Hong Life CalculatorsUnderstanding the cake pan size converter — concept and principle
Your recipe calls for a 20 cm round tin, but you only have a 24 cm one, or a square pan. Using the same amount of batter in a bigger pan gives a thin, dry cake; in a smaller one it may overflow or stay raw in the middle. This converter tells you how much to multiply the ingredients by so the batter fills the new pan to the same depth.
How it is calculated
- Area of a round pan = π × (d ÷ 2)², where d is the diameter in centimetres.
- Area of a square pan = side².
- Multiply ingredients by = new pan area ÷ original pan area. For two round pans this simplifies to (d₂ ÷ d₁)².
If you enter a square side greater than 0, the calculator uses the square pan as the new pan and ignores the second diameter. Measure pans across the inside top edge.
The principle
Batter volume equals pan area times batter depth. To keep the cake the same height, and so bake it in a similar way, the depth must stay the same, which means the batter volume must change in proportion to the area. Area grows with the square of the diameter, so a pan only 20% wider holds 44% more batter. This is why small changes in diameter matter so much, and why "a 24 cm pan is close to a 20 cm one" is a common baking mistake.
Worked example
- Inputs: original round pan 20 cm, new round pan 24 cm, no square pan.
- Original area: π × 10² = 314.16 cm².
- New area: π × 12² = 452.39 cm².
- Factor: 452.39 ÷ 314.16 = (24 ÷ 20)² = 1.2² = 1.44.
Multiply every ingredient by 1.44; for example 200 g of sugar becomes 288 g. For a 20 cm square instead, the factor would be 400 ÷ 314.16 ≈ 1.27.
| Or new square pan side (cm, 0 = skip) | Multiply ingredients by |
|---|---|
| 0 | 1.44 |
| 1 | 0 |
| 2 | 0.01 |
| 3 | 0.03 |
| 4 | 0.05 |
| 5 | 0.08 |
| 6 | 0.11 |
How to read the result
A factor above 1 means more batter; below 1 means less. With the same depth, baking time changes only modestly, but a much larger cake may need a slightly lower temperature and a longer time so the centre sets before the edges dry, and a much smaller one will be done sooner. Check with a skewer rather than the clock. Eggs are easiest to scale by weight: a large egg without shell weighs roughly 50 g.
Common mistakes
- Scaling by the diameter ratio (1.2) instead of the area ratio (1.44).
- Measuring the outside of the pan or the base of a sloped pan.
- Ignoring depth: a shallow pan cannot hold the same depth of batter.
- Using the same baking time for a very different size.
Frequently asked questions
How do I convert an 18 cm recipe to 21 cm?
(21 ÷ 18)² ≈ 1.36, so multiply all ingredients by about 1.36.
Can I bake a round recipe in a rectangular pan?
Yes; compare areas: a rectangle's area is length × width.
What about inch pans?
Use either unit for both pans; the ratio is the same. 1 inch is 2.54 cm.
Sources: OpenStax — Prealgebra 2e (area of circles and squares) · Harold McGee — On Food and Cooking (Scribner, 2004)