# Ajustar receita

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

Versão interativa: https://www.calcopenly.com/pt/everyday/recipe-scaler
Tema: Calculadoras do dia a dia

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.

## Dados

- **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**

## Resultados

- Scale factor — resultado principal
- Scaled recipe
- Lines scaled
- Lines kept as written

## Fórmula

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

## Exemplos resolvidos

### 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**
- Fonte de verificação: 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**
- Fonte de verificação: 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**
- Fonte de verificação: 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**
- Fonte de verificação: 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**
- Fonte de verificação: Hand calculation: 125 × 0.75 = 93.75; 0.5 × 0.75 = 0.375, shown to 2 decimals (half-up)

## Perguntas

### 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.

### Qual é a precisão de “Ajustar receita”?

A precisão depende dos dados inseridos e das hipóteses do método. O cálculo decimal usa 50 algarismos significativos, mas estimativas, métodos numéricos e dados de origem podem ter menor precisão; o arredondamento exibido não elimina essas limitações. Exemplos resolvidos verificados com fontes independentes: 5. Por exemplo, “Default recipe from 4 to 6 servings” é verificado com 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.

### De onde vem o método?

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

## Fontes

- [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)