In the metric system mass is measured in kilograms and grams and these will be the units we will most often use. (In the United States today, almost no one knows what the unit of mass is called--it's not the pound. The pound is a unit of weight--more about weight in the next paragraph.ou will measure the mass of objects by comparing them to the mass of pennies with a thing we will call a Mass Balance. Although mass is usually measured in kilograms or grams, we will measure mass in pennies.