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In the adiabatic cloud droplet number retrieval, the independently retrieved liquid-water path fixes the geometrical thickness in the adiabatic model:Define $C_c=(3/5)\pi Q_{\mathrm{ext}}{k}^{1/3}[3c_w/(4\pi {\rho }_w){]}^{2/3}$. Since ${\tau }_c=C_c{N}^{1/3}{H}^{5/3}$, eliminating $H$ givesUse SI units to obtain $N$ in ${\mathrm{m}}^{-3}$, then divide by $10^6$ for $\mathrm{c}{\mathrm{m}}^{-3}$. The sensitivity is substantial: $d\log N=3d\log {\tau }_c-(5/2)d\log W+(1/2)d\log c_w-d\log k-3d\log Q_{\mathrm{ext}}$. Thus a numerical retrieval additionally needs the adiabatic condensation coefficient, shape factor and extinction efficiency. A nonadiabatic water profile, mixed phase, horizontal inhomogeneity or a biased water-path retrieval can produce a large number-concentration bias.