Recipe Scaling Calculator (Servings or Tin Size)
Recipe Scaling Calculator (Servings or Tin Size)
Scale a recipe by servings or by tin size, with the area arithmetic shown, the new batter depth, a physics-based estimate of what happens to the baking time, and an explicit list of what does not scale — eggs, leavening, salt and time.
Recipe scaling
A recipe for a 20 cm round tin, baked in a 23 cm round tin
Area for the quantities, depth squared for the time
- A
- base area of the tin in cm². Round: πd²/4. Square: s². Rectangular or loaf: length × width
- scale
- the factor every ingredient is multiplied by. For a tin change it is the ratio of AREAS
- depth
- how deep the raw batter sits. Same depth, same time; this is the quantity that decides the bake
- time ∝ depth²
- heat diffusion: the time for the centre to reach a temperature goes with the square of the distance heat must travel
Worked example
A recipe for a 20 cm round tin, baked in a 23 cm round tin
The 20 cm tin has a base area of π × 20² / 4 = 314.2 cm²
The 23 cm tin has π × 23² / 4 = 415.5 cm²
So the batter has to grow by 415.5 / 314.2 = 1.3225× to sit at the same depth
The diameters differ by only 1.15×. Using that instead would leave the cake about 13% short of batter
The depth is unchanged at 4 cm, so the baking time barely moves: keep the 35 minutes and start checking at 30
Common tin swaps, and what they really cost
| From | To | Length ratio | Area ratio — the real factor | Extra batter needed |
|---|---|---|---|---|
| 20 cm round | 23 cm round | 1.150 | 1.3225 | +32% |
| 20 cm round | 25 cm round | 1.250 | 1.5625 | +56% |
| 23 cm round | 20 cm round | 0.870 | 0.7561 | -24% |
| 20 cm round | 20 cm square | 1.000 | 1.2732 | +27% — a square tin of the same nominal size holds more |
| 20 cm square | 23 cm square | 1.150 | 1.3225 | +32% |
| 20 x 30 cm rectangle | 23 x 33 cm rectangle | 1.150 and 1.100 | 1.2650 | +26% |
What does not scale, and what to do instead
| Thing | Does it scale with the recipe? | What to do |
|---|---|---|
| Flour, sugar, fat, liquid, most flavourings | Yes, linearly | Multiply by the scale factor. This is what the page does |
| Baking time | No | Time follows the DEPTH of the batter, not the quantity. Keep the depth the same and the time barely moves; double the depth and the time roughly quadruples |
| Oven temperature | No, and not linearly either | Keep it the same for a similar depth. For a much deeper bake the outside sets before the middle cooks, which is why bakers lower the temperature — by how much depends on the recipe, so test rather than take a number |
| Eggs | Not cleanly | They come in whole units. Round, and adjust the liquid a little to compensate; beaten egg can be weighed if you need a fraction |
| Baking powder and bicarbonate of soda | Not reliably | Chemical leavening scales with the batter but the gas has to escape through a surface that has grown more slowly. Scaling up much past 2x usually needs less than the arithmetic says |
| Yeast | Not linearly | A bigger dough ferments warmer and faster. See the yeast conversion calculator |
| Salt | Yes by mass, but check the measure | Scale by weight. If the recipe gives salt in spoons, see the salt conversion calculator |
| Tin depth and shape | No | This is an input, not an output. A deeper tin is a different bake |
Area, depth and the things that refuse to scale
Ingredients scale. Baking time does not. Tins scale by area. Those three facts are the whole of recipe scaling, and only the first is arithmetic.
Tin size goes with the square. You fill a tin to a depth, so the batter you need is the area of the base times that depth. Going from a 20 cm round tin to a 23 cm round one is a 15% increase in diameter and a 32% increase in area: the scale factor is 1.3225, not 1.15. Use the diameter ratio and the cake comes out about a quarter too shallow, which means it bakes faster than the recipe says, dries out and looks mean. The same trap catches the swap between a round tin and a square one of the same nominal size: a 20 cm square holds 4/π, about 27%, more than a 20 cm round.
Time follows depth, and it follows it as a square. This is the part most scaling advice gets wrong. Baking is heat travelling inwards from the surfaces, and the time for the centre to reach a given temperature scales with the square of the distance the heat has to cover — which is the depth of the batter, not its volume. Spread twice as much batter over twice the area at the same depth and the baking time is very nearly unchanged. Put twice as much batter in the same tin, so it is twice as deep, and the time goes up by something close to a factor of four. That is why this page reports the batter depth as prominently as the scale factor, and why the time figure it gives is labelled an estimate: it is the depth-squared law and nothing more, with no allowance for the crust, the evaporation or the fact that a cake is not a slab of custard.
Temperature, honestly. There is no reliable number for this and the page does not offer one. At the same batter depth, keep the oven where the recipe put it. At a greater depth the outside sets and colours while the middle is still raw, and the standard response is to drop the oven a little and give it longer — but how much depends on how rich the batter is, how much sugar is in it and how dark the tin is. Test with a skewer, start checking early, and cover the top with foil if it is colouring too fast.
What will not scale. Eggs come in whole units, so a factor of 1.32 applied to three eggs asks for four and would be better served by weighing beaten egg. Chemical leavening scales with the batter but the gas has to get out through a surface that grew more slowly than the volume, so a doubled cake often wants slightly less baking powder than the arithmetic says. Salt scales by mass, but if the recipe gives it in spoons the salt conversion calculator is the page you need first. Yeast does not scale linearly at all, because a larger dough holds its own fermentation heat: see the yeast conversion calculator.
And where to stop. Past about twice, or below about half, a recipe usually needs reworking rather than multiplying. Mixing behaves differently, aeration behaves differently, and the geometry of the tin stops matching the formulation. The page flags both ends rather than pretending the arithmetic still means something. If the original recipe is in cups, convert it to grams first with the cups to grams converter — scaling a cup measure multiplies its error along with everything else.
Frequently asked questions
How do I convert a 20 cm cake recipe to a 23 cm tin?
Multiply everything by 1.322, not by 1.15. The tins differ by 15% in diameter but by 32% in area, and it is the area that the batter has to cover at the same depth. Keep the oven temperature and check a few minutes early.
Why does tin size scale by area and not by length?
Because you fill a tin to a depth, and the volume of batter is the area of the base times that depth. Double the diameter of a round tin and the area goes up four times. This page also draws the two tins one inside the other, so you can see the ring of extra area you are being asked to fill.
Does baking time scale with the recipe?
No. Baking time is set by how long heat takes to reach the centre, which depends on the DEPTH of the batter and not on how much of it there is. Spread twice the batter over twice the area at the same depth and the time is almost unchanged. Put twice the batter in the same tin, so it is twice as deep, and the time roughly quadruples — heat diffusion goes with the square of the distance.
Should I change the oven temperature when I scale up?
Only if the batter gets deeper. At the same depth, keep it. At a greater depth the surface sets and browns long before the centre is done, and bakers lower the temperature to let the middle catch up — but how much depends on the recipe, the tin and the oven, so the honest answer is to test with a skewer rather than take a number from a table. The oven temperature converter handles the dial itself.
Can I just double any recipe?
Usually up to about twice, and not much beyond. Ingredients scale linearly but mixing, aeration, leavening and heat transfer do not, and at two or three times the size a recipe often stops working for reasons no multiplier fixes. Below about half it is the egg count that breaks first. Both ends are flagged by this page.
How do I handle eggs when scaling?
Round to whole eggs and adjust the liquid slightly. A medium egg is roughly 50 g out of the shell, so if you need 2.6 eggs you can weigh 130 g of beaten egg instead. The page shows both the fractional figure and the rounded one.
Related calculators
References
- Singh RP, Heldman DR. Introduction to Food Engineering, 5th edition. Academic Press / Elsevier, 2014 (ISBN 978-0-12-398530-9), chapter 4, Heat Transfer in Food Processing. The unsteady conduction treatment there is the basis of the statement that the time for the centre of a slab to reach a given temperature goes with the square of its half-thickness — constant Fourier number, Fo = αt/L².
- The area law is geometry: the base area of a round tin is πd²/4, so the volume of batter at a fixed depth goes with the square of the diameter. This page’s own figures were checked against a numerical integration of the disc area and a two-dimensional Riemann sum of the batter volume, rather than against a rearrangement of the same formula.
- The depth-squared scaling of the baking time was checked against an explicit finite-difference solution of the one-dimensional heat equation for a slab with both faces held at oven temperature, at batter depths of 3, 4, 5 and 6 cm. The computed times follow the square of the depth to better than 1%.
- U.S. Department of Agriculture, Agricultural Research Service. FoodData Central, SR Legacy. fdc.nal.usda.gov. A work of the United States Government and in the public domain. The gram weights for household measures used on this page are the food portions USDA publishes with each food, and the FDC id of each is given in the table.