The volume densities of giant molecular clouds in M81

H I features near young star clusters in M81 are identified as the photodissociated surfaces of giant molecular clouds (GMCs) from which the young stars have recently formed. The H I column densities of these features show a weak trend, from undetectable values inside R = 3.7 kpc and increasing rapidly to values around 3 x 10(21) cm(-2) near R approximate to 7.5 kpc. This trend is similar to that of the radially averaged H I distribution in this galaxy, and implies a constant area covering factor of approximate to 0.21 for GMCs throughout M81. The incident UV fluxes G(0) of our sample of candidate PDRs decrease radially. A simple equilibrium model of the photodissociation-reformation process connects the observed values of the incident UV flux, the H I column density, and the relative dust content, permitting an independent estimate to be made of the total gas density in the GMC. Within the GMC this gas will be predominantly molecular hydrogen. Volume densities of 1 < n < 200 cm(-3) are derived, with a geometric mean of 17 cm(-3). These values are similar to the densities of GMCs in the Galaxy, but somewhat lower than those found earlier for M101 with similar methods. Low values of molecular density in the GMCs of M81 will result in low levels of collisional excitation of the CO(1-0) transition, and are consistent with the very low surface brightness of CO(1-0) emission observed in the disk of M81.