Cooking
Pan area ratio
Compare tins by area, never by diameter. Ten squared over eight squared is 1.5625.
The Formula
area ratio = (new diameter)^2 / (old diameter)^2
Compare tins by area, never by diameter. Ten squared over eight squared is 1.5625.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| old diameter | Diameter of the tin the recipe was written for | length | Eight inches in the worked example. Halve it first if the recipe gives a radius instead. |
| new diameter | Diameter of the tin you want to use | length | Ten inches in the worked example. |
| area ratio | How much more batter the new tin holds at the same depth | dimensionless | 1.5625, which is 56.25 percent more, not the 25 percent the two diameters suggest. |
What Each Symbol Means
old diameterlength
Diameter of the tin the recipe was written for
Eight inches in the worked example. Halve it first if the recipe gives a radius instead.
new diameterlength
Diameter of the tin you want to use
Ten inches in the worked example.
area ratiodimensionless
How much more batter the new tin holds at the same depth
1.5625, which is 56.25 percent more, not the 25 percent the two diameters suggest.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to scale a recipe page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Scale A Recipe, filed under Everyday Life. Every number the guide produces comes from substituting into this one line.