A tin holds batter by area, not width
This is the whole thing, and it catches almost everyone. Swapping a 9-inch round for an 8-inch feels like an eleven percent change, because the diameter dropped by eleven percent. The batter has to drop by twenty-one.
What the diameter suggests against what the area requires| Swap | By diameter | By area | Out by |
|---|
| 9″ → 8″ | −11% | −21% | 1.9× |
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| 9″ → 10″ | +11% | +24% | 2.1× |
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| 10″ → 9″ | −10% | −19% | 1.9× |
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| 8″ → 6″ | −25% | −44% | 1.8× |
|---|
The error runs about a factor of two every time, and always in the same direction: the real adjustment is bigger than the intuitive one. That is why a cake baked in the wrong tin tends to come out noticeably wrong rather than slightly wrong.
The reason is that area goes as the square of the diameter. Halve the width and you quarter the area — a 6-inch tin holds less than half what a 9-inch does, which surprises people looking at two tins that seem fairly similar.
The calculator shows both numbers deliberately. Returning only the correct one would answer the question and teach nothing, and this is a mistake worth being cured of once rather than looked up repeatedly.
A square is bigger than a round of the same name
An 8-inch square tin and an 8-inch round tin are not the same size, and the difference is larger than most people would guess.
A square of side n has area n², and a circle of diameter n has area πn²/4. Divide one by the other and the n² cancels: the ratio is 4/π, or 27.32%, and it is the same at every size. A square tin always holds a little over a quarter more.
Common tins ranked by what they actually hold| Tin | Area (in²) | vs a 9″ round |
|---|
| 6″ round | 28.3 | 0.44× |
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| 8″ round | 50.3 | 0.79× |
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| 9″ round | 63.6 | 1.00× |
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| 8″ square | 64.0 | 1.01× |
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| 10″ round | 78.5 | 1.23× |
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| 9″ square | 81.0 | 1.27× |
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| 9 × 13″ sheet | 117.0 | 1.84× |
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Read that ordering carefully. An 8-inch square holds fractionally more than a 9-inch round, despite the smaller number on the label — which makes it the ideal substitute, and one almost nobody reaches for.
The 9 × 13 row is the other useful one. It is nearly twice a 9-inch round, so halving a traybake recipe to fit a layer tin still leaves about eight percent too much. Two 9-inch rounds come to 127 square inches against the sheet’s 117, which is close enough to swap in either direction.
Depth is not capacity
Area tells you how much batter fits. Depth tells you how to bake it, and the two questions get run together.
Put the same batter into a smaller tin and it does not simply overflow — it sits deeper. A 9-inch recipe poured into an 8-inch tin is about 27% deeper, which changes the bake in a specific way: the middle takes longer to reach setting temperature, so at the original oven setting the outside will be done before the centre is.
The usual correction is to drop the oven by around 15 °C and extend the time, so the heat has longer to reach the middle without overcooking the edge. Going the other way — the same batter in a larger tin — the cake is shallower and bakes faster, and the risk is drying it out rather than undercooking it, so start checking well before the stated time.
This is also why capacity in litres is less useful than it looks. Two tins with the same capacity but different depths bake differently, and a recipe developed in a 2-inch tin behaves differently in a 3-inch one even at the same diameter. The calculator asks for depth only when you want a capacity figure, and says so, rather than assuming a standard tin and quietly getting it wrong.
A practical limit worth knowing: most cake batters want a tin filled between half and two thirds. Below that the cake is thin and dries; above it, the batter rises over the rim before the structure sets.
Tins that look alike and are not
Three pairs cause most of the trouble, and in each case the two tins sit next to each other in the shop.
The two loaf tins. An 8½ × 4½ × 2½ inch tin holds 1.57 litres; a 9 × 5 × 3 holds 2.21. That is 41% more from a tin that looks barely different, and it is why the same banana bread recipe overflows one and underfills the other. Loaf recipes are unusually sensitive to this because the batter is deep to begin with.
Inches against centimetres. A 20 cm round is often sold as the European 8-inch, and it is about 3% smaller. A 23 cm round stands in for a 9-inch and is 1.2% larger. Both are close enough to substitute without adjusting anything, which is worth knowing so you can stop worrying about it — but they are not the same tin, and a recipe that specifies one and gets the other is being scaled slightly whether you meant to or not.
Nominal against actual. Tins are measured across the top, inside the rim, and many have sloped sides — so the base is smaller than the nominal size and the true capacity sits below the geometric figure. Makers also differ in whether they measure inside or outside. If a substitution is marginal, measuring the tin you actually have beats trusting the number stamped on it.
Scaling a recipe sensibly
The arithmetic gives you a factor. Applying it takes a little judgement, because not everything in a recipe scales the same way.
- Scale everything by the same factor first, then look at the result. That is the right starting point and it is right for flour, sugar, fat, eggs and liquid.
- Round eggs sensibly. Two and a bit eggs is the most common practical problem in scaling. Beat an egg and weigh out the fraction rather than rounding to a whole one — a large egg is about 50 g out of the shell, so 0.4 of one is 20 g, and guessing that is a meaningful error in a small cake.
- Raising agents scale slightly less than proportionally in large increases. Doubling a recipe and doubling the baking powder often gives a cake that rises fast and collapses; going a little under the scaled figure is the safer error.
- Do not scale the bake time. Time follows depth, not quantity. A cake with twice the batter in a tin twice the area bakes in approximately the same time; the same batter in a smaller, deeper tin takes considerably longer.
- Salt and strong flavourings scale by taste. A tripled recipe with tripled spice is usually too much, because perception of concentration is not linear.
Where the factor comes out close to one — within about five percent — the honest answer is to change nothing. That is inside the variation between two tins of the same nominal size, and adjusting for it is false precision.
Sources and methodology
There is nothing to cite for most of this page, because it is geometry — the area of a circle has not changed and needs no authority. The references cover the unit definitions that make the imperial and metric comparisons exact rather than approximate, which is the only place a standard enters at all.