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Use the amphiphile packing parameter $P=v/(a_0{\ell }_c)$, where $v$ is tail volume, $a_0$ the effective head-group area and ${\ell }_c$ the maximum tail extension. The conventional cylindrical-micelle window is $1/3\lesssim P\lesssim 1/2$. Its upper limit follows directly from cylindrical micelle geometry: a long core of radius $R$ has volume-to-area ratio $R/2$, so $v/a_0=R/2\le {\ell }_c/2$. The spherical packing limit is $P=1/3$; above it a filled spherical core cannot accommodate the assumed head-group area and chain length.

Inverting both positive inequalities givesThus the useful estimate is a head-group area of approximately $0.25$–$0.37\mathrm{n}{\mathrm{m}}^2$. If phase-boundary configurations are excluded, use strict inequalities. These endpoints are geometric morphology crossovers, rather than exact thermodynamic phase boundaries: chain conformations and head-group interactions also affect which micelle minimizes the free energy. The supplied molecular volume is interpreted as the tail-core volume required by this packing model.^[ref]