To derive higher-level information regarding our sources in extra-galactic astronomy, cosmological calculations are necessary. In Gnuastro, CosmicCalculator is in charge of such calculations. Before discussing how CosmicCalculator is called and operates (in Invoking CosmicCalculator), it is important to provide a rough but mostly self sufficient review of the basics and the equations used in the analysis. In Distance on a 2D curved space the basic idea of understanding distances in a curved and expanding 2D universe (which we can visualize) are reviewed. Having solidified the concepts there, in Extending distance concepts to 3D, the formalism is extended to the 3D universe we are trying to study in our research.
The focus here is obtaining a physical insight into these equations (mainly for the use in real observational studies). There are many books thoroughly deriving and proving all the equations with all possible initial conditions and assumptions for any abstract universe, interested readers can study those books.