# Recipe scaler

> Scale a recipe to any number of servings: each ingredient is multiplied by new ÷ original servings, with cups and spoons shown as kitchen fractions.

Interactive version: https://www.calcopenly.com/everyday/recipe-scaler
Subject: Everyday calculators

Every amount is multiplied by the scale factor: the servings you need divided by the servings the recipe makes. Cup, spoon and count amounts are rounded to the nearest measure a kitchen set holds (eighths, quarters, thirds and halves) and marked ≈ when rounded. Grams, kilograms, millilitres and litres stay as decimals.

The default recipe goes from 4 to 6 servings, a factor of 1.5, so 3/4 cup of sugar becomes 1 1/8 cups and 250 g of butter becomes 375 g. The Institute of Child Nutrition teaches the same two steps for school kitchens: 35 servings from a 25-serving recipe is a factor of 1.4, which turns 3 cups of tomatoes into 4.2 cups, rounded to 4 1/4.

Lines without a number, such as "salt to taste", are kept as written. Baking time, pan size and seasoning do not scale in proportion, so check them separately.

## Inputs

- **Ingredients, one per line**: Start each line with the amount: 2, 1 1/2, 3/4, 1.5 or ½. Lines without an amount are kept as written.
- **Recipe makes (servings)**
- **Servings you need**

## Results

- Scale factor — main result
- Scaled recipe
- Lines scaled
- Lines kept as written

## Formula

$$
\text{new} = \text{old} \times \frac{\text{servings needed}}{\text{servings made}}
$$

## Worked examples

### Default recipe from 4 to 6 servings

- Ingredients, one per line: 2 cups flour / 1 1/2 tsp salt / 3/4 cup sugar / 2 eggs / 1/3 cup milk / 250 g butter
- Recipe makes (servings): 4
- Servings you need: 6
- **Scale factor: 1.5**
- **Scaled recipe: 3 cups flour; 2 1/4 tsp salt; 1 1/8 cup sugar; 3 eggs; 1/2 cup milk; 375 g butter**
- Checked against: Python fractions: 2×3/2 = 3, 3/2×3/2 = 9/4, 3/4×3/2 = 9/8, 1/3×3/2 = 1/2, 250×3/2 = 375

### Halving

- Ingredients, one per line: 1 cup sugar / 2 tbsp butter / 1 egg
- Recipe makes (servings): 4
- Servings you need: 2
- **Scale factor: 0.5**
- **Scaled recipe: 1/2 cup sugar; 1 tbsp butter; 1/2 egg**
- Checked against: Python fractions: each amount × 1/2

### Unscaled line, unicode fraction, range and an approximate fraction

- Ingredients, one per line: Salt to taste / 1½ cups oats / 2-3 cloves garlic / 1 cup milk
- Recipe makes (servings): 6
- Servings you need: 5
- **Scaled recipe: Salt to taste; 1 1/4 cups oats; 1 2/3–2 1/2 cloves garlic; ≈ 7/8 cup milk**
- **Lines kept as written: 1**
- **Lines scaled: 3**
- Checked against: Python fractions: 3/2×5/6 = 5/4; 2×5/6 = 5/3, 3×5/6 = 5/2; 5/6 = 0.833 is nearest 7/8 among eighths and thirds

### 25 to 35 servings (ICN worked example)

- Ingredients, one per line: 3 cups tomatoes
- Recipe makes (servings): 25
- Servings you need: 35
- **Scale factor: 1.4**
- **Scaled recipe: ≈ 4 1/4 cups tomatoes**
- Checked against: Institute of Child Nutrition, Adjusting Standardized Recipes: 35 ÷ 25 = 1.4; 3 cups × 1.4 = 4.2 cups, rounded to 4 ¼ cups

### Decimal metric amounts

- Ingredients, one per line: 125 g sugar / 0.5 L stock
- Recipe makes (servings): 4
- Servings you need: 3
- **Scale factor: 0.75**
- **Scaled recipe: 93.75 g sugar; 0.38 L stock**
- Checked against: Hand calculation: 125 × 0.75 = 93.75; 0.5 × 0.75 = 0.375, shown to 2 decimals (half-up)

## Questions

### How do you scale a recipe up or down?

Divide the servings you need by the servings the recipe makes, then multiply every ingredient by that factor. Going from 4 to 6 servings is a factor of 1.5, so 2 cups of flour becomes 3 cups; going from 4 to 2 is 0.5. The Institute of Child Nutrition advises converting mixed amounts such as 1 lb 8 oz to one unit (1.5 lb) before multiplying.

### What is half of 1/3 cup or 3/4 cup?

Half of 1/3 cup is 1/6 cup: 2 tablespoons plus 2 teaspoons, because a US cup holds 16 tablespoons and a tablespoon holds 3 teaspoons. Half of 3/4 cup is 3/8 cup, or 6 tablespoons. When no standard measure matches, the calculator shows the nearest eighth or third with ≈ and gives the exact decimal in the table.

### Does baking time change when you double a recipe?

Often, because baking time depends on the depth of the batter more than on its amount. Doubled batter in the same pan is twice as deep and needs longer; spread over a pan with twice the area, it keeps its depth and bakes in close to the original time. Keep the oven temperature the same and test for doneness early.

### Is a cup the same size in every country?

No. A US customary cup is 8 US fluid ounces, 236.6 mL, while the metric cup used in Australia and New Zealand is 250 mL, about 6% larger. Scaling works the same in both systems because every amount is multiplied by the same factor. NIST advises weighing ingredients on a kitchen scale for accuracy rather than measuring by volume.

### How accurate is the recipe scaler?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “Default recipe from 4 to 6 servings” is checked against Python fractions: 2×3/2 = 3, 3/2×3/2 = 9/4, 3/4×3/2 = 9/8, 1/3×3/2 = 1/2, 250×3/2 = 375.

### Where does the method come from?

Institute of Child Nutrition — Adjusting standardized recipes (factor = new yield ÷ old yield); NIST Metric Kitchen — Culinary measurement tips.

## Sources

- [Institute of Child Nutrition — Adjusting standardized recipes (factor = new yield ÷ old yield)](https://theicn.org/cacfp-itrain-simple-lesson-plans/training-scripts/Adjusting-Standardized-Recipes.pdf)
- [NIST Metric Kitchen — Culinary measurement tips](https://www.nist.gov/pml/owm/metric-si/metric-kitchen/metric-kitchen-culinary-measurement-tips)