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A carbon-carbon double bond is a covalent bond of bond order two between carbon atoms, conventionally written $\mathrm{C}=\mathrm{C}$. In a localized orbital description it consists of one sigma bond and one pi bond. The distinction describes the symmetry of the bonding orbitals: the localized pi interaction has a nodal plane containing the internuclear axis, whereas the sigma interaction does not.^[ref]

Ethylene, ${\mathrm{H}}_2\mathrm{C}=\mathrm{C}{\mathrm{H}}_2$, illustrates the counting. Its four carbon–hydrogen connections are sigma bonds, and the carbon–carbon connection contributes another sigma bond plus one pi bond. The localized picture therefore has five sigma bonds and one pi bond, representing six shared electron pairs. Calling the central connection a double bond does not mean that the two bonding interactions are geometrically identical.

Maintaining the pi bond favors an aligned arrangement of the participating orbitals. Rotation that destroys this overlap has an energetic cost, which helps make cis-trans isomerism meaningful when each double-bonded carbon has suitable distinct substituents. Ethylene itself has identical hydrogens at each end, so it does not furnish that geometric distinction.

Chemical reactions can change the connection while retaining the carbon skeleton. Fumarate hydratase adds water across the carbon-carbon double bond of fumarate to produce L-malate; the reverse reaction removes water and restores the double bond.^[ref] Counting atoms and identifying bond order thus reveal different parts of the transformation.

Fumarate hydratase, also called fumarase, is the enzyme that reversibly interconverts fumarate plus water with L-malate. The activity is EC4.2.1.2:In the hydration direction, water adds across the carbon-carbon double bond of fumarate. In the reverse direction, water is eliminated. Its lyase classification describes this transformation; the mere presence of water does not make the reaction hydrolysis.^[ref]

For an invented inventory, begin with ten micromoles of fumarate and let six micromoles undergo hydration. Four micromoles of fumarate remain and six micromoles of L-malate form. Each retains a four-carbon skeleton, so the counted carbon inventory remains $4(4+6)=40$ micromoles of carbon atoms. The chosen extent does not determine chemical equilibrium or enzyme kinetics.

A 1995 X-ray crystallography study of Escherichia coli fumarase C found a four-subunit assembly at $2.0\text{A˚}$ resolution. A competitive tungstate derivative helped locate the active site, which included atoms from three of the four protein subunits.^[ref] The example shows why counting subunits and locating a catalytic site are different tasks: several chains can cooperate to build one local reaction environment.