Elements of the SI: Base & Derived Units

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  • 0:00 SI Units
  • 1:23 Base Units
  • 4:12 Derived Units
  • 6:14 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Discover what we mean by SI units. Then explore SI units further by learning about all the base units, and several examples of the derived units that make up the system.

SI Units

In all of the sciences, one of the most common things students and professional scientists do alike is work with measurements. When we write down the numbers from these measurements, we distinguish them from pure numbers, like we see in a math course, by using dimensions and units.

A number's dimension determines the type of measurement you are working with. Dimensions include things such as length, volume, time, mass, etc. A number's units determines the scale of the dimension's measurement. For instance, the dimension of length can have units of inches, yards, miles, and so on. In a science course, you'll see units represented by a symbol after a number.

In the sciences, we use a standard set of units called the International System of Units or SI units for short. SI units consist of an extension of the original metric system and were first put into place during the 11th General Conference on Weights and Measures in 1960. This unit system is fluid and can be updated as needed when new, more precise methods of measurement become available.

The SI units can be separated into the two main categories of base and derived units. In this lesson, we'll review all the base units and several examples of the numerous derived units.

Base Units

In the International System of Units, the base units are the seven most basic units from which all other units are obtained. Each one is for a unique dimension, and they can't be broken down into other units. Let's look at each of the seven base units and their corresponding dimension.

The meter is the base unit for distance, represented by the symbol m. If you've ever seen a meter stick, you already know exactly how long this is. If you're more familiar with yard sticks, it's just slightly longer than that.

The second is the base unit for time, represented by the symbol s. This is the smallest increment on a microwave, or the fastest hand on a clock. It's the tiniest amount of time people deal with on a day-to-day basis.

The kilogram is the base unit for mass, represented by the symbol kg. One reason kilograms are a nice unit for students is that, unlike pounds, they're only a measure of mass. Pounds can be used as a name for a mass unit or a weight (i.e., force) unit. This can be confusing for students.

The ampere is the base unit for electric current, represented by the symbol A. Electric current is the rate of flow of electricity. It is responsible for powering everything from flashlights to the computer you're watching this on now.

The kelvin is the base unit for temperature, represented by the symbol K. Kelvin is a unique temperature scale because it never goes to negative numbers. Nothing in the universe can be colder than zero kelvin.

The candela is the base unit for luminous intensity, represented by the symbol cd. From the name, you might be able to guess that a standard candle has a luminous intensity of about 1 candela. If you look at a lit candle and a light bulb right next to each other, you'll be able to tell that the light bulb is a much more intense light. The candela is how we represent these different intensities using numbers.

The mole is the base unit for amount of substance, represented by the symbol mol. When we say a mole is measuring the amount of substance, we are talking about the number of elements, such as molecules, atoms, electrons, etc., in that amount of substance. A mole is equal to 6.023 x 10^23 elements of the substance you are measuring. For example, 1 mole of water contains 6.023 x 10^23 water molecules.

We often think of mass as a measure of the amount of a substance. To understand the difference between mass and moles, think of purchasing some grapes at the grocery store. Mass would be like measuring the grapes by putting them on a scale, and moles would be like measuring them by counting the individual grapes on the vine.

Derived Units

Derived units are created by combining base units using algebra. To see this, let's look at the dimension of volume. Volume measures the amount of 3-D space an object takes up. No matter what shape your object is, we find volume by multiplying three lengths together.

So volume = length * length * length.

Here we are talking about volume and length as general dimensions, and not as part of a specific object. For instance, the volume of a rectangular prism is length times height times width. In this formula, length, height, and width are specific parts of an object, but they all have the general dimension of length.

As far as units go, we already know that length has a base unit of meters.

volume units expanded

volume units

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