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In bent molecular geometry, two neighbours and their central chemical atom form a noncollinear triangle, with an interior bond angle strictly between $0^{\circ }$ and $180^{\circ }$. Water, ${\mathrm{H}}_2\mathrm{O}$, is the standard example. The NIST CCCBDB experimental water entry, internal coordinates, citing Hoy and Bunker (1979) gives the equilibrium H–O–H bond angle as $104.4776^{\circ }$ with quoted uncertainty $0.0019^{\circ }$, usually rounded to $104.5^{\circ }$.

The oxygen in water has two bonding electron domains and two lone pairs. Its ideal electron pair geometry is tetrahedral, while the three atomic nuclei give bent molecular geometry. Three points always lie in a plane; this does not make the four-domain scaffold planar. Nor does the word bent by itself determine an electron domain count: the same atomic shape can arise from other domain arrangements.

In an illustrative model with two equal bond-dipole contributions of magnitude $p$ separated by bond angle $\theta$, their sum of vectors points along the bisector and has magnitude $2p\cos (\theta /2)$. At $180^{\circ }$ it vanishes; at $104.4776^{\circ }$ it is approximately $1.2247p$. This ratio is a geometric calculation, not a prediction of water's measured electric dipole moment. The entire electron density, including contributions represented by lone pairs, matters. Water is a polar molecule; chemical polarity helps explain its interactions with other polar molecules. See McMurry, Organic Chemistry, §2.2: water, lone-pair contributions, and polarity.

Chemical polarity concerns unequal distribution of electron density in a chemical bond or molecule. A polar molecule has a permanent electric dipole moment; the effects of individual bonds must be combined with their spatial arrangement. In a symmetric linear carbon dioxide molecule, opposing bond-dipole contributions cancel. In water, its bent molecular geometry prevents that cancellation, giving a permanent electric dipole moment.^[ref]

An electric dipole is a pair of equal and opposite charges in a small separation limit with their charge-times-separation vector held fixed.

The electric dipole moment measures the first spatial moment of signed electric charge. For localized point charges $q_i$ at positions ${\mathbf{r}}_i$, or an integrable charge density $\rho (\mathbf{r})$ with a finite first moment, define^[ref].

The electric dipole moment is a vector with SI units $\mathrm{C}\mathrm{m}$: coulombs times length in metres. Opposite electric charges can cancel in $Q$ while contributing in the same direction to $\mathbf{p}$. For a neutral pair with positive electric charge $q>0$ at ${\mathbf{r}}_{+}$ and negative electric charge $-q$ at ${\mathbf{r}}_{-}$,Thus the electric dipole moment points from negative to positive electric charge, not along the attraction between the two point charges. ^[ref].

Changing the coordinate origin changes the position vectors, not the physical electric charge distribution. If the new origin is at $\mathbf{a}$ relative to the old origin, ${\mathbf{r}}_i^{\prime }={\mathbf{r}}_i-\mathbf{a}$, so direct substitution givesConsequently charge neutrality makes the electric dipole moment independent of the origin. For a system with nonzero total electric charge, always specify the origin: a single point charge at the old origin has $\mathbf{p}=0$ but ${\mathbf{p}}^{\prime }=-Q\mathbf{a}$. This is coordinate bookkeeping, not a newly created electric dipole. The full electric potential stays the same at the same physical point; the terms of its electric multipole expansion and the observation coordinates change together.

As a stipulated numerical example, put $+2\mathrm{nC}$ at $(1,0,0)\mathrm{mm}$ and $-2\mathrm{nC}$ at $(-1,0,0)\mathrm{mm}$. Their total electric charge is zero and $\mathbf{p}=(4\times 10^{-12},0,0)\mathrm{C}\mathrm{m}$. Translating the origin by $(3,-2,0)\mathrm{mm}$ leaves this electric dipole moment unchanged. Adding $+1\mathrm{nC}$ at the old origin instead gives $Q=1\mathrm{nC}$ and ${\mathbf{p}}^{\prime }=(1,2,0)\times 10^{-12}\mathrm{C}\mathrm{m}$. Distinguishing these two cases prevents the mistaken claim that every electric dipole moment is independent of the origin.

The usefulness of the electric dipole moment is compression: many internal electric charges determine one vector governing the leading distant electric potential of a neutral localized object when $\mathbf{p}\ne 0$. ^[ref]. A polar molecule need not literally contain two point charges; its atomic nuclei and electron density collectively give an electric dipole moment. For example, the chemical polarity of water reflects its bent molecular geometry, whereas the symmetric linear molecular geometry of carbon dioxide makes its permanent electric dipole moment vanish. ^[ref]. A collection of such electric dipole moments per unit volume gives electric polarization. ^[ref].

A polar molecule has a nonzero permanent electric dipole moment because of its internal electric charge distribution. It can still have zero total electric charge. Water is polar; a nonpolar molecule has no permanent electric dipole moment.

In trigonal pyramidal molecular geometry, three neighbouring chemical atoms form a triangular base and the central chemical atom lies outside its plane. The pyramid has four atomic nuclei; its central chemical atom is the apex, not the centre of the base. Ammonia, ${\mathrm{NH}}_3$, has this arrangement. The ^[ref] lists an H–N–H bond angle of $106.67^{\circ }$, commonly rounded to $106.7^{\circ }$ or about $107^{\circ }$.

The Lewis structure of ammonia allocates eight valence electrons as three bond pairs and one lone pair. Four electron domains therefore suggest tetrahedral electron pair geometry; removing the lone pair marker leaves three hydrogen chemical atoms below nitrogen. The VSEPR model treats the lone pair as more space-demanding and predicts compression relative to $109.4712^{\circ }$, but it does not calculate the precise $106.67^{\circ }$ value. See Chemistry 2e, §7.6: lone-pair effects.

Three equal bond-dipole contributions in this pyramid cancel sideways, but retain a component along its axis. By contrast, three equal contributions lying in one plane at $120^{\circ }$ would cancel completely. This shows how a small change in molecular geometry can permit a permanent electric dipole moment. Ammonia is a polar molecule; NIST lists a measured magnitude of about $1.476$ debye in the same ^[ref]. The vector argument predicts allowed direction and cancellation, not the full measured magnitude.