money
did you know a bigger pizza is actually better value?
area grows with the square of the diameter, so a 14-inch pizza holds nearly twice as much pizza as a 10-inch one.
pizza b gives you more pizza per pound — and it isn’t close if the bigger one is only a little pricier.
the idea
pizza is priced by diameter, but you eat area. and area grows with the square of the diameter — so a pizza that sounds 40% bigger can actually be almost twice the food.
how it works
work out the area of each pizza, then divide the price by the area. the cheaper number wins.
go deeper
you eat area, not diameter
menus sell pizza by width: 10-inch, 14-inch, 18-inch. your stomach cares about something else — how much pizza there actually is.
a 14-inch pizza is only 40% wider than a 10-inch. but it has about 96% more pizza. nearly double, for what is usually much less than double the price.
compare price per square inch
work out the area of each pizza, then divide the price by the area. the cheaper number wins.
this is the same “unit price” trick supermarkets print in tiny type on shelf labels — pizza menus just don’t print it for you.
area = π × (diameter ÷ 2)² value = area ÷ price
why small increases explode
area depends on the radius squared. double the diameter and you get four times the pizza.
so going from 10 to 14 inches multiplies the area by (14 ÷ 10)² = 1.96. the price rarely doubles to match.
squaring punishes intuition: our brains are wired for linear comparisons, and pizza is not linear.
(14 ÷ 10)² = 1.96 → 96% more pizza
things to wonder about next
- the same maths explains why two medium pizzas can be a worse deal than one large — run the numbers before you order.
- crust changes the calculation: if you leave the crusts, the edible area shrinks more on small pizzas.
- where else does squaring hide? house prices per square metre, storage in hard drives, the brightness of stars.
sources & further reading
concepts: area of a circle · unit pricing · geometry
3 minute read