Someone asked for the math…
OK, Papa John’s Pizza - the math would work much the same for most national chains.
Their sizes are 10 inches (small), 12 inches (Medium), 14 inches (Large), 16 inches (XL). Let’s say the crust is a consistent 1" on all pizzas.
But remember - the formula for area of a circle is Area = pi * (Radius^2). The above sizes are diameters, not radius. The formulas I used is: Total Area: Pi*((D/2)^2), topped Area: Pi*(((D/2)-1)^2), Crust Area: Total Area - Topped Area.
So a 10" small pizza has an area of 78.54 inches, a topped area of 50.27 inches, and a crust of 28.27 inches.
A 12" medium Pizza has an area of 113.10 inches, a topped area of 78.54 inches, and a crust of 34.56 inches.
A 14" Large Pizza has an area of 153.94 inches, a topped area of 113.10 inches, and a crust of 40.84 inches.
A 16" XL Pizza has an area of 201.06 inches, a topped area of 153.94 inches, and a crust of 47.12 inches.
That means that a large pizza has a topped area 1.44x larger than a medium, and an XL is 1.96x larger.
In my market, Papa John’s has a consistent special of (for 5-toppings pies), $10 for a medium, $12 for a large, and $15 for an XL. If the pizza prices were consistent (based on cost per square inch of topped medium pizza times the topped area of each size pizza), the Large would cost $14.40, and the XL would cost $19.60.
In practice, sometimes the lowest cost per square inch isn’t the end-all be-all. If you only need a medium pizza’s worth of pizza and don’t care to store left overs, save the money. If you need a variety of toppings without cross-contamination, buy the mediums. The price difference is enough to be aware of but not enough to really override practical concerns. A Large pizza costs 83% as much as a medium; an XL is only 76% as much as a Medium (based on topped square inches).