About

Substituting a 9in round pan for an 8in square one changes the baking area by roughly 20%. That mismatch causes overflow or underbaked centers. This converter calculates the exact volume ratio between any two pan geometries and outputs a scaling factor k for your batter quantity. It also estimates adjusted baking temperature and time based on depth ratio, because heat diffusion through batter is proportional to the square of the pan depth. The tool covers standard shapes (round, square, rectangular) and specialty forms (bundt, loaf, springform, heart). All dimensions accept both imperial and metric input.

Note: baking time estimates assume conventional oven heating. Convection ovens, dark-coated pans, and glass pans introduce additional variables not modeled here. For bundt and heart shapes, the tool uses empirical area correction factors (C ≈ 0.78 and 0.82 respectively) derived from measured pan footprints. Pro Tip: always fill pans only 50% to 67% full to allow for rise.

Formulas

The batter scaling factor k is the ratio of the target pan volume to the source pan volume:

k = V_targetV_source

Volume for each shape is computed as area multiplied by depth d:

V = A × d

Area formulas by pan shape:

Round / Springform: A = π × r²

Square: A = s²

Rectangle / Loaf / Sheet: A = l × w

Bundt / Tube: A = π × (R² − r_inner²)

Heart: A ≈ 0.82 × s²

Baking time adjustment uses the depth ratio. Heat diffusion time scales approximately with the square of characteristic thickness:

t_adjusted ≈ t_original × d_target²d_source²

Where r = radius (half of diameter), s = side length, l = length, w = width, d = depth, R = outer radius, r_inner = inner hole radius (typically 40% of R), t = baking time, k = scaling factor applied to all ingredient quantities.

Reference Data

Pan Shape	Common Size	Approximate Area	Volume (2 in deep)	Cups Batter	Servings
Round	6in × 2in	28.3 in²	56.5 in³	3.5	6-8
Round	8in × 2in	50.3 in²	100.5 in³	6	10-12
Round	9in × 2in	63.6 in²	127.2 in³	8	12-16
Round	10in × 2in	78.5 in²	157.1 in³	10	14-18
Round	12in × 2in	113.1 in²	226.2 in³	14	20-24
Square	8in × 8in × 2in	64.0 in²	128.0 in³	8	12-16
Square	9in × 9in × 2in	81.0 in²	162.0 in³	10	16-20
Rectangle	9 × 13in × 2in	117.0 in²	234.0 in³	14	20-24
Rectangle	11 × 15in × 1in	165.0 in²	165.0 in³	10	18-24
Springform	9in × 3in	63.6 in²	190.9 in³	12	12-16
Springform	10in × 3in	78.5 in²	235.6 in³	15	16-20
Loaf	8.5 × 4.5in × 2.5in	38.3 in²	95.6 in³	6	8-10
Loaf	9 × 5in × 3in	45.0 in²	135.0 in³	8	10-12
Bundt	10in × 3.5in	61.3 in² (eff.)	214.4 in³	12	16-20
Heart	8in × 2in	41.2 in² (eff.)	82.4 in³	5	8-10
Tube	10in × 4in	58.9 in² (eff.)	235.6 in³	16	20-24
Muffin (std)	2.75in × 1.375in	5.9 in²	8.2 in³	0.33	1
Sheet (half)	13 × 18in × 1in	234.0 in²	234.0 in³	14	24-36
Sheet (quarter)	9 × 13in × 1in	117.0 in²	117.0 in³	7	12-18

Frequently Asked Questions

Baking time scales approximately with the square of the depth ratio. A pan that is 1.5× deeper requires roughly 2.25× the original baking time (1.5²). This follows from heat diffusion physics: thermal energy must penetrate further into the batter. Reduce oven temperature by 25°F (15°C) for significantly deeper pans to prevent the crust from over-browning before the center sets.

Not directly. An 8in round pan has an area of π × 4² ≈ 50.3 in², while an 8in square pan has 64 in². The square pan holds about 27% more batter. Using the converter with these exact dimensions gives you the precise scaling factor k to adjust your recipe.

Bundt pans have a central tube that removes approximately 16% of the total circular area (inner radius ≈ 40% of outer radius, so removed area ≈ 0.4² = 0.16). The tool computes the annular area π(R² − r²). Heart-shaped pans are approximated at 82% of the bounding square area, based on geometric measurement of commercial pans.

The converter calculates geometry-based scaling only. Material effects are significant: dark metal pans absorb more radiant heat and typically require reducing temperature by 25°F. Glass pans retain heat longer, also requiring a 25°F reduction. Silicone pans conduct heat poorly and may need 5 - 10 minutes extra. Apply these adjustments on top of the converter's time estimate.

Calculate the total source volume: two 9in rounds at 2in deep each give 2 × 127.2 = 254.5 in³. A 9×13×2in sheet pan holds 234 in³. The scaling factor k is 0.92, meaning you use about 92% of the original recipe. In the converter, set source to "round" with the combined volume consideration.

Fill pans between 50% and 67% of total volume. Cakes typically rise 50 - 100% during baking depending on leavening. If the scaled batter exceeds 67% fill, either use a deeper pan or split across two pans. The converter displays the fill percentage estimate to help you decide.