Mathematics is not only useful for solving problems and equations, but also for everyday activities such as cooking and baking. In this article, we will explore some of the ways that mathematics can help us in the kitchen, especially with the various unit conversions, measurements, ratio math and other calculations one encounters daily whether cooking at home or as a professional in a restaurant.
Recipe Unit Conversions
One of the challenges of cooking is dealing with different units of measurement. For example, some recipes may use grams, while others may use ounces (oz), cups (US or Imperial), teaspoons (tsp), or tablespoons (tbsp) which again can be defined using either the US Legal or the Imperial standard. How can we convert between these units and make sure we have the right amount of ingredients?
One way is to use a conversion chart or a recipe conversion calculator that can do the conversions for us. For example, here are some common conversions that may be needed in the kitchen:
- 1 gram = 0.035 ounces
- 1 ounce = 28.35 grams
- 1 cup = 237 milliliters
- 1 milliliter = 0.004 cups
- 1 teaspoon = 5 milliliters
- 1 tablespoon = 15 milliliters
- 1 cup = 16 tablespoons
- 1 tablespoon = 3 teaspoons
Using these conversions, we can easily change the units of any ingredient. For example, if a recipe calls for 200 grams of flour, we can convert it to ounces by multiplying by 0.035:
200 grams x 0.035 = 7 oz
2 cups x 237 = 474 ml
Another way to deal with unit conversions is to simply use kitchen measuring tools that have different units marked on them. For example, some measuring cups have both cups and milliliters on them, and some measuring spoons have both teaspoons and milliliters on them. This way, we can simply fill the measuring tool to the desired unit and avoid doing any calculations.
Weight to Volume and Volume to Weight Conversions in Kitchen Recipes
The mathematics of recipe unit conversions are straightforward when both measure the ingredient in the same kind of unit. However, sometimes we may encounter recipes using different types of measurement units for the same ingredient. For example, some recipes may measure flour by weight (grams or ounces), while others may measure it by volume (cups or tablespoons). How to convert between these units and make sure we have the right amount of flour for our recipe?
Weight to Volume Conversions
Weight to volume conversions are necessary when we want to measure an ingredient by volume using a measuring cup or spoon, but the recipe gives us the weight of the ingredient. To do this, the density of the ingredient needs to be known, or in other words we need to know how much space it occupies per unit of weight. Different ingredients have different densities, so we cannot use the same conversion factor for all of them.
For example, one cup of all-purpose flour weighs approximately 160 grams, while one cup of granulated sugar weighs 202 grams. This means that flour is less dense than sugar, and more flour than sugar is needed to fill the same volume. To convert 240 grams of flour to cups, we can use this formula:
volume in cups = weight in grams / weight per cup
volume in cups = 240 / 160 = 1.5 cups
Therefore, 240 grams of flour is equivalent to one-and-a-half cups, which can be checked using a g to cups converter.
To convert 100 grams of caster sugar to cups, use the same formula but with a different weight per cup:
volume in cups = 100 / 202 = 0.495 cups
So, 100 g of sugar is approximately equivalent to half a cup (using U.S. Legal Cups) (see “How Many Grams of Sugar in a Cup?” for more conversions).
Volume to Weight Conversions
Volume to weight conversions are the exact opposite of the above. It is when we want to measure an ingredient by weight using a scale, but the recipe gives us the volume of the ingredient. For example, one cup of water weighs 240 grams, while one cup of honey weighs 339 grams meaning that honey is more dense than water so a smaller amount of honey by mass is needed to fill the same volume.
To convert two cups of water to grams, use this formula:
weight in grams = volume in cups x weight per cup
weight in grams = 2 x 240 = 480 g
To convert a cup of honey to grams, plug in a its weight per cup in the same equation:
weight in grams = 1 x 336 = 336 g
Therefore, 1 U.S. Legal Cup of honey is equivalent to 336 grams, which can be double-checked using an online cups to g converter. Note that Imperial Cups are larger and so 1 Imperial Cup contains 398 grams of honey instead.
Some other kitchen recipe converters to consider:
Note that both volume to weight and weight to volume conversions are not exact and results may vary depending on the type and quality of the ingredient in each individual case. For this reason, it is always advisable to use a scale for more accuracy and consistency when following a recipe.
Another aspect of mathematics in the kitchen is measuring the ingredients accurately and precisely. Measuring ingredients is important for following recipes and ensuring consistent results. There are two main types of measuring tools: volume measures and weight measures.
Volume measures are used for measuring liquids and dry ingredients that can be poured or scooped, such as milk, water, oil, flour, sugar, etc. Volume measures include measuring cups, measuring spoons, and graduated cylinders. To use volume measures correctly, follow these steps:
- Choose the right size of the measuring tool for the amount of ingredient needed.
- Fill the measuring tool to the level indicated by the unit mark.
- Level off any excess ingredient with a knife or a spatula.
- Pour or scoop the ingredient into the mixing bowl or pan.
Weight measures are used for measuring solid ingredients that are too bulky or irregular to be measured by volume, such as meat, cheese, butter, etc. Weight measures include scales and balance beams. To use weight measures correctly, follow these steps:
- Choose the right unit of weight for the ingredient needed (grams or ounces).
- Place a container or a plate on the scale or balance beam and zero it out.
- Place the ingredient on the container or plate until it reaches the desired weight.
- Transfer the ingredient to the mixing bowl or pan.
The third aspect of mathematics in the kitchen is doing calculations with numbers and fractions. Calculations are useful for adjusting recipes, doubling or halving quantities, estimating cooking times, counting calories, etc. Here are some examples of calculations that we may encounter in the kitchen:
- Adjusting recipes: Sometimes we may want to make more or less servings than what a recipe provides. In that case, we need to adjust the quantities of ingredients proportionally. For example, if a recipe makes six cookies but we want to make twelve cookies, all ingredients need to be multiplied by two. If a recipe makes twenty-four cookies but we only want to make six cookies, all ingredients must be divided by four. A recipe scaling calculator can do this math for you.
- Doubling or halving quantities: Sometimes we may want to double or halve a recipe for convenience or preference. In that case, we need to multiply or divide all ingredients by two. For example, if a recipe calls for two teaspoons of baking powder and we want to double it, we need four teaspoons of baking powder. If a recipe calls for one cup of milk and we want to halve it, we need half a cup of milk.
- Estimating cooking times: Sometimes we may need to estimate how long to cook something based on its weight, type, and desired doneness. For example, how long do we need to roast a turkey, a chicken, or a beef roast? One way to estimate cooking times is to use a calculator or a chart that can give us the approximate time and temperature for different meats and cuts.
For example, here is a formula for calculating the cooking time for a turkey in minutes:
cook time = (weight in pounds x 3) + 5
Using a thermometer
Another way to estimate how long to cook a meat is to use a thermometer that can measure the internal temperature of the meat. This way, we can check if the meat is cooked to our liking and avoid overcooking or undercooking it.
Here are the recommended internal temperatures for several different meats:
- Turkey: 165°F (74°C)
- Chicken: 165°F (74°C)
- Beef: 145°F (63°C) for medium rare, 160°F (71°C) for medium, 170°F (77°C) for well done
- Pork: 145°F (63°C)
- Lamb: 145°F (63°C) for medium rare, 160°F (71°C) for medium, 170°F (77°C) for well done
While this may feel like cheating as it avoids time calculations altogether, it may be preferable as different slices of meat may have varying thickness and therefore require slightly longer or shorter time to properly cook.
Using cooking ratios
Another common type of kitchen math involves applying different kinds of recipe ratios, typically the ratio of a smaller quantity ingredient to that of a base ingredient which makes the majority of what’s cooked. For example, Baker’s math, or Baker’s percentages, express the ratio (proportion) of all ingredients of a baked good in terms of the weight of the flour. This type of ratio can be seen in use in our pizza calculator as well as our Baker’s math calculator.
A major reason to use ratios is that they make scaling recipes really easy, as long as you can do some ratio math. This is why recipes for cooking rice, making brine, the perfect cup of coffee, and others use ratios.
The basic way of using cooking ratios is:
- take the weight of the base ingredient
- multiply it by the ratio to get the weight of the other recipe ingredient
- if it is expressed as a percentage, divide by 100 at the end
For example, how to determine how much water is needed given a recipe with a water to flour ratio of 1:0.55 and knowing that for the amount of dough required, the flour weight is 2 lb? The solution is to multiply 2 lb by 0.55 to find the required amount of water which is 1.1 lb. If given as a percentage (55%), the calculation will be 2 x 55% = 2 x 55 / 100 which again results in 1.1 lb of water.
Mathematics is everywhere in the kitchen, and it can help us cook and bake better and more efficiently. By using unit conversions, measurements, and calculations, we can follow recipes accurately, adjust quantities easily, and estimate cooking times precisely. Mathematics can become more fun and engaging for both you and your kids and can be used to explore and learn about different mathematical concepts such as equal spacing, equal groups, partitioning, multiplication, division, addition, and subtraction. Cooking and baking are not only delicious but can also be educational activities that enhance our math skills and understanding. Bon appétit!
An applied statistician, data analyst, and optimizer by calling, Georgi has expertise in web analytics, statistics, design of experiments, and business risk management. He covers a variety of topics where mathematical models and statistics are useful. Georgi is also the author of “Statistical Methods in Online A/B Testing”.