Aims. We aim to study the fraction of stellar radiation absorbed by dust, f_abs, in 814 galaxies of different morphological types. The targets constitute the vast majority (93%) of the DustPedia sample, including almost all large (optical diameter larger than 1′), nearby (v ≤ 3000 km s⁻¹) galaxies observed with the Herschel Space Observatory. Methods. For each object, we modelled the spectral energy distribution from the ultraviolet to the sub-millimetre using the dedicated, aperture-matched DustPedia photometry and the Code Investigating GALaxy Evolution (CIGALE). The value of f_abs was obtained from the total luminosity emitted by dust and from the bolometric luminosity, which are estimated by the fit. Results. On average, 19% of the stellar radiation is absorbed by dust in DustPedia galaxies. The fraction rises to 25% if only late-type galaxies are considered. The dependence of f_abs on morphology, showing a peak for Sb-Sc galaxies, is weak; it reflects a stronger, yet broad, positive correlation with the bolometric luminosity, which is identified for late-type, disk-dominated, high-specific-star-formation rate, gas-rich objects. We find no variation of f_abs with inclination, at odds with radiative transfer models of edge-on galaxies. These results call for a self-consistent modelling of the evolution of the dust mass and geometry along the build-up of the stellar content. We also provide template spectral energy distributions in bins of morphology and luminosity and study the variation of f_abs with stellar mass and specific star-formation rate. We confirm that the local Universe is missing the high f_abs, luminous and actively star-forming objects necessary to explain the energy budget in observations of the extragalactic background light.