Quick answer
The batter scale factor is the new pan's area ÷ the original pan's area. A 9 inch round pan (63.62 in²) and a 9 × 13 inch pan (117 in²) give a factor of 1.839, so the recipe should be multiplied by about 1.84.
Enter the original and new pan shape and sizes. The calculator returns the scale factor and both areas. Use this cake pan size conversion calculator to check your own figures.
Related tools: Baker's Percentage Calculator: Each ingredient as a percentage of flour weight. Dough Hydration Calculator: Hydration percentage of a dough. Butter Conversion Calculator: Convert butter between sticks, tablespoons, cups, grams and ounces.
How to use the Cake Pan Size Conversion Calculator
- Choose original pan: Round (diameter) and Rectangular (a × b).
- Enter original pan: diameter or length (in) (above 0).
- Optionally, enter original pan: width (in) (above 0).
- Choose new pan: Round (diameter) and Rectangular (a × b).
- Enter new pan: diameter or length (in) (above 0).
- Optionally, enter new pan: width (in) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Original pan | Choose one: Round (diameter); Rectangular (a × b) | Starts at Round (diameter) |
| Original pan: diameter or length | A number, in in | > 0 |
| Original pan: width (optional) | A number, in in | > 0 |
| New pan | Choose one: Round (diameter); Rectangular (a × b) | Starts at Rectangular (a × b) |
| New pan: diameter or length | A number, in in | > 0 |
| New pan: width (optional) | A number, in in | > 0 |
Formula and method
Formula
scale = new pan area ÷ original pan area
IEEE-754 double precision; shown to the decimals indicated.
Matches batter depth; baking time may change with pan depth.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Original pan = Round (diameter); Original pan: diameter or length = 9; New pan = Rectangular (a × b); New pan: diameter or length = 9; New pan: width = 13.
| Result | Value |
|---|---|
| Batter scale factor | 1.839 |
| Original pan area | 63.62 |
| New pan area | 117 |
Example 2
Inputs: Original pan = Rectangular (a × b); Original pan: diameter or length = 8; New pan = Round (diameter); New pan: diameter or length = 10; Original pan: width = 8.
| Result | Value |
|---|---|
| Batter scale factor | 1.227 |
| Original pan area | 64 |
| New pan area | 78.54 |
Example 3
Inputs: Original pan = Round (diameter); Original pan: diameter or length = 8; New pan = Round (diameter); New pan: diameter or length = 10.
| Result | Value |
|---|---|
| Batter scale factor | 1.563 |
| Original pan area | 50.27 |
| New pan area | 78.54 |
The first line is the headline result (batter scale factor). Below it the cake Pan Size Conversion Calculator lists original pan area and new pan area, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
The area rule
Batter depth should stay about the same, so the recipe scales with area. Round pan area is π × r²: π × 4.5² = 63.62. Rectangular is length × width: 9 × 13 = 117.
Baking time
Pans should be the same depth. Larger shallow pans bake faster, so check for doneness early; deeper batter needs a longer time at a slightly lower temperature.
How the result changes with original pan: diameter or length
Holding every other input at the first worked example, this table changes only original pan: diameter or length. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Original pan: diameter or length | Batter scale factor | Original pan area | New pan area |
|---|---|---|---|
| 4.5 | 7.356 | 15.9 | 117 |
| 9 | 1.839 | 63.62 | 117 |
| 18 | 0.46 | 254.47 | 117 |
| 36 | 0.115 | 1,017.88 | 117 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Original pan: width: left empty shows "Enter the pan width." beside that field and no result.
- New pan: width: left empty shows "Enter the pan width." beside that field and no result.
Choosing between the Cake Pan Size Conversion Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Baker's Percentage Calculator](/cooking/baker-percentage-calculator/) | flour weight and other ingredient weights | Flour |
| [Dough Hydration Calculator](/cooking/dough-hydration-calculator/) | flour and water | Hydration |
| [Butter Conversion Calculator](/cooking/butter-conversion-calculator/) | i have and amount | Butter |
| [Portion Size Calculator](/cooking/portion-size-calculator/) | total amount of food and people | Per person |
| [Tire Size Calculator](/automotive/tire-size-calculator/) | section width, aspect ratio and rim diameter | Overall diameter |
Background: cooking measurements
For baking, weight is more reliable than volume. A cup holds a fixed volume but its weight depends on the ingredient's density, and a cup of flour can vary by 20 to 30 grams depending on how it is scooped, so published gram-per-cup values for the same ingredient differ from site to site. Spoon and level flour if you must measure by volume.
Check which cup a recipe uses: the US cup is 236.588 mL, while a metric cup is 250 mL.
Assumptions and limitations
- Pans should be the same depth
Cooking times are guides. Use a food thermometer to confirm safe internal temperatures.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for original pan: width and new pan: width to confirm this.
Frequently asked questions
Can I use a 8 inch square instead of a 9 inch round?
Yes: 64 in² against 63.6 in², nearly identical.
What about bundt pans?
Use volume, not area.
Should I change the oven temperature?
Usually not, unless the batter is much deeper.
What does the Cake Pan Size Conversion Calculator calculate?
Batter scale factor between two pan sizes. It returns Batter scale factor, Original pan area and New pan area.
What formula does the Cake Pan Size Conversion Calculator use?
scale = new pan area ÷ original pan area. Matches batter depth; baking time may change with pan depth.
What do I need to enter in the cake Pan Size Conversion Calculator?
You enter Original pan, Original pan: diameter or length (in), New pan and New pan: diameter or length (in). Optional: Original pan: width (in) and New pan: width (in).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Pans should be the same depth.
What does the “Original pan” option change?
It sets how the cake Pan Size Conversion is worked out. The choices are Round (diameter) and Rectangular (a × b).
What is an example of a cake Pan Size Conversion result?
With original pan Round (diameter), original pan: diameter or length 9, new pan Rectangular (a × b), new pan: diameter or length 9 and new pan: width 13, the batter scale factor is 1.839.
Can I rely on this calculator for a decision?
Cooking times are guides. Use a food thermometer to confirm safe internal temperatures. For this calculator in particular: Pans should be the same depth.
Related calculators
- Baker's Percentage Calculator — Each ingredient as a percentage of flour weight.
- Dough Hydration Calculator — Hydration percentage of a dough.
- Butter Conversion Calculator — Convert butter between sticks, tablespoons, cups, grams and ounces.
- Portion Size Calculator — Amount of food per person.
- Tire Size Calculator — Overall diameter, sidewall height and revolutions per mile from a tire size such as 225/45R17.
- Sample Size Calculator — Sample size for estimating a mean or a proportion.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.