Abstract The potential field (PF) solution of the solar corona is a vital modeling tool for a wide range of applications, including minimum energy estimates, coronal magnetic field modeling, and empirical solar wind solutions. Given its popularity, it is important to understand how choices made in computing a PF may influence key properties of the solution. Here we study PF solutions for the global coronal magnetic field on 2012 June 13, computed with our high-performance finite-difference code POT3D. Solutions are analyzed for their global properties and locally around NOAA AR 11504, using the net open flux, open-field boundaries, total magnetic energy, and magnetic structure as metrics. We explore how PF solutions depend on (1) the data source, type, and processing of the inner boundary conditions; (2) the choice of the outer boundary condition height and type; and (3) the numerical resolution and spatial scale of information at the lower boundary. We discuss the various qualitative and quantitative differences that naturally arise by using different maps as input, and we illustrate how coronal morphology and open flux depend most strongly on the outer boundary condition. We also show how large-scale morphologies and the open magnetic flux are remarkably insensitive to model resolution, while the surface mapping and embedded magnetic complexity vary considerably. This establishes important context for past, current, and future applications of the PF for coronal and solar wind modeling.