Hong Life CalculatorsUnderstanding the pizza size value calculator — concept and principle
This calculator tells you which of two pizzas gives more pizza for the money by comparing the price per unit of area instead of the price per pizza. It is useful whenever a menu lists several sizes, because the difference in diameter looks small while the difference in food is large.
How it is calculated
- Area of a round pizza = π × (d ÷ 2)², where d is the diameter.
- Price per area = price ÷ area, calculated for A and for B.
- Better deal = the pizza with the lower price per area.
- Total area of the B pizzas ÷ A = number of B × (d_B ÷ d_A)², and total price of the B pizzas = number of B × price B.
Enter both diameters in the same unit. With inches, the result is price per square inch; with centimetres, price per square centimetre. The "number of B pizzas" field lets you compare, say, two small pizzas with one large: it changes the totals, not the price per area or the better deal.
The principle
Area scales with the square of a length. If a diameter grows by a factor of 4/3, as from 12 to 16 inches, the area grows by (4/3)² ≈ 1.78. Prices on menus usually rise roughly in step with the diameter, not its square, so the bigger size is very often the better value per bite. Price per area puts both options on the same scale, just like a price per kilogram at the grocery store.
Worked example
- Inputs: A is 12 in for 12, B is 16 in for 18.
- Area A = π × 6² ≈ 113.10 sq in; price per area A = 12 ÷ 113.10 ≈ 0.106.
- Area B = π × 8² ≈ 201.06 sq in; price per area B = 18 ÷ 201.06 ≈ 0.0895.
- B is cheaper per square inch, so the better deal is B.
- With one B pizza: total area ÷ A = (16 ÷ 12)² ≈ 1.78 and total price 18, so B has about 78% more pizza for 50% more money.
| Pizza A diameter (in or cm) | Price per area A |
|---|---|
| 3 | 1.7 |
| 6 | 0.424 |
| 9 | 0.189 |
| 12 | 0.106 |
| 15 | 0.0679 |
| 18 | 0.0472 |
| 24 | 0.0265 |
How to read the result
A lower price per area means more food per unit of money. The ratio is the most intuitive number: if B costs less than this many times A's price, B is the better buy. Here B would have to cost more than 12 × 1.778 ≈ 21.33 before A became the better deal.
Common mistakes
- Comparing diameters directly, as if a 16-inch pizza were only a third bigger.
- Mixing inches and centimetres for the two pizzas.
- Ignoring the crust: a thick rim takes up a bigger share of a small pizza, so the edible topping area favours the large size even more.
- Comparing a square or rectangular pizza with the circle formula; use length × width for those.
Frequently asked questions
Are two medium pizzas more than one large?
Not always. Two 12-inch pizzas are about 226 sq in, while one 18-inch pizza is about 254 sq in, so the single large pizza has more.
How much bigger is a 14-inch pizza than a 10-inch?
(14 ÷ 10)² = 1.96, almost twice the area.
Does this work in centimetres?
Yes. The ratio is unitless, and the price per area simply becomes price per square centimetre.
Sources: Area of a circle, A = πr² (Euclid, Elements, Book XII, Proposition 2: circles are to one another as the squares on their diameters)