Rule of three (proportion) calculator
Solve simple and compound proportions, including direct and inverse proportions, with the formula.
The scaling factor
It all starts with one number: the scaling factor, which is the desired yield divided by the original yield. If a recipe serves 8 and you want to make it for 12, the factor is 12 ÷ 8 = 1.5. To make half the recipe, the factor is 0.5. Multiply each ingredient by the factor.
Example: a simple cake recipe scaled by a factor of 1.5:
| Ingredient | Original | × 1.5 |
|---|---|---|
| All-purpose flour | 2 cups | 3 cups |
| Sugar | 1 1/2 cups | 2 1/4 cups |
| Milk | 240 ml | 360 ml |
| Eggs | 3 | 4.5 (see below) |
| Baking powder | 1 tablespoon | 1 1/2 tablespoons |
If your recipe uses grams, the math is easier and more precise. The Rule of three (proportion) calculator can calculate each ingredient, and the Unit converter can help convert cups and tablespoons to ml.
What about half an egg?
A large egg weighs about 50 g without the shell, including about 30 g of egg white and 20 g of yolk. To use half an egg, beat the whole egg in a cup and use half (about 25 g, or 1 1/2 to 2 tablespoons). For 4.5 eggs, use 4 whole eggs and half of a beaten egg.
In cakes, rounding 4.5 eggs up to 5 can make the batter wetter and heavier, while rounding down to 4 can make it drier. When in doubt, weigh the egg.
Changing pan size: compare the area
When you switch to a different pan, what matters is the bottom area (to keep the batter at the same depth):
- Round pan: area = 3.14 × radius². A pan with a 22 cm diameter has an 11 cm radius and an area of about 380 cm². A 24 cm pan has an area of about 452 cm².
- Rectangular pan: area = length × width. A 20 × 30 cm pan has an area of 600 cm².
To adapt a recipe from a 22 cm round pan to a 20 × 30 cm rectangular pan, the factor is 600 ÷ 380 ≈ 1.58. Rounding to 1.5 works well for most cakes. Going from a 22 cm pan to a 24 cm pan gives a factor of about 1.19: increasing the diameter by just 2 cm means you’ll need almost 20% more batter.
What doesn’t scale linearly
- Baking time: it doesn't double when you double a recipe. If the batter is deeper, baking time will increase slightly, and you may need to lower the temperature by 10 °C so the center cooks through without the edges burning. If you divide it between two pans, the baking time should be close to the original. Use the Online Timer to check 10 minutes before the recipe's suggested time, then test with a toothpick.
- Salt and strong seasonings: when doubling a recipe, start with 1.5 times the amount and adjust at the end, tasting as you go.
- Baker's yeast in bread: larger batches rise faster, so watch the dough's size instead of the clock.
- Sauces: doubling a sauce in a small pot takes longer to reduce. Use a wider pot.
- Frying and grilling: don't overcrowd the pan or grill; cook in batches.
Worked example: savory pie from 6 to 4 servings
The original recipe serves 6; you want 4 servings. Factor: 4 ÷ 6 ≈ 0.67.
| Ingredient | Original | × 0.67 (rounded) |
|---|---|---|
| All-purpose flour | 300 g | 200 g |
| Milk | 360 ml | 240 ml (1 cup) |
| Oil | 120 ml | 80 ml (1/3 cup) |
| Eggs | 3 | 2 |
| Filling | 450 g | 300 g |
| Baking powder | 1 tablespoon | 2 teaspoons |
Notice the baking powder: 1 tablespoon is 15 ml, and two-thirds of that is 10 ml, or 2 teaspoons. Converting to a smaller measure avoids awkward partial spoonfuls that are hard to measure. The pan should also be smaller—about two-thirds the area of the original—so the batter stays the same depth.
Quick guide
- Calculate the factor (desired yield ÷ original yield, or new area ÷ old area).
- Convert measurements to grams or ml when possible.
- Multiply each ingredient and round to practical amounts.
- Adjust salt and seasonings to taste.
- Check the oven before the original baking time is up.
See also our kitchen measurement conversion chart in grams and ml. Updated October 2026.
Frequently asked questions
Can I triple a cake recipe in one pan?
You can if the pan has about three times the bottom area of the original. In very large, deep pans, the center takes longer to bake, so it's often better to divide the batter between two or three pans.
How do I halve a recipe that calls for 1 egg?
Beat the egg and use half, about 25 grams. Use the rest in an omelet or to brush on bread.
Should I double the baking powder too?
Generally, yes—proportionally to the flour. For very large recipes, some bakers use a little less; start with the same ratio and see how it turns out.