θ. In every case q and d enter only through their product, which makes p the natural figure for comparing one dipole with another.

The page computes the magnitude for the idealised case of two equal and opposite point charges. The direction of the moment, a spread-out charge distribution and its higher multipole terms are left out. Charges below 2 × 10⁻¹⁸ C, about 12.5 electron charges, are outside the accepted range, so single-electron molecular cases have to be worked by hand.

What is dipole moment calculator?

The electric dipole moment of two equal and opposite point charges, +q and −q, is a vector of magnitude p = q·d, where d is the distance between them, pointing from the negative charge toward the positive one. It measures how strongly the pair behaves as a dipole: the field it produces at a distance, the torque it feels in an external field, and its energy there. The SI unit is the coulomb-metre, written C·m.

How to use this calculator.

1. 01Enter the magnitude of one of the two charges in coulombs — not their sum, and without a sign. A charge of 2 µC is entered as 0.000002.
2. 02Enter the distance between the two charge centres in metres: 3 cm is 0.03 and 5 mm is 0.005.
3. 03Read the dipole moment in coulomb-metres. To express it in debye, divide by 3.336 × 10⁻³⁰.
4. 04Keep the scope note in mind: the result is a magnitude for two point charges, so direction and the detail of a spread-out charge are not included.

The formula.

p = q × d, where q is the magnitude of each charge in coulombs and d the separation in metres, giving p in coulomb-metres. The formula is exact for two point charges. For a continuous distribution the moment is the sum, or integral, of each bit of charge times its position vector, and for a neutral distribution that sum does not depend on where the origin is placed. The two inputs act symmetrically: doubling either one doubles the moment, and halving the charge while doubling the gap leaves it unchanged. What the moment then controls follows from standard results — far from the dipole the field on its axis is E = 2kp/r³, with k = 8.988 × 10⁹ N·m²/C²; the torque in a uniform field is pE sin θ; the potential energy is −pE cos θ. A zero charge or zero gap gives no dipole at all, so both entries must be greater than zero.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 2, section 5.4, Electric Field of a Dipole.
2. [2]Griffiths, Introduction to Electrodynamics, 4th ed. (PRINT), section 3.4.1, electric dipole moment.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.