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Use an ideal feed in which every starting molecule has exactly two suitable functional groups: either one $A$ and one $B$, or two $A$ groups mixed with two $B$ groups. Only an $A$–$B$ pairing can form a joining chemical bond. Assume no loss of feed-derived material, no splitting of chains, no competing consumption of the counted functional groups, no branching, and no cyclization in step-growth polymerization. Linear here describes connectivity; a chain can bend in space. Small byproducts of polycondensation do not enter the chain-bearing molecule count.

Let $N_0$ count all initial feed molecules, $J$ the number of intermolecular joins, and $N$ all remaining chain-bearing molecules, including unreacted monomers. Each join turns two molecules into one, so $N=N_0-J$ exactly. If chain $i$ contains $j_i$ feed-derived monomeric units, conservation gives ${\sum }_{i=1}^N{j}_i=N_0$. Consequently the number-average degree of polymerization isThis is a count of both feed species' monomeric units, rather than a count of interior constitutional repeating units. For $AA+BB$ chemistry an interior repeat often contains two feed-derived units, as explained in monomer. Equal functional group reactivities are not needed for this bookkeeping at a specified $J$; predicting a time course or a chain-length probability distribution requires additional assumptions.

For the figure's eight $AB$ feed molecules, three joins can give lengths $(2,3,1,1,1)$, so $N=5$ and $X_n=8/5$. Joining the first two chains gives $(5,1,1,1)$: the incorporated total stays eight, $N$ becomes four, and $X_n=2$. A graph makes the bookkeeping visible: each starting monomer molecule is a vertex of a graph, and each intermolecular joining chemical bond connects two previously distinct connected components of a graph. The connected pieces are the counted molecules.

Polycondensation is step-growth polymerization in which joining reactions eliminate small molecules. Its chain-bearing molecule count excludes those byproducts; otherwise two chains joining while releasing one small product would misleadingly appear to conserve the counted population.^[ref]

In step-growth polymerization, suitable reactive groups on molecules of different chain lengths can join. The linear count and its assumptions are given in polymerization.

A one-unit monomer, a two-unit chain, and a twenty-unit chain can all be joining partners if their functional groups are compatible and accessible. Schematically, $P_j+P_k⟶P_{j+k}$: the subscripts count monomeric units, and end-group chemistry is suppressed. In chain-growth propagation, by contrast, $P_j^{\ast }+M⟶P_{j+1}^{\ast }$ requires a free monomer and a polymerization-active site. An arbitrary pair of existing chains is not a propagation pair in that mechanism. The practical consequence of step-growth polymerization is that most monomers can have joined something while the average chain is still short.

Whether a joining step releases a small molecule is a separate question. Polycondensation releases small products during the joining chemistry, as in the Nylon 6,10 demonstration in polymerization. Polyaddition joins suitable chains without that elimination: reacting a diol with a molecule bearing two isocyanate groups can build a polyurethane. Thus step-growth polymerization and polycondensation are not synonyms.^[ref]