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SI Units

SI Units: Fundamental and Derived Units

The table below gives the fundamental SI units that we use in our study of physics. This tutorial uses non-SI units in a few applications where they are in very common use, such as the measurement of blood pressure in millimeters of mercury (mm Hg). Whenever we discuss non-SI units, we will tie them to SI units through conversions.

Fundamental SI Units

LengthMassTimeElectric Current
meter (m)kilogram (kg)second (s)ampere (A)

It is an intriguing fact that some physical quantities are more fundamental than others. In fact, the most fundamental physical quantities can be defined only in terms of the procedure used to measure them. As a result, we refer to the units in which we measure these quantities as fundamental units.

Here, we take the fundamental physical quantities to be length, mass, time, and electric current. (Note that we will not introduce electric current until a later physics tutorial.) Basically, we can express all other physical quantities, such as force and electric charge, as algebraic combinations of length, mass, time, and current. For example, speed is length divided by time. As a result, we refer to these units as derived units.

Units of Time, Length, and Mass

The Second

The SI unit for time, the second (abbreviated s), has a long history. For many years, scientists defined it as 1/86,400 of a mean solar day. More recently, we adopted a new standard to gain greater accuracy and to define the second in terms of a non-varying, or constant, physical phenomenon (because the solar day is getting longer due to very gradual slowing of the Earth’s rotation).

Cesium atoms can be made to vibrate in a very steady way. In fact, scientists can readily observe and count these vibrations. As a result, in 1967 the second was redefined as the time required for 9,192,631,770 of these vibrations. (See image below.) Accuracy in the fundamental units is essential, because all measurements are ultimately expressed in terms of fundamental units and can be no more accurate than are the fundamental units themselves.


An atomic clock such as this one uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year. The fundamental unit of time, the second, is based on such clocks. This image is looking down from the top of an atomic fountain nearly 30 feet tall! Image credit: Steve Jurvetson/Flickr

The Meter

The SI unit for length is the meter (abbreviated m). Its definition has also changed over time to become more accurate and precise. The meter was first defined in 1791 as 1/10,000,000 of the distance from the equator to the North Pole. This measurement was improved in 1889 by redefining the meter to be the distance between two engraved lines on a platinum-iridium bar now kept near Paris. (See image below.)


The main problem with defining the length standard by an artifact such as the meter bar is that there is no sure way to determine if it has changed length due to age, deterioration, or misuse. We can compare it to other bar standards, but these may have changed length themselves. Image Credit: Wikimedia Commons (public domain)

By 1960, it had become possible to define the meter even more accurately in terms of the wavelength of light. So it again got a new definition as 1,650,763.73 wavelengths of orange light emitted by krypton atoms. In 1983, the meter got its present definition (partly for greater accuracy) as the distance light travels in a vacuum in 1/299,792,458 of a second. (See image below.) This change defines the speed of light to be exactly 299,792,458 meters per second. The length of the meter will change if we someday measure the speed of light with greater accuracy.


We define the meter to be the distance light travels in 1/299,792,458 of a second in a vacuum. Distance traveled is speed multiplied by time. Image credit: OpenStax College Physics

The Kilogram

The SI unit for mass is the kilogram (abbreviated kg). Scientists define it to be the mass of a platinum-iridium cylinder. Actually, this cylinder stays with the old meter standard at the International Bureau of Weights and Measures near Paris. Exact replicas of the standard kilogram are also kept at the United States’ National Institute of Standards and Technology, or NIST, in Gaithersburg, Maryland outside of Washington D.C., and at other locations around the world. (See image below.) Ultimately, we can trace the determination of all other masses to a comparison with the standard mass.


A national prototype kilogram standard mass, number K4, kept by the National Institute of Standards and Technology, USA, one of two which serve as the official standard for defining all units of weight and mass in the United States. Image credit: “Standard kilogram 2” via Wikimedia Commons (public domain)

Electric current

We will introduce electric current and its accompanying unit, the ampere, in another tutorial when we cover electricity and magnetism. Generally, this tutorial explores mechanics—motion and forces producing motion. In this tutorial, we can express all pertinent physical quantities in terms of the fundamental units of length, mass, and time.

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