Studies on high-entropy materials often speculate about the effects of lattice distortion and disorder on characteristics such as hardness, thermal expansion, and electronic properties. Notwithstanding the ongoing race to discover new compositions, investigations of the local structure at the atomic level remain sparse at best. Additionally, assessments of the homogeneity of the distribution of metals within the lattice sites are often restricted to techniques such as energy dispersive spectroscopy which might lead to an inaccurate picture of the bulk material. Herein, we report an extensive and systematic study of a class of emerging high-entropy ceramics that uses a combination of high-resolution synchrotron powder diffraction and extended X-ray absorption fine structure analysis. Our data are consistent with a random distribution of atoms with local strain around the d-metals sites, which describes the bulk structure of these materials. Moreover, a linear trend is observed between the average structure and the first-neighbor distances, regardless the number (from 3 to 5) and type (Ti, Zr, Nb, Hf, Ta, Mo, W) of metals that constitute the high-entropy ceramic, which suggests that any description of properties for such materials need to go beyond the simple dichotomy of long-range order and local structure.