Measuring Out Butter

Suppose you have a solid chunk of butter and a measuring cup in the kitchen. You desire to accurately measure one-half cup of butter chunks without melting them. What is a quick, easy way to do so? Often one encounters the statement in cookbooks that Archimedes’ principle is being used. What is this principle, and why is the statement erroneous?

Answer

Butter floats on water because its density is less than the density of water. The recommended procedure in many cookbooks for measuring one-half cup of butter is: put one-half cup of water into the measuring cup and then add pieces of butter until the water level is pushed up to the one-cup level. Often a reference to Archimedes’ principle is given. (According to Archimedes’ principle, a body wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid that it displaces.) However, this recommended measuring procedure does not use Archimedes’ principle! And the measured amount of butter is not exactly one-half cup!

If ice chunks were used instead of butter, then the procedure is correct. As a check, when floating ice melts, the water level does not change. Therefore, the recommended procedure is correct for measuring one-half cup of ice. But the density of butter is not the same as that of the ice, and the density of melted butter is not the same as that of the water. Therefore, the immersed volumes of ice and butter would be different.

However, if the butter is held under the water surface when water is added, then the butter measurement is correct when the water reaches the one-cup level. One is simply measuring the volume of the butter, and one does not use Archimedes’ principle for this measurement.