The International System of Units

When you measure something in physics, you need a standard everyone agrees on. Without that, measurements are meaningless. Over the centuries, different countries developed their own systems, and three of them became widely used:

• The CGS system (centimeter, gram, and second)
• The MKS system (meter, kilogram, and second)
• The FPS system (foot, pound, and second)

The internationally accepted system today is the Systeme Internationale d’ Unites, abbreviated as SI. You’ll see it called the International System of Units in most textbooks. SI is built on the metric system, which means conversions are based on powers of 10. That makes your calculations far simpler than working with feet and inches.

Units: Fundamental and Derived

Physical quantities fall into two categories based on how their units are defined. The units for base or fundamental quantities are called fundamental units. You cannot break these down into simpler units. The units of all other physical quantities, which you can express as combinations of fundamental units, are called derived units.

A complete set of fundamental and derived units together is called a system of units.

For any unit to be useful in science, it must satisfy four basic properties:

1. It should be readily available and reproducible.
2. It must be well-defined, leaving no room for ambiguity.
3. It should be invariable, meaning it does not change with time, location, or conditions.
4. It should be universally acceptable across all countries and scientific disciplines.

The Seven SI Base Units

The SI system rests on seven fundamental or base units. These are completely independent of each other, and you can express every other physical quantity in terms of these seven. Think of them as the building blocks of all measurement in physics.

Base Quantity	SI Unit	Symbol	What It Measures
Length	Meter	m	Distance between two points
Mass	Kilogram	kg	Amount of matter in an object
Time	Second	s	Duration of an event
Electric Current	Ampere	A	Flow of electric charge
Temperature	Kelvin	K	Thermodynamic temperature
Amount of Substance	Mole	mol	Number of elementary entities (atoms, molecules, etc.)
Luminous Intensity	Candela	cd	Power of light emitted in a given direction

Let’s look at each one so you understand exactly what it represents and how it’s defined.

Meter (m)

The meter is the SI unit of length. It’s defined as the distance light travels in a vacuum in exactly 1/299,792,458 of a second. This ties the meter directly to the speed of light, making it one of the most precisely defined units you’ll encounter.

Kilogram (kg)

The kilogram is the SI unit of mass. Until 2019, it was defined by a physical platinum-iridium cylinder kept in a vault in France. Now it’s defined using the Planck constant (h = 6.62607015 x 10^-34 J s). This means the kilogram is no longer tied to any physical object, which makes it far more stable and reproducible.

Second (s)

The second is the SI unit of time. It’s defined as the duration of 9,192,631,770 periods of the radiation corresponding to a specific transition of the cesium-133 atom. Atomic clocks based on this definition are so accurate that they would lose less than one second over millions of years.

Ampere (A)

The ampere is the SI unit of electric current. It’s now defined by fixing the elementary charge (e) to exactly 1.602176634 x 10^-19 coulombs. In simpler terms, one ampere corresponds to the flow of about 6.24 x 10¹⁸ electrons per second past a given point.

Kelvin (K)

The kelvin is the SI unit of thermodynamic temperature. It’s defined by fixing the Boltzmann constant (k) to exactly 1.380649 x 10^-23 J/K. Zero kelvin (0 K) represents absolute zero, the lowest temperature theoretically possible, where all molecular motion would cease.

Mole (mol)

The mole is the SI unit for the amount of substance. One mole contains exactly 6.02214076 x 10²³ elementary entities. This number is called the Avogadro constant. When you use the mole, you must always specify what entities you’re counting, whether atoms, molecules, ions, or electrons.

Candela (cd)

The candela is the SI unit of luminous intensity. It measures the power of light emitted by a source in a particular direction, weighted by the sensitivity of the human eye. It’s defined by fixing the luminous efficacy of monochromatic radiation of frequency 540 x 10¹² Hz to be 683 lumens per watt.

The 2019 SI Redefinition

On 20 May 2019, the SI system underwent its most significant overhaul in decades. Four of the seven base units (kilogram, ampere, kelvin, and mole) were redefined in terms of fixed numerical values of fundamental physical constants. The kilogram was the last unit still defined by a physical artifact, and that changed with this revision.

What this means for you as a student is that every SI base unit is now anchored to an unchanging constant of nature, not to any physical object that could degrade or vary over time. The definitions became more elegant and, more importantly, more precise and universally reproducible.

Supplementary Units

Apart from the seven base units, the SI system also recognizes two supplementary quantities for measuring angles:

1. Plane angle (dθ) is defined as the ratio of the length of arc (ds) to the radius (r). Its unit is the radian (rad).
2. Solid angle (dΩ) is defined as the ratio of the intercepted area (dA) of a spherical surface, described about the apex O as the center, to the square of its radius (r²). Its unit is the steradian (sr).

Both the radian and steradian are dimensionless quantities. They were originally classified as “supplementary units” by the SI, but since 1995 they are treated as derived units with a special status.

Derived Units

Every physical quantity that isn’t one of the seven base quantities is a derived quantity. Its unit is a derived unit, formed by combining base units through multiplication or division. For example, speed is measured in meters per second (m/s), which combines the base units for length and time.

Some derived units are used so frequently that they get their own names and symbols. You’ll encounter the newton (N) for force, the joule (J) for energy, the watt (W) for power, and the pascal (Pa) for pressure, among many others. Each of these can ultimately be broken down into combinations of the seven base units.

Whenever you express a derived unit, make sure you can trace it back to the base units. For instance, 1 N = 1 kg m s^-2. This skill of dimensional analysis will help you verify equations and catch errors in your calculations.

Frequently Asked Questions