The crystal structures of four samples of anhydrite, CaSO4, were obtained by Rietveld refinements using synchrotron high-resolution powder X-ray diffraction (HRPXRD) data and space group Amma. As an example, for one sample of anhydrite from Hants County, Nova Scotia, the unit-cell parameters are a = 7.00032(2), b = 6.99234(1), c = 6.24097(1) Å, and V = 305.487(1) Å3 with a > b. The eight-coordinated Ca atom has an average <Ca-O> distance of 2.4667(4) Å. The tetrahedral SO4 group has two independent S-O distances of 1.484(1) to O1 and 1.478(1) Å to O2 and an average <S-O> distance of 1.4810(5) Å. The three independent O-S-O angles [108.99(8) × 1, 110.38(3) × 4, 106.34(9)° × 1; average <O-S-O> [6] = 109.47(2)°] and S-O distances indicate that the geometry of the SO4 group is quite distorted in anhydrite. The four anhydrite samples have structural trends where the a, b, and c unit-cell parameters increase linearly with increasing unit-cell volume, V, and their average <Ca-O> and <S-O> distances are nearly constant. The grand mean <Ca-O> = 2.4660(2) Å, and grand mean <S-O> = 1.4848(3) Å, the latter is longer than 1.480(1) Å in celestite, SrSO4, as expected.