# Units of Measurement

Cups, grams, ounces, milliliters, teaspoons… Recipes use so many units to tell us how much of each ingredient we need. Why are there so many? What’s the difference? Can we use grams when the recipe is written in cups? In this post, we’ll discuss what these units represent and which units are best to use for different ingredients. We’ll also describe how to convert between units so that you can try any recipe regardless of the measuring equipment you have. In the next post, we’ll use this information to discuss how to measure accurately and precisely in the kitchen.

## We can measure ingredients by volume or mass.

Different units reflect different properties of our ingredients that we measure. Just as the doctor can measure our height or weight, we can the volume or mass of our ingredients.

### Volume

Volume is a measure of how much space something takes up. Any unit where we fill up a cup or a spoon (cups, tablespoons, teaspoons, fluid ounces, milliliters) is a measure of volume. It doesn’t really matter what shape our ingredients take⁠—a tablespoon of butter cut from the stick is the same as a tablespoon of butter in the measuring spoon⁠—but a tablespoon of butter should fill the tablespoon exactly, no matter which spoon you use.

For powdered ingredients like flour, cocoa powder, and sugar, where we can pack the ingredient into the cup, volume isn’t a very accurate way to measure. Depending on how much you compact it, for example, a cup of flour, which should weigh 125 grams, can weigh anywhere from about 110 to 170 grams! Flour is so important for texture that this difference can lead to drastic changes to the recipe. If you must measure by volume, flour should be gently spooned into the measuring cup and leveled with the back of a knife or a chopstick. As you can see below, inaccurate measurement of flour often leads to dense baked goods. Similarly, we can fit more granulated sugar into a cup if we shake the cup and settle the sugar, and we can pack brown sugar loosely or tightly. The nature of these ingredients introduces error when we measure them by volume. And although these differences won’t break a recipe in most cases, they won’t yield consistent results.

For liquids, measuring by volume is accurate although liquids actually expand and contract as temperatures rise and fall. As temperatures increase, liquid molecules move faster, and they bounce further apart when they collide. Thus, the molecules occupy more space and the volume of the liquid increases. (This is why water circulates when it heats up on the stove. The hotter water at the bottom of the pot space expands and becomes less dense, so it rises to the top while the cooler, denser water at the top of the pot sinks.) However, changes in volume due to temperature are too small to detect in the kitchen, so we don’t have to worry about them.

### Mass and weight

The other common units of measure, such as grams and ounces, require a scale. These are technically units of mass, but in common usage, the word “mass” is used interchangeably with “weight.” While they are two different concepts, the distinction doesn’t really apply in the kitchen. Nevertheless, it’s a helpful one to understand.

Mass is a measure of how much matter there is. It’s an intrinsic property, which means that it doesn’t change. If I have a rock in my hand, the rock’s mass is constant, even if I take it to the moon. The rock will feel lighter on the moon, but that’s because its weight changes. Weight is a measure of force, of the force of gravity pulling down on an object. Gravity on the moon is weaker than it is here on Earth. That’s why astronauts can jump so high there. It also means that the rock will weigh less on the moon even though it’s the same size. Its mass remains constant, but its weight does not.

If we were to bake cookies on the moon, we wouldn’t use more of each ingredient to make up for the difference in weight. We’d use the same amount because grams, pounds, and ounces are units of mass in a recipe. If they were truly units of weight, our recipes would yield many more cookies on the moon than on the Earth! More relevantly, Earth’s gravitational field also fluctuates a little depending on where we are. Since we measure ingredients by mass, however, we don’t need to check the force of gravity when we move to a new city. The differences would be too small to matter much anyway.

Because mass is an intrinsic property of matter, it’s the most accurate way to measure ingredients. It’s like a way to count the number of molecules we have, regardless of how tightly they’re packed. For powdered solids like flour, the scale tells us if we have the correct number of particles. Mass can also tell us if we have the right number of liquid molecules, so it presents an accurate alternative to measuring by volume. (I prefer to measure liquids by mass because then I don’t have a measuring cup to wash.)

## We can convert between units

If there are only two properties of ingredients we measure, volume and mass, why are there still so many units? First, just as there are different systems for measuring height across the world (in centimeters or in inches), there are different systems for measuring both volume and mass. Volume can be measured in milliliters and liters or in teaspoons, tablespoons, cups, and fluid ounces. Mass is measured in grams or in ounces and pounds.

Second, just as it’s easier to measure small distances in centimeters and long distances in kilometers, it’s convenient to have different units for small and large amounts. But just as we can easily convert centimeters to inches to yards to meters, we can convert between units of the same property. A tablespoon, for example, contains about 15 milliliters. Because both of these are units of volume, this relationship will never change, just as there are always 2.54 centimeters in an inch. The conversion factors are easy to find with a quick Google search, and Google even does the math for you.

But what if we want to change the units from volume into mass? What if a recipe only provides measurements in cups but we want to bake in grams, or vice versa? In this case, we have to consider the ingredient’s density.

### Density

Density is a property of matter that reflects how close together the molecules are. Just as flour can be packed tightly into a measuring cup, molecules can be packed tightly into a given amount of space. The more molecules there are, the denser the ingredient. As I mentioned earlier, the density of liquids changes a tiny bit with temperature because the molecules spread apart. But more importantly in the kitchen, density varies between different ingredients. One cup (237ml) of water, for example, weighs 237 grams, but a cup of oil (still 237ml because both cups and milliliters are units of volume) weighs 224 grams. This means that the molecules in oil are packed less densely than the molecules in water. And because fewer molecules fit in the cup, the oil weighs less. Variation in density is usually caused by differences at the molecular level. Water molecules, for example, are tiny so they can pack together closely like pebbles, while oil molecules are larger and leave gaps.

We can also describe the density of solid ingredients. All-purpose flour, for example, weighs about 125 grams for every cup. Sugar weighs about 200. A Google search (such as “sugar grams to cups”) finds websites like King Arthur Flour that give conversion tables between units of volume and mass. For less common ingredients, you can use the information printed on the packaging to estimate how much you need. The serving size on a bag of Baker’s Corner semisweet chocolate chips, for example, is listed as “1 Tbsp (15g)”—a unit of volume equated to a unit of mass! From here, we can calculate that 30 grams equals two tablespoons, 60 grams equals four tablespoons (which is also a quarter cup), and so on. I was also recently gifted The Baker’s Appendix, a hard-copy reference of these conversion factors which I’ve found handy, especially when I’m already in the middle of something in the kitchen.

## Conclusions

Recipes are written in many units because people across the world use different measuring systems, and some recipe developers refuse to provide volumes because they believe mass is the best way to measure. To try recipes from all over the world, it’s helpful to convert them into units we can measure. Although Google can perform these conversions for us, understanding the relationship between volume, mass, and density can give us better insights into how recipes are written and into our own baking. Furthermore, as we’ll see in the next post, it’s important to be cognizant of what we’re measuring to choose the best way to do it. We’ll be discussing the practical side of measurement: how to be both accurate and precise when baking, and how much leeway we have. Hint—despite what we discussed today, the scale isn’t always your friend!

## References

Figoni, P. How Baking Works, 3rd ed.; John Wiley & Sons, Inc.: Hoboken, 2011.

Reed, J. The Baker’s Appendix, 1st ed.; Clarkson Potter/Publishers: New York, 2017.

Wilbraham, A.; Staley, D. D.; Matta, M. S.; Waterman, E. L. Chemistry, Prentice Hall: Upper Saddle River, 2008.