We report on measurements of the hyperfine A, B and C -constants of the 3d4s2 2 D5/2 and 3d4s2 2 D3/2 atomic states in 45Sc. High-precision atomic calculations of the hyperfine fields of these states and second-order corrections are performed, and are used to extract C5/2 = −0.06(6) kHz and C3/2 = +0.04(3) kHz from the data. These results are one order of magnitude more precise than the available literature. From the combined analysis of both atomic states, we infer the nuclear magnetic octupole moment Ω = −0.07(53)μN b, including experimental and atomic structure-related uncertainties. With a single valence proton outside of a magic calcium core, scandium is ideally suited to test a variety of nuclear models, and to investigate in-depth the many intriguing nuclear structure phenomena observed within the neighbouring isotopes of calcium. We perform nuclear shell-model calculations of Ω, and furthermore explore the use of Density Functional Theory for evaluating Ω. From this, mutually consistent theoretical values of Ω are obtained, which are in agreement with the experimental value. This confirms atomic structure calculations possess the accuracy and precision required for magnetic octupole moment measurements, and shows that modern nuclear theory is capable of providing meaningful insight into this largely unexplored observable.