Using our interferometric angular diameter measurements of seven classical Cepheids reported in Kervella et al. (\cite{kervella04}, A&A, 416, 941 - Paper I), complemented by previously existing measurements, we derive new calibrations of the Cepheid period-radius (P-R) and period-luminosity (P-L) relations. We obtain a P-R relation of log R = [0.767 ± 0.009] log P + [1.091 ± 0.011], only 1 σ away from the relation obtained by Gieren et al. (\cite{gieren98}, ApJ, 496, 17). We therefore confirm their P-R relation at a level of Δ(log R) = ± 0.02. We also derive an original calibration of the P-L relation, assuming the slopes derived by Gieren et al. (\cite{gieren98}) from LMC Cepheids, αK = -3.267 ± 0.042 and αV = -2.769 ± 0.073. With a P-L relation of the form Mλ = αλ (log P - 1) + βλ, we obtain log P = 1 reference points of βK = -5.904 ± 0.063 and βV = -4.209 ± 0.075. Our calibration in the V band is statistically identical to the geometrical result of Lanoix et al. (\cite{lanoix99}, MNRAS, 308, 969).
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