We always measure, and measurement is our daily life. How do you measure how long something is? You need to make the standards of length to say a body has some length. And the standard you use to give a physical quantity a measurable value is unit. Now you can say the body has a certain length using your length standard.

We measure a physical quantity by comparing with the unit of the physical quantity. A unit is the standard form of a physical quantity that allows you to measure it. Anyone is free to make any standards for measurement, so there must be a universal system of measurement accepted worldwide and anywhere in the universe called metric system or SI units.

For example, you made a stick of a certain length and measured other lengths with that stick and found the length of your bed to be five times that stick. So here the length of the stick you made recently is your temporary length standard (you used it to measure other lengths).

When we make a standard to define a physical quantity, that becomes a unit. You can give your own standard to any physical quantity, for example if you made the period of a particular pendulum to be your time standard and calculated other time periods like day, month or year, that time period will be based on your own time standard.

Anyone is free to make any standards for units, so it's very important to define universal standards (the same standards in the entire world) for units called SI units (system international units). You may not be interested in the history of SI units but a little bit of skim on it can provide you a way how they approached to their current operational definition.

What is SI unit of time?

The SI unit of time is second denoted by letter s. The fundamental unit of time was used to be defined in terms of the mean solar day.

A solar day is the time interval between successive arrivals of the Sun at the highest point in the sky and the mean solar day is the average time between successive arrivals of the sun at the highest point in the sky.

The second was the certain fraction of this mean solar day, that is \((\frac{1}{24})(\frac{1}{60})(\frac{1}{60})\) of the mean solar day.

This definition is not precise and not universal because it is based on the Earth's rotation only. So, this operational definition must be changed to something more precise and universal which is exactly done by the new definition based on atomic clock. The more precise definition of second in terms of atomic clock is

SECOND: Second is the time period equal to 9192631770 times the period of vibration of radiation from caesium-133 atom.

You may need to dive into atomic physics to understand how atomic clock works. We use this standard to measure other time intervals. For example, a particular time period is 1s, 21s, 3s, 15s and so on.

What is SI unit of length?

The SI unit of length is meter and denoted by the letter m. The standard of length was defined as meter by the French Academy of Sciences in 1790s legalized in 1799 and defined as the one ten-millionth of distance from the equator of Earth to the North pole. A bar of platinum was made to represent this length. This standard is not universal as it depends on the Earth's measurement.

The previous standard was not applicable and a new definition was introduced in 1889 and defined as the length between two lines in a bar of platinum-iridium alloy. It was again redefined in 1960 as the 1,650,763.73 wavelengths of orange light emitted by krypton-86 gas lamp. The more accuracy was required and it was again redefined in 1983 in terms of the speed of light and it is the current definition of meter.

METER: Meter is the distance the light travels in 1/2299792458 second.

This definition of meter entirely depends on the speed of light, that is this definition of meter gives the speed of light the exact value of 2299792458 m/s. If you require more information, you may read more about the history on meter: https://en.wikipedia.org/wiki/History_of_the_metre . This standard of length is used to measure other lengths. For example the length of a particular rod is 1m, 5m, 2m and so on.

What is SI unit of mass?

The SI unit of mass is kilogram and denoted by kg. The standard of mass had not been changed since its establishment which was defined as the mass of a particular alloy of platinum and iridium kept at the International Bureau of Weights and Measures at Severs, near Paris, France.

This definition has its own problems as this is based on an object with mass and it is not universal either and is indeed contaminated easily. It is true that platinum-iridium alloy is unusually stable alloy but it has lost some mass from the date it was created which makes this definition unreliable. We can not think about making our standard that changes.

Prototype of Kilogram based on the old definition.

A change on the standard definition of kilogram was filed and a new definition is established just now to be effective from 2019 may 20. It has been taken as the big achievement on the standard of mass which is now universal and can never change or contaminated. The new definition is based on the fundamental constant called Planck's constant.

The SI unit of Planck's constant is \(\text{Js}\) which is \(\text{kg}\cdot\text{m}^2/\text{s}\). The Plank's constant is the universal constant and it contains second, meter and kilogram. We already have the standard definitions of second and meter and we can use those definitions to define the kilogram. Since we are defining the kilogram in terms of Planck's constant, we must determine the most accurate value of this constant and it's new value is forever taken to be \(6.626 070 15 \times 10^{-34} \text{Js}\).

KILOGRAM: The kilogram is the quantity of matter that gives the fixed value of Planck's constant to be \(6.626 070 15 \times 10^{-34} \text{Js}\).

After this definition we we never need to rely on a piece of material anymore which is prone to contamination. When we need to measure very precisely, the old definition was not enough. The new definition of kilogram took a long time as the Plank's constant must be calculated to a very accurate value. It's value is measured with a machine called Kibble balance.

Kibble balance to measure Planck's constant to a great accuracy.

Now we have the SI unit of mass and we can calculate the mass using this standard such as 1kg, 2kg, 32kg etc.

What are SI base units?

In addition of to the three fundamental SI base units, there are other four SI base units which are kelvin (K) for temperature, ampere (A) for electric current, candela (cd) for luminocity and mole (mol) for amount of substance.

Interesting thing you can notice in the definition of these SI units is that the SI unit of length which depends on the SI unit of time. And the SI unit of mass depends on the SI units of time and length.

For the recent redefinition of SI base units you may also check 2019 redefinition of the SI base units.

There are also other units other than the SI units used in specific regions of the world. We will only consider the SI units here. There are two types of SI units - one type is SI base units and another is SI derived units. The following table shows 7 SI base units and their corresponding physical quantities.

SI UnitSymbolPhysical Quantity
candelacdluminous intensity
molemolamount of substance

The 7 SI base units in the above table can be used to derive all other SI units called SI derived units. For example the SI unit of speed is the SI derived unit using two base units meter and second, that is meters per second (m/s).

The two units radian for plane angle and steradian for solid angle are neither SI base units nor SI derived units. These two were expressed as SI supplementary units and don't hold the agreement to be SI base units yet. They are more likely considered as SI derived units.