What this calculator does
Scaling a cake between pans is an area comparison. A 23 cm round pan has an area of 415 cm² and a 20 cm round has 314, so a recipe moving between them needs about three quarters of the batter.
Using area rather than diameter is the whole point. The diameter drops by 13% between those two pans while the batter drops by 24%, because area goes with the square of the diameter. Scaling by diameter overfills the smaller pan by a substantial margin.
The formula
The area of each pan is calculated from its shape, π times the radius squared for round or length times width for rectangular. The area ratio is the new pan divided by the original, and the batter quantity is scaled by that ratio. Both pans are assumed to be filled to a similar depth, which is what makes the area comparison valid.
| Term | Meaning |
|---|---|
| Area ratio | New pan area divided by original pan area, the factor the batter is scaled by. |
| Fill depth | How deep the batter sits. The comparison assumes both pans are filled similarly, usually to about two thirds. |
| Bake time adjustment | A shallower or deeper batter changes baking time, which the area calculation does not account for. |
The inputs explained
| Field | What to enter |
|---|---|
| Original pan shape | Shape of the original pan. |
| Original diameter (round) (cm) | Diameter of the original pan, if round. |
| Original length (rect) (cm) | Length of the original pan, if rectangular. |
| Original width (rect) (cm) | Width of the original pan, if rectangular. |
| New pan shape | Shape of the new pan. |
| New diameter (round) (cm) | Diameter of the new pan, if round. |
| New length (rect) (cm) | Length of the new pan, if rectangular. |
| New width (rect) (cm) | Width of the new pan, if rectangular. |
| Original recipe batter volume (L) | The batter quantity the original recipe makes, in any unit. The result comes back in the same unit. |
When to use it
Baking a recipe in the pan you own
Recipes specify a pan size and kitchens have whatever they have. Scaling the batter is more reliable than hoping the difference is small.
Converting between round and square
A square pan holds noticeably more than a round one of the same nominal size, and the area comparison quantifies it rather than leaving it to guesswork.
Splitting a recipe across multiple pans
Working out the combined area of several smaller pans against the original shows whether one batch of batter covers them.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much batter does each pan size need?
A 23 cm round recipe scaled to a range of round pan sizes.
| New pan diameter | Scaled batter needed | Area ratio | New pan area |
|---|---|---|---|
| 18 cm | 0.92 L | 0.612× | 254 cm² |
| 20 cm | 1.13 L | 0.756× | 314 cm² |
| 23 cm | 1.50 L | 1.000× | 415 cm² |
| 25 cm | 1.77 L | 1.181× | 491 cm² |
Questions
Can I substitute a square pan for a round one?
Yes, with the batter scaled by area. A 20 cm square pan has an area of 400 cm² against 314 for a 20 cm round, about 27% more, so the same batter sits shallower and bakes faster. Scaling the batter up keeps the depth similar.
Does baking time change with pan size?
Yes, and this calculation does not adjust it. A wider, shallower cake bakes faster and a deeper one slower, even at the same total volume. Start checking earlier than the recipe says for a shallower bake, and expect longer for a deeper one.
How full should a cake pan be?
About two thirds is the usual guidance, leaving room to rise without overflowing. A pan filled much beyond that risks spilling, and one filled well below produces a thin cake that bakes faster and can dry out.
What about pan depth?
The comparison here is area only, so it assumes similar depths. Two pans of the same footprint but different wall heights hold the same batter to the same depth; what changes is the headroom for rise. A shallow pan with a well-risen batter will overflow regardless of the area calculation.
For how many servings the finished cake gives, see the cake servings calculator. For pricing it, see the cake pricing calculator.