This research presents a comprehensive re-evaluation and improvement of map projection distortion analysis, building upon the foundational framework of Goldberg and Gott. The fundamental challenge in cartography lies in representing the Earth’s spherical surface on a flat plane, called map projection, a process that inevitably introduces distortions in area, shape, or distance. This study aims to refine the quantification of these distortions by employing an improved distance metric that accurately measures projected geodesics, utilising high-precision numerical methods with over 10 million sample points to minimise error, and introducing an unbiased total distortion score that eliminates the arbitrary normalisation of previous methods. The results identify the Winkel Tripel projection as the best-performing overall map based on the improved, unbiased total distortion score.

Furthermore, this work critically investigates the viability of using the fractal dimension of coastlines as a novel distortion metric, leading to a shift in analysis towards evaluating distortions specifically along coastal geometries. However, theoretical computations using fractal dimension show that it is unsuitable as a global distortion metric due to its invariance under the bi-Lipschitz transformations that define many map projections. By establishing a normalisation approach based on coastline arc length, this study provides a robust and resolution-independent framework for tailored cartographic evaluation. The findings underscore the sensitivity of distortion scores to globe orientation and establish a foundational methodology for future property-specific distortion analyses, ensuring a more reliable and application-focused approach to selecting map projections than previously done. For the specific application of representing coastlines with minimal distortion, the Azimuthal Equidistant projection is found to be the most fitting.