NOTE

This document expects a very basic understanding of multiplication and division.

NOTE

This document is meant to be read after the Standards for Distance document. If you have not read that document yet, please do so before continuing.

Standards for Mass

Mass is a measure of how heavy an object is.

Weight vs Mass

NOTE

This section expects a simple understanding of the concept of planets, and the idea of gravity. It may be skipped if you are not familiar with these concepts.

As a summary, "mass" can generally be swapped out for "weight" in everyday conversation. However, in scientific contexts, they are different. This document uses the scientific definitions.

The difference between weight and mass can be complicated to understand if you are not aware of gravity and how it affects objects. In simple terms, weight is the force of gravity acting on an object, while mass is the amount of matter in an object.

For example, if you were to take a scale and weigh yourself on the Moon, you would weigh less than you do on Earth. This is because the Moon has less gravity than Earth. However, your mass would remain the same, because the amount of matter in your body does not change.

In scientific contexts, weight is measured in newtons, while mass is measured in kilograms. However, in everyday conversation, the two terms are often used interchangeably.

To calculate weight from mass, you can use the formula:

$$\text{Weight}=\text{Mass}\times \text{Gravity}$$

Where "gravity" is the acceleration due to gravity, which will change depending on where you are. On Earth, the acceleration due to gravity is approximately $9.81{\text{ m/s}}^2$. This is why we often use the formula:

$$\text{Weight}=\text{Mass}\times 9.81$$

This formula is a simplification, but it is accurate enough for most everyday purposes. Weight is measured in "newtons", while mass is measured in kilograms.

Kilograms

The basic unit of mass in the metric system is the kilogram. A kilogram is defined as the mass of a one regular liter of water.

A kilogram is approximately equal to the mass of a small textbook. Kilograms are represented with the symbol kg.

Calculating Mass from Density and Volume

TIP

"Density" is a measure of how much mass is in a given volume. It is calculated by dividing the mass of an object by its volume.

For example, if you have a 2.5 kilogram object that takes up 0.25 cubic meters of space, you can calculate its density like this:

$$\text{Density}=\frac{2.5\text{ kg}}{0.25{\text{ m}}^3}=10{\text{ kg/m}}^3$$

Density uses special "composite" units, which are units that are made up of other units. In this case, the unit is "kilograms per cubic meter" (${\text{kg/m}}^3$).

If you know the density of an object and its volume, you can calculate its exact mass using the formula:

$$\text{Mass}=\text{Density}\times \text{Volume}$$

For example, if you have a 10 kilogram object that takes up 2 cubic meters of space, you can calculate its weight like this:

$$\text{Mass}=10{\text{ kg/m}}^3\times 2{\text{ m}}^3=20\text{ kg}$$

Metric Prefixes

Just like with distance and volume, we can use metric prefixes to make it easier to work with very large or very small masses. The conversion factors are the same as for distance (standard linear measurements).

For example, a "kilo"gram is equal to 1,000 grams, and a "milli"gram is equal to 0.001 grams.

Some special names can be used specifically for mass:

• Ton (t): 1,000 kilograms. Also called a "metric ton". Not to be confused with the old "short ton" used in the United States.

Mass Examples

• A small apple is about 0.2 kilograms.
• A human brain is about 1.4 kilograms.
• A car tire is about 10 kilograms.
• A small dog is about 5 kilograms.
• A standard car is about 1,500 kilograms, or 1.5 metric tons.
• A large elephant is about 5,000 kilograms, or 5 metric tons.
• The entire mass of the Earth is about 5,972,000,000,000,000,000,000,000 kilograms (or $5.972\times {10}^{24}$ kg).
• Humans can generally lift about 20 kilograms without much effort.
• An adult human is about 70 kilograms.

Other Units

Other units of mass exist, such as the pound, the ounce, and the stone. These units are generally outdated and not used in scientific contexts. However, they are still used in some countries, such as the United States and the United Kingdom.

Rough conversions between some of these units and kilograms are as follows:

• 1 pound is about 0.45 kilograms.
• 1 ounce is about 0.03 kilograms.
• 1 stone is about 6.35 kilograms.