How To Calculate Mass & Weight

If you spend any time interacting with people at work or school and watch any kind of television-style programming, it would be unusual for you to go even a full day without hearing at least one of the words mass or weight. This is especially true of the latter, given the number of people at any time who are attempting to slim their bodies through some combination of physical activity and dietary modification.

Finding the mass and weight of objects in the modern world is easy enough: Find a suitably sized scale, put the object on it, and read the digital or analog numbers that result. But calculating mass from weight or conversely can be confusing because these terms are used incorrectly or imprecisely in everyday language.

Mass is one of two fundamental quantities in physics, the other being length. By "fundamental," this means that all other units (e.g., velocity, force, acceleration and so on) are derived from one or more of these units, whereas neither mass nor length is itself derived.

Mass is a measure of "stuff," apart from whatever influence gravity has on that stuff. At root level, everything that has mass is made up of electrons, protons and neutrons (or if you want to be choosy, subatomic particles). One key property of mass is that gravity does act on it if it is present, resulting in a force called weight.

• For reference, 1 kg = 2.204 lb, treating lb in the "everyday" Earth sense.

Weight is the result of gravity acting on mass: w = mg. The value of g on Earth's surface is 9.8 m/s³ with units of acceleration. To find the weight of something, simply multiply its mass by the value of the local gravitational field, and you get a result in newtons (N). For example, if your mass is 50 kg (about 110 pounds), then your weight is (50)(9.8).

The point that must be overwhelmingly emphasized is that weight is a force. Mass does not require gravity for its own existence, whereas weight does. It is easy to conflate the two because it is rare for anyone on Earth to operate in zero-gravity conditions.

For this reason, when you calculate your mass on a scale designed for use on Earth, weight is already factored into the operation of the scale. Mass is not weight, but they are always directly proportional to each other by the value of g, whatever it may be.

But what does this mean in terms of imperial (pounds and ounces) units? In fact, a unit of mass exists in this scheme, called the slug, but it is ignored today. If someone says she weighs 110 pounds, think of this as her mass, which would be 50 kg in SI units.

Mass and length together give rise to an important variable called density. Volume, which is a measurement of a "chunk" of three-dimensional space, is derived from length units, and in the metric system, it has units of m³. Density is mass divided by volume and offers a sense of the "heaviness" of an object in relation to its size.

Numerically, density ρ = m/V and has SI units of kg/m³, though units such as g/cm³ are more common in science settings.

• What is the mass of an 0.25-m³ object with a density of 2.5 kg/m³?

Since ρ = m/V, m = ρV. In this case, you have:

(0.25 m3)(2.5 kg/m³) = 0.625 kg.