Cake Pan Converter
Scale a cake recipe from one pan size to another by comparing volume.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
This estimate compares pan volume using a cylinder for round pans and a square prism for square pans. It assumes the pans have similar usable fill depth; it cannot model a rectangular pan with unequal sides, pan shape details or baking-time changes.
Worked example
calculated with the default values below
Pan shape Round · Original width or diameter 8 in · Original depth 2 in · New width or diameter 9 in · New depth 2 in Recipe scale factor 1.266 x · Original pan volume 100.5 in³ · New pan volume 127.2 in³ · New batch size 126.6 %
Method and assumptions
f = V₂ ÷ V₁; V₂ = (1 − s)·π(d ÷ 2)²·h + s·d²·h, s ∈ {0,1} Multiply ingredient quantities by f; assumes equal relative fill depth (volumes in in³). This estimate compares pan volume using a cylinder for round pans and a square prism for square pans. It assumes the pans have similar usable fill depth; it cannot model a rectangular pan with unequal sides, pan shape details or baking-time changes. The references provide context and limitations. They do not validate this page’s illustrative multipliers, lookup values or predictions.
Data sources
The references provide context and limitations. They do not validate this page’s illustrative multipliers, lookup values or predictions.
Disclaimer
These calculators give general cooking guidance. Ingredient density, oven calibration, altitude and equipment all vary, and safe minimum internal temperatures always take precedence over timings. Follow the food-safety advice issued by your national authority.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
f = V₂ ÷ V₁; V₂ = (1 − s)·π(d ÷ 2)²·h + s·d²·h, s ∈ {0,1}
- f
- Recipe scale factor
- V₁
- Original pan volume
- V₂
- New pan volume
- d
- Diameter (round) or side (square)
- h
- Pan depth
- s
- Pan shape: 0 round, 1 square
Multiply ingredient quantities by f; assumes equal relative fill depth (volumes in in³).
Frequently asked questions
Why does moving from an 8-inch to 9-inch pan add 27 percent?
Volume scales with the square of the radius, not the diameter, so the jump from 8 to 9 inches looks small but is not. With a 2-inch depth on both pans, the new volume is π × 4.5² × 2 against π × 4² × 2, a ratio of about 1.27, or 27% more batter. A round-to-square switch changes the formula entirely, because the square pan uses width squared instead of π r².
Which inputs and limits apply to Cake Pan Converter?
Use the units shown beside each field. These are form limits, not recommended settings. Original width or diameter: 1–30 in; Original depth: 0.5–6 in; New width or diameter: 1–30 in; New depth: 0.5–6 in f = V₂ ÷ V₁; V₂ = (1 − s)·π(d ÷ 2)²·h + s·d²·h, s ∈ {0,1} Multiply ingredient quantities by f; assumes equal relative fill depth (volumes in in³). This estimate compares pan volume using a cylinder for round pans and a square prism for square pans. It assumes the pans have similar usable fill depth; it cannot model a rectangular pan with unequal sides, pan shape details or baking-time changes. The references provide context and limitations. They do not validate this page’s illustrative multipliers, lookup values or predictions.
What is a complete worked example for Pan shape = Round; Original width or diameter = 8 in?
Inputs: Pan shape = Round; Original width or diameter = 8 in; Original depth = 2 in; New width or diameter = 9 in; New depth = 2 in. Calculation: f = V₂ ÷ V₁; V₂ = (1 − s)·π(d ÷ 2)²·h + s·d²·h, s ∈ {0,1}. Results: Recipe scale factor = 1.266 x; Original pan volume = 100.5 in³; New pan volume = 127.2 in³; New batch size = 126.6 %.