Scale a Round-Pan Recipe by Area Rather Than Diameter — Free
A pan twenty percent wider has forty-four percent more area. Use the squared diameter ratio to scale ingredient quantities for a similar fill depth, rather than adding twenty percent to everything.
The proof surface
Freezer portion tools divide cooked yield. This changes a round-pan recipe’s ingredient quantities using geometry before cooking; it does not predict cooked portions.
Why the flat version breaks
Scaling by diameter alone
Diameter is a length; the batter footprint grows with its square.
Adding unlike ingredient units
Every row must be grams. A recipe’s millilitres or cups cannot be entered unchanged.
Scaling oven time by the same factor
Heat transfer depends on shape, depth and the recipe, not just ingredient quantity.
How to work the pan-area scaling chart
Weigh each ingredient in grams, with labels such as Flour or Sugar. Convert spoon or cup measures using a recipe-specific source before entry; the tool never converts volume to mass.
This model assumes circular pans and similar fill depth. Tapered sides, different depths and rectangular tins need a separate volume or area model.
Scaled amount = original amount × (target diameter ÷ original diameter)². Moving from 20 to 24 cm multiplies 200 g by 1.44 to give 288 g.
The summary totals the scaled mass of the entered ingredients only; omitted ingredients are not inferred. Baking time, leavening, egg rounding and safe cooking temperatures do not scale automatically.
What the pan-area scaling chart replaces
| Question | Before | Visible working |
|---|---|---|
| Scaling by diameter alone | Diameter is a length; the batter footprint grows with its square. | Use internal pan diameters |
| Adding unlike ingredient units | Every row must be grams. A recipe’s millilitres or cups cannot be entered unchanged. | Square the diameter ratio |
| Scaling oven time by the same factor | Heat transfer depends on shape, depth and the recipe, not just ingredient quantity. | Interpret each ingredient separately |
A local arithmetic aid replaces hand calculation, not expert review. No paid AI service is needed.
Run it on the samples, right here
FIRST-LOAD
Research prototype — checkout unavailable. Input is processed locally and a draft is saved automatically in this browser profile when storage is available. Reset to sample clears that draft; Pro history has its own clear button. A state link encodes your inputs in its URL: share only non-sensitive rows. Browser history, clipboard and anyone receiving the link may retain it. Optional AI use below leaves this device; it is not required.
Recipe geometry only, not food-safety or nutrition advice. Follow a tested recipe’s safety guidance and check appropriate cooking temperatures independently.
Data note: Everything runs in this browser tab on the pan-area scaling chart: your ingredient | original quantity grams | original round pan diameter cm stays on this device, nothing is uploaded, and the reading is rebuilt only when you press run.
Go deeper: the companion app files the same reading as a plotted bar chart sheet
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the pan-area scaling chart reading, and holds your drafts on this device — one complete free run; the proposed $4 one-time filing layer is not currently for sale.
The pan-area scaling chart reading is complete for free. The optional $4 layer adds print, row CSV and the last five local reading summaries; it does not add hidden answers. Checkout is not configured yet; the article demo remains unlimited.
Open the scale a round-pan recipe by area rather than diameter companionBoundary
Recipe geometry only, not food-safety or nutrition advice. Follow a tested recipe’s safety guidance and check appropriate cooking temperatures independently.
What this is built on
- Method: Scaled amount = original amount × (target diameter ÷ original diameter)². Moving from 20 to 24 cm multiplies 200 g by 1.44 to give 288 g.
- All sample records are invented examples. The app does not fetch measurements, policies, files or personal records.
- Google’s official pricing page, fetched 2026-09-29, lists free-tier access including AI Studio. Optional formatting only; limits and availability can change. Free-tier content may be used to improve products. Never paste private records there.
Before: Diameter is a length; the batter footprint grows with its square. After: the pan-area scaling chart shows the working beside each named row so the reader can change the assumption and inspect the consequence.
Optional AI formatting, not calculation
For this pan-area scaling chart, use the free AI Studio interface only if available to you, with no paid API key. Manual entry completes the same workflow for free. Supply only fictional or non-sensitive notes. Review its output against the source; never paste unresolved questions into the numeric rows.
Format my non-sensitive notes for a pan-area scaling chart. Return plain rows only: ingredient | original quantity grams | original round pan diameter cm. Preserve supplied quantities exactly. Do not guess missing values; list questions separately. Do not calculate or add advice. I will check every row before pasting into the local tool.
Accepted schema: ingredient | original quantity grams | original round pan diameter cm. No AI response is executed as code.