Tin sizes are quoted in a single dimension, which hides how much the capacity changes. An inch on the diameter of a round tin is not a small adjustment; it is a quarter more surface for the batter to spread across. The cake pan converter above turns that into the one number you need — the factor to multiply every ingredient by — and works across shapes, so a recipe written for two rounds can be moved into a rectangular tin or a tube tin without guesswork.
Arb Digital publishes free calculators for the arithmetic that decides whether a recipe survives a substitution. This page does one job: it scales a recipe between tins. It does not tell you how many portions a cake yields, which is a different question about how the finished cake is cut and is handled by our cake serving calculator. Nor is it a general geometry tool — the circle calculator and rectangle area calculator cover raw shapes.
What This Cake Pan Converter Does
Describe the tin the recipe was written for and the tin you actually own, and the tool returns a scale factor. Multiply every ingredient by it and the layer comes out the same thickness as the original, which is what keeps the bake behaving the way the recipe expects.
Two scaling bases are offered. Base area is the usual choice: it holds batter depth constant, so the only thing changing is how wide the cake is. Batter volume is the choice when you deliberately want a different depth — a deeper layer for a celebration cake, or a shallower one for a roll or a traybake — and the tool then scales to the volume you have specified rather than preserving thickness.
Four shapes are supported, including tube and bundt tins, where the centre hole is subtracted from the area. That subtraction is why a tube tin holds considerably less than its outside diameter suggests, and it is the single most common source of overflow when a recipe is moved into one.
How to Use It
- Measure both tins across the base, not the rim. Many tins are slightly flared, and the rim measurement overstates the area the batter actually occupies.
- Enter the batter depth, not the tin height. Depth is how deep the mixture sits before baking. Most single-layer recipes fall somewhere between one and two inches.
- Set the counts if the recipe makes several layers or you are dividing between several tins. The scale factor accounts for the total, not the individual tin.
- Add the centre hole diameter for a bundt or tube tin. Leaving it at zero treats the tin as solid and overstates its capacity substantially.
- Check the fill level before committing. A tin filled much beyond two thirds with a strongly rising batter will go over the side.
The Formula and How It Is Calculated
Each shape gives a base area:
Round: π × (diameter ÷ 2)². Square: side². Rectangular: length × width. Tube: π × (outer ÷ 2)² − π × (hole ÷ 2)².
Batter volume is that area multiplied by the batter depth, and the scale factor is the ratio of the totals:
Area basis: scale = (new count × new area) ÷ (original count × original area)
Volume basis: scale = (new count × new area × new depth) ÷ (original count × original area × original depth)
Work through the loaded values. An 8 inch round has an area of π × 4² = 50.27 square inches; a 9 inch round has π × 4.5² = 63.62. The area ratio is 63.62 ÷ 50.27 = 1.27, which is also 9² ÷ 8² = 81 ÷ 64. So every ingredient is multiplied by 1.27, and the layer stays 1.5 inches deep.
The grid shows what happens if you do not scale. The original batter is 50.27 × 1.5 = 75.4 cubic inches. Poured into the 9 inch tin, that spreads to 75.4 ÷ 63.62 = 1.19 inches deep instead of 1.5 — a fifth thinner, which bakes faster, browns more and dries at the edges. That, rather than the diameter, is what actually goes wrong when a tin is substituted.
Why Diameter Deceives and Squares Beat Rounds
Area grows with the square of the linear dimension, so every proportional change in diameter is roughly doubled in capacity. A 10 per cent wider tin holds about 21 per cent more; a tin one third wider holds about 78 per cent more. Recipe writers know this and readers rarely do, which is why "use a slightly bigger tin" is such reliably bad advice.
The shape comparison is the other surprise. A square tin holds noticeably more than a round tin of the same nominal size, because the round loses the corners: 8 × 8 is 64 square inches against an 8 inch round's 50.27, which is about 27 per cent more. That is very close to the difference between an 8 inch round and a 9 inch round, so the common rule of thumb that a square tin substitutes for a round one an inch larger is arithmetically sound.
Tube tins invert the intuition again. A 10 inch tube tin with a 4 inch centre hole has an area of 78.54 minus 12.57, which is 65.97 square inches — barely more than a 9 inch round despite being an inch wider. The hole is there so heat reaches the middle of a deep batter, and its cost in capacity is exactly what makes a bundt recipe overflow when it is scaled from a solid tin.
What the Scale Factor Cannot Carry With It
The arithmetic is exact; the baking is not. Three things change even when the layer depth is held constant, and none of them appear in the ratio.
The first is edge-to-centre distance. A wider layer at the same depth still has more of its mass further from the tin wall, so heat reaches the centre marginally more slowly even though the thickness is unchanged. In practice this is a few minutes on a domestic cake and is dwarfed by the second factor.
The second is the tin itself. A dark, heavy tin absorbs and holds far more heat than a shiny thin one, and the difference in browning and bake time between two tins of identical dimensions can exceed the difference between two sizes. Glass and ceramic behave differently again, heating slowly and holding heat after the oven is off. If you change size and material at the same time, you have changed two variables and the ratio only accounts for one.
The third is that not every ingredient wants to be multiplied by 1.27. Eggs come in whole units, and rounding a scale factor on a three-egg recipe is a real decision rather than a rounding error. The honest approach is to scale by weight where you can — beat the eggs and weigh out the fraction — and our butter converter and cooking measurement converter handle the ingredients that arrive in awkward units. For quick proportional work the percentage calculator and ratio calculator are faster than doing it by hand.
Measuring Tins Properly, and Where the Numbers Come From
Tins are labelled by their nominal size and manufactured to it loosely. A tin sold as 9 inches is often 8.75 across the base with a flared rim that reaches 9 at the top, and using the rim figure overstates the area by several per cent. Measure across the inside of the base, and measure the depth from the base to the rim on the inside as well.
Unit conversion is the other place errors creep in. An inch is defined as exactly 25.4 millimetres, a definition maintained through the NIST reference on SI units of length, so a 9 inch tin is 22.86 centimetres and a 23 centimetre tin is very slightly larger than a 9 inch one. That gap is small enough to ignore in a sponge and large enough to matter when you are already near the top of a tin. Broader guidance on measurement standards is published by the NIST Office of Weights and Measures.
If you are scaling to hit a particular finished weight rather than a particular tin, work from ingredient weights instead of volumes throughout; composition and density data for baking ingredients is published in USDA FoodData Central. Weighing removes the compounding error that volume measurement introduces every time a recipe is scaled by a fractional factor.
Arb Digital publishes hundreds of free calculators across food, finance, health and maths — no sign-up, no limits. If the one you need is missing, tell us and we will look at building it.
Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Scaling by diameter instead of area — capacity grows with the square of the dimension, so an inch on a round tin is a quarter more batter, not a tenth.
- Treating a tube tin as a solid round — the centre hole removes a substantial share of the area, and ignoring it is the usual cause of overflow.
- Measuring across the rim — flared tins read larger at the top than at the base where the batter actually sits.
- Changing tin material and size together — a dark heavy tin bakes very differently from a thin shiny one, and the scale factor accounts for none of it.
- Filling much beyond two thirds — a strongly rising batter needs headroom, and the fill figure alone does not tell you whether you have enough.
Related Free Tools From Arb Digital
Work out portions from a finished cake with the cake serving calculator, and price it with the cake pricing calculator if you are baking to sell. The butter converter and cooking measurement converter handle ingredients that arrive in awkward units, the percentage calculator and ratio calculator cover quick proportional work, and the circle calculator and rectangle area calculator deal with raw geometry. Everything else is on the free online tools hub.
Frequently Asked Questions
Multiply every ingredient by the ratio of the areas, which is 9 squared over 8 squared, or 1.27. That keeps the layer the same depth. Poured unscaled into the larger tin, the batter sits about a fifth thinner and bakes faster.
Because capacity depends on area, which grows with the square of the linear dimension. A tin ten per cent wider holds about twenty-one per cent more batter, so scaling by diameter understates the change every time.
Yes, by about a quarter, because the round tin loses the corners. An 8 inch square is 64 square inches against a 50 square inch 8 inch round, which is why a square tin substitutes reasonably well for a round tin one inch larger.
Enter the outer diameter and the centre hole diameter, and the tool subtracts the hole from the area. The hole removes a substantial share of the capacity, which is why a recipe scaled from a solid tin so often overflows a tube tin.
If you scale by area the layer depth is unchanged, so the time stays close to the original, though a wider layer and a different tin material can both shift it. Doneness should be tested rather than timed, and a deeper layer needs materially longer.
Around two thirds is the usual working limit for a batter that rises strongly, less for one that rises dramatically. The tool reports the fill level so you can check before mixing rather than after pouring.
Beat them together and weigh out the fraction you need. That is the only way to apply a factor like 1.27 accurately, and it is more reliable than rounding up or down, which changes the structure of the batter.
Almost. Nine inches is 22.86 centimetres, so a 23 centimetre tin is very slightly larger. The difference is negligible in a sponge and worth knowing when you are already close to the top of the tin.
This converter performs geometric arithmetic on dimensions you supply and is provided for general reference. It scales quantities only; it does not predict bake times or results, which depend on your oven, your tin material and the batter itself. Test doneness rather than relying on a calculated time.
