Pipe cross-sectional area is the area of a circle as seen when looking at the end of a pipe. The flow capacity of different size pipes is easily compared when the velocity is held constant. The flow capacity will vary in direct proportion to the change in area. The area varies directly with the square of the inside diameter.
When one speaks of a one inch pipe, it is a nominal one inch; the true inside diameter usually is not 1 inch. For a Class 160 PVC pipe, the inside diameter is actually 1.195 inches. The outside diameters are kept constant so pipe fittings will fit. Inside diameters vary depending on the wall thickness. Higher pressure rated pipes will have thicker walls and smaller inside diameters.
The comparison process is developed from the cross-sectional area of a pipe, described by the area equation for a circle:
A ratio of the two areas will reduce to a ratio of the two diameters squared. Therefore, the flow of water in the two pipes is compared using a ratio of their diameters squared.
Too frequently the benefits -- present and future -- of the larger pipe are overlooked. Yes, pipe costs will be greater for larger diameter pipe, but the larger pipe allows future expansion. More on that later!