How this is calculated
Every part of this comes from one number: the volume of each tin. A tin’s volume is its base area multiplied by its usable depth, and base area is where almost every published conversion chart goes wrong, because area rises with the square of the width.
- Round. π × radius². A 9-inch round is 63.62 sq in; an 8-inch round is 50.27. The tins differ by one inch in name and by 26.6% in capacity.
- Square and rectangular. Length × width. An 8-inch square is 64 sq in — within 0.6% of a 9-inch round, which is why the two are freely swapped.
- Loaf tin. Length × width × depth × 0.92. Loaf tins taper towards the base, so the box measurement overstates them. A 9 × 5 × 2.75-inch tin comes out at 113.8 cu in, or about 7.9 cups, which is the 8 cups it is sold as.
- Bundt and tube. π × radius² × depth × 0.63. The centre tube and the flutes take out about a third of the cylinder. A 10-inch bundt 3.5 inches deep works out at 173 cu in — 12.0 cups, exactly the “12-cup bundt” on the label.
- Sheet and tray. Length × width × depth, straight.
The scale factor is simply the volume of the tin you have divided by the volume of the tin the recipe wants. Every quantity is multiplied by it and then snapped to something you can actually measure — eighths of a cup, quarters of a spoon, five-gram steps.
The depth check, and why two thirds
Batter volume is taken as the fill percentage you set multiplied by the original tin’s volume. Dropped into a new tin, the depth it reaches is that volume divided by the new tin’s base area. A creamed or chemically leavened batter climbs by roughly a half to two thirds as it bakes; past about two thirds of the tin’s depth there is nowhere left for it to go, so it domes hard, splits down the middle and sends the overflow onto the oven floor. The dashed line on each tin above is that two-thirds mark.
The bake window
Heat travels to the centre of the batter, and the centre is defined by depth rather than width. The time is scaled by the depth ratio raised to the power of 0.8 — slightly less than proportional, because the top surface and the sides both contribute. Temperature moves in the opposite direction to depth: a deeper cake wants a cooler oven so the crust does not set before the middle cooks, a shallower one tolerates a hotter, faster bake. What comes out is a window with a start-checking time, and it is never a promise. Ovens differ by more than this calculation does.
Worked example. A recipe written for a 9-inch round, 2 inches deep, filled to 65% of its depth, baked 32 minutes at 350°F. You own 8-inch rounds, also 2 inches deep.
The 9-inch has π × 4.5² = 63.62 sq in of base and holds 63.62 × 2 = 127.23 cu in, which is 8.81 US cups or 2,085 ml. The 8-inch has π × 4² = 50.27 sq in and holds 100.53 cu in — 6.96 cups, 1,647 ml.
127.23 ÷ 100.53 = 1.266, so the 9-inch holds 26.6% more. The scale factor is the other way round: 100.53 ÷ 127.23 = 0.79. One and a half cups of flour becomes 1⅛ cups, one cup of sugar becomes ¾, two eggs become 1½ — beat two and use 75 g of the 100 g you get.
Batter volume is 0.65 × 127.23 = 82.70 cu in. Poured into the 8-inch tin unscaled it would stand 82.70 ÷ 50.27 = 1.65 inches deep in a 2-inch tin — 82% full, well past the two-thirds line, so it overflows. Scaled by 0.79 it stands 1.30 inches deep, the same as in the original tin, so the bake time does not change. Split across both 8-inch tins it stands 0.82 inches deep, and (0.82 ÷ 1.30)0.8 = 0.69, so 32 minutes becomes about 22 — start checking at 20.
What this does not account for
- Nominal sizes lie. Tins are sold by a rounded number and measured inconsistently — some at the base, some at the rim, some outside the wall. Measure the inside of your own tin, base to rim, and use that.
- Pan material and colour. A dark non-stick tin bakes faster and browns harder than a light anodised one; glass holds heat and keeps cooking after it leaves the oven. Neither changes the volume, both change the time.
- Batter behaviour. A genoise, a pound cake and a brownie batter rise by very different amounts. The two-thirds rule is a good default and a poor law.
- Structure at scale. Doubling a delicate sponge does not always work — the batter can deflate before it sets. Above about 2× it is usually safer to make two batches.
- Baking soda, salt and spices. These scale linearly here, which is right at moderate factors and drifts at extremes. At the very small end, round leavening up rather than down.
- Tin count. Two tins on one shelf bake differently from one. Give them air, swap positions halfway, and expect the back of the oven to run hotter.
- Altitude. Above about 3,000 feet the whole thing shifts — see the altitude guide.
Common questions
Can I use an 8-inch pan instead of a 9-inch?
Not with the full recipe. The 9-inch holds about 27% more, so the whole batch stands four fifths of the way up an 8-inch tin and will dome, crack and spill. Multiply everything by 0.79, or split the full batch between two 8-inch tins and bake them shallower and quicker.
Is an 8-inch square really the same as a 9-inch round?
Within half a percent, yes: 64 sq in against 63.6. At the same depth they take the same batter and the same bake time. It is the one swap in baking you can make without doing any arithmetic at all.
Why does a one-inch difference matter so much?
Because you are not adding an inch of anything — you are adding a ring around the whole circumference. Area goes with the square of the radius, so going from 8 to 9 inches adds more than a quarter of the tin’s capacity. The name on the tin is a length; what holds batter is an area.
Do I bake longer in a bigger tin?
Only if the batter ends up deeper. Bake time follows depth, because that is the distance heat has to travel. The same batter spread thinner across a wider tin bakes faster. This is the single most common misconception about pan conversion.
How do I deal with half an egg?
Beat two eggs together, weigh the result — a large egg out of the shell is about 50 g — and use the fraction you need. Half an egg is 25 g of beaten egg, and it is a great deal more accurate than trying to divide a yolk.
What if my tin is deeper than the recipe’s?
Then it holds more and takes a bigger batch, but if you scale up you also end up with a deeper cake — which needs the oven about 25°F lower and noticeably longer. Deep tins are where cakes most often come out raw in the middle with a burnt edge.
Can I convert a round recipe to a loaf tin?
Yes, and the tool does it, but be careful with the depth: a loaf tin is much deeper than a cake tin, so the same volume of batter stands far taller and needs a longer, cooler bake. Loaf tins also taper, which is why they hold about 8% less than length × width × depth suggests.
Should I scale the tin or the recipe?
Whichever costs less. If your tin is close in volume — within about 10% — leave the recipe alone and adjust the bake window. Beyond that, scale the quantities. Beyond about 1.5× in either direction, consider using two tins instead, because depth changes start to fight the recipe.