For much of human history, quantities have been measured in a perplexingly complicated system based on the number three, and the various types of quantity* were completely unrelated. For example, length was measured in inches ( the length of some pharaoh's thumb), yards (the length from Henry VIII's nose to the tip of his middle finger), and feet (the length of that king's foot). These were eventually standardized so that there were twelve inches in a foot and three feet in a yard, but these quantities had no link to the units of mass, the ounce, the pound, and the hundredweight*. This made measuring things such as pressure, which depends on both mass and area* rather difficult. To make matters worse, the American and British units which had the same name were not equal in quantity; for example, one UK gallon* was equal to 4.564 metric litres, whereas the US gallon was equal to 3.7854 litres. The British system did eventually change from the pound/ poundal system of mass and weight to the slug/ pound system, the second of which used g , a number representing acceleration due to gravity and equal to about 9.806 metres per second, but it was clear for a long time that a simpler, more logical, worldwide system was needed. However, until relatively recently, few people actually bothered to do anything about it.

History Of The Metric System

The idea of the metric system actually dates back to the year 1585, when one Simon Stevin wrote a book entitled The Tenth , in which he suggested that a decimal system of measurement should be used for things such as length, weight, coinage, and measurement of arcs. However, his work went largely unnoticed until 1670, when a French scientist by the name of Gabriel Mouton came up with some measurements based on the number ten, and Louis XVI authorized a scientific investigation into creating an entire system based on this principle in 1790. This led to the first version of the metric system, officially adopted by France in 1795.

Ninety years later, in 1885, eighteen countries signed the Convention of the Metre *. The result of this was that metric masses and lengths became standard across the world, and a new organization was set up, the General Conference on Weights and Measurements (CGPM) , whose job was to officially regulate international agreements on metric units. This convention also made it illegal to refuse to trade in metric units, something which merchants had been doing frequently up until then.

The first version of the metric system was known as the CGS system, due to the units it used: the centimetre, gramme, and second. A second system was brought into being in 1954, called the MKS system, so called because it used the metre, kilogramme, and second. This was declared the International system on Units at the 10th CGPM. The MKS system could not measure everything, and so a new unit, the ampere (aka amp), the unit of electrical current, was introduced, creating the MKSA (metre/ kilogramme/ second/ ampere) system.

A major change to the metric system occurred in 1960 at the 11th CGPM. Firstly, the metre was redefined in terms of the wavelength of light (prior to this, it was 10 ^-7 of the distance from the equator to the North Pole). Secondly, a new unit of temperature, the kelvin, was added to the MKSA system. The new system could measure practically anything, and so was adopted at the SI* system. This SI system is what is used across the world today, except in America*

How the Metric System Works

Essentially, for every quantity, there is a basic metric unit, and this is normally (but not always) also the SI unit. The SI unit is the one used in scientific calculations, and the standard metric unit is the one from which all other metric units of that quantity are derived. The system works as follows:

Table of Metric Prefixes

For example, to get the unit for 1,000 metres, put 'kilo' before 'metre,' and you get 'kilometre.' The abbreviation for this is km (k for kilo + m for metre). Similarly, to obtain the word for 1/1,000 of a metre, place 'milli' before it, to get 'millimetre,' the abbreviation for which is 'mm.'

Metric Units

In the SI system, there are five fundamental measurements: length, mass, time, electric current, and temperature. All other measurements are derived from these. The derivative units were conceived primarily for convenience; for example, 'newton' is much easier to say and more distinctive to write than 'kilogramme per square metre.'

Over the years, certain metric units have undergone change for various reasons. For example, the calculation of some units would involve π. The convention of whether this should be included in the formula for a unit or be absorbed by changing to unit has been a changeable fashion. The modern metric system utilizes the latter convention, as did the so-called rationalized MKS system.

Time

The standard metric unit and SI unit of time is the second, generally written as 's.' The definition of a second has changed over time, however. Originally, it was 1/86,400 of the average time taken for Earth to spin once on its axis *. Later, it was adapted to mean the length of time taken for light to travel 2.99792*10⁸kilometres. Nowadays, it is defined by atomic clocks, as 9,192,631,770 periods of the radiation of a certain energy transition of the caesium 133 atom
Atomic clocks are accurate to 1s in 4 ½ *10¹² years, so there is little fear of the measure of time getting tremendously inaccurate any time soon.

Time is somewhat different to the other metric quantities for two reasons. Firstly, its unit has been around since ancient times, and was in fact first conceived by the ancient Sumerians. Also, the higher divisions of time are still based on a number other than ten, i.e. sixty; there are 60 seconds in a minute and 60 minutes in an hour. There are then 24 hours in a day. The reason for this is that this system has been in use since the Sumerian Empire, and attempting to force metric time on the population of the world would cost a lot of money to tell people about and would also seriously mess up a lot of people's schedules and timetables. As well as that, scientists would have little use for 'kiloseconds' and the like. However, the regular metric subdivisions of the second (millisecond, microsecond, etc.) are used regularly, generally in computer applications and nuclear physics.

Another common unit of time is the year, which is the time it takes for Earth to orbit the sun. 1 year is equal to approximately 365 days and six hours; however, it is generally measured as just 365 days, and so an extra day is added every fourth year, creating a leap year. The year has metric multiples, but they are not called 'kiloyears.' 10 years forms one decade, 100 years is one century, and 1,000 years is known as 1 millennium.

According to quantum physics, the smallest unit of time possible is the Planck time. Conceived by Max Planck, one Planck time is equal to 10^-43s. All other units of time are a positive discrete real whole number of Planck times. 1 Planck time is believed to have been the 'age' of the Universe at the instant of the Big Bang *

Length

Length is a measure of 1 dimensional space. The standard metric unit and SI unit of length is the metre. Originally, the metre was defined as 1*10^-7 of the distance from the North Pole the Equator. Later, it was redefined as the distance light travels in 2.99792*10^-8* seconds. Other frequently used lengths are the nanometre, micrometre (both used in atomic and wave physics) millimetre (generally used in engineering), centimetre (generally the first metric unit children are thought in school), and kilometre (used on road signs and for measuring distances over land; known in the US military as a 'klick').

When talking about astronomical distances, numbers of metres and kilometres get uncomfortably huge. For this reason, there are different measurements used here. Within the solar system, distances are measure in astronomical units, which are defined as the average distance between Earth and the sun. 1 astronomical unit is equal to 148,804,800 km. Mars is an average of one astronomical unit from Earth.

Interstellar distances are measured in light years. 1 light year is the distance light travels in one year, and so is equal to 9.454240512*10¹² km. This makes the nearest star to our, own Proxima Centauri, 4.06532342*10¹³ km away, or alternatively, a much more convenient 4.3 light years away.

Quantum physics tell us that the smallest possible unit of length is the Planck length, equal to 10^-35m, or 10^-33cm. It is the distance light can travel in 1 Planck time. All distances are a positive whole discrete real number of Planck lengths.

Area

Area is a measure of 2 dimensional space, or the amount of space that a flat object takes up. The SI unit of area is the square metre, written as sq m or m². 1 m² is a square where each side measures 1m. Other frequently used units of area are the square centimetre (cm²) and square kilometre ( km²). In area, 100mm² is equal to 1cm², whereas in length, 10mm equals 1cm. The rest of the square measurements follow a similar pattern.

The standard metric unit of area is the are (a). 1a is equal to 100m². It is used for measuring plots of land, but is not particularly large, and so hectares are more commonly used. Unlike the SI units of area, the standard metric units follow the regular pattern, i.e. 1a = 100ha.

As with time and length, there is a fundamental minimum unit of area, dubbed the 'Planck area.' It is a square of 1 Planck length on each side, and is equal to 10^-66cm². All areas are a discrete positive whole real number of 'Planck areas.'

Volume

Volume is a measure of 3 dimensional space, or the amount of space a solid object takes up. The standard metric unit and SI unit is the cubic metre, written a m³. The cubic metre is defined as a cube, all of whose edges are exactly 1m long. However, since 1m³ is quite large, the cubic decimetre (dm³) is much more often used.

Medicine volume is generally measured in cubic centimetres, known as cm³ or cc. Therefore, next time you're watching ER and someone calls for '500 ccs of blood, stat!" you'll know what they're talking about.

While cubic kilometres theoretically exist, there is no real use for them. Cubic light years have even less value and would be incredibly hard to implement.

Once again, quantum physics describes the smallest possible unit of volume, known as the 'Planck cube.' 1 Planck cube is a cube where all the sides are 1 Planck length long, and is equal to 10^-99cm³. As you can probably guess, all volumes are a discrete positive whole real number of 'Planck cubes.'

Capacity

Capacity is a measure of how much space a liquid or gas takes up. The standard metric unit is the litre, and the SI unit is still the m³. The symbol for the litre is l, and 1l is defined as being equal to 1dm³. The other common measure of capacity is the millilitre, which is equal to 1cm³.

Mass

Mass, not to be confused with weight, is a measure of how much matter an object contains. The standard metric unit is the gramme (symbol g) and the SI unit is the kilogramme (often shortened to 'kilo'). 1 kg is defined as the mass of 1l of water, and it may thus be extrapolated that 1g contains equal mass to 1ml of water. Other common measurements of mass are the milligramme (mg, used in measuring medicine), and the tonne (t), equal to 1,000 kg.

When talking about atomic masses, these metric units are rather unwieldy, and so a new unit is used, the atomic mass unit (amu). Officially, 1amu is 1/12 the mass of the ¹²C isotope, i.e. it is 1/12 the mass of a normal carbon atom. A proton has a mass of 1.007 amu, a neutron is slightly heavier at 1.008 amu, and an electron has a mass of 1/1836 amu.

Density

Density is a measure of how tightly the matter in a solid is packed together. The SI unit is the kilogramme per cubic metre (kg m^-3), but for small objects, a common unit is the gramme per cubic centimetre (g cm^-3).

Force

Technically, force is that which causes acceleration. It is measured in newtons (N). 1N is the force which a mass of 10g exerts due to gravity.

Weight, as opposed to mass, is the force an object has due to gravity.

Speed, Velocity, and Acceleration

Officially, speed is the rate of displacement of a mass, and the common definition is how fast an object is moving. The SI unit of acceleration is the metre per second, or m s^-1. Another frequently used unit is the kilometre per hour (kph) which is used to measure the overall speed of vehicles.

Velocity is speed in a given direction, for example 10m s^-1 is speed but 10m s^-1 north is velocity. In most cases, the two are interchangeable.

Acceleration is the rate of change of velocity, or how fast speed is increasing. The SI unit of acceleration is the metre per second per second, or m s^-2.

Pressure

The definition of this is force per unit area, or newtons per metre squared (N m^-2; the SI unit). It is the force an object exerts over an area.

Atmospheric pressure is measured differently. The standard metric unit is the atmosphere (atm), and 1atm is normal, average atmospheric pressure. However, since current temperature fluctuates, another system is required.

The standard metric unit of air pressure is the paschal (Pa). It is actually a derivative unit of atmospheric pressure, as at 1 atm, the height of mercury in a mercury barometer is 76cm. Multiplying this by g by the density of mercury (13,600 kg m^-3), one comes up with 101,292.8 units. If g is taken at its more precise value of 9.81, the result is 101,400 units. One of these units is termed a paschal. The most commonly used unit of pressure is the hectopaschal (hPa). It is therefore shown that normal atmospheric pressure is 1,014 hPa.

Temperature

Not to be confused with heat, temperature is a measure of how hot or cold something is. It is measured in degrees . The standard metric unit is the degree Celsius (or Centigrade) (°C) and the SI unit is the Kelvin (or absolute) (K). An increase in temperature of X°C is equal to an increase in temperature on XK. Some important temperatures and the interrelationship between C and K is shown below.

To convert Celsius to Kelvin, simply add 273.

Electricity

The standard metric unit and SI unit of electricity is the ampere (A). It measures electric current, and is officially defined as one the current which, if maintained in two straight parallel conductors of infinite length, or negligible cross section and placed one metre apart in a vacuum, would produce a force on each conductor of 2*10^-7 N m^-1 of length.. The coulomb (C) is the standard metric unit of electrical charge, and is equal to the charge any point on a conductor where 1A passes through for 1s. As it happens, 1C is also the charge on 6.25*10¹⁸ electrons. Therefore, an easier to understand method of defining an ampere is simply 1C s^-1.

The standard metric unit of resistance is the ohm (Ω), which is defined as the resistance of a substance which causes 1 watt of energy to be dissipated when 1A passes though it.

Magnetism

The primary measurement of magnetism is the magnetic flux density. The standard metric unit of this is the tesla (T). 1T is defined as the magnetic flux density is a point in a magnetic field where an electric conductor 1m long placed at 90° to the field would experience a force on 1N when carrying 1A.

Interestingly, the unit of magnetic flux is a derivative unit of magnetic flux density, and not the other way around as one might expect. The standard metric unit of magnetic flux is the weber (Wb). If the magnetic flux density over an area of 1m² is 1T, then the flux through that area is 1Wb.

Energy

Energy, defined as the ability to do work, is measured in Joules (J). A Joule is defined as the energy used when a force of 1 newton is moved a distance of 1 metre. Since this is quite small, kilojoules (kJs) are generally used instead. When talking about the energy produced by organisms (i.e. in photosynthesis and respiration), the units used are the calorie (cal) and kilocalorie (kcal). A calorie is defined as the quantity of heat required to make 1g of water increase in temperature by 1C degree at normal air pressure. There are nine forms of energy: potential, kinetic, heat, light, sound, electric, magnetic, chemical, and nuclear.

Work and Power

The technical definition of work is what is done when a force or mass is moved a distance, or what is done when energy is used. The SI unit of work is the Newton-metre (Nm *), and is equal to 1J. Therefore, work may also be measured in Joules and kiloJoules.

Power is the rate of doing work. The SI unit of power is the watt (W), and 1W is defined as 1J per second.

Light and Sound

Frequency is one quantity in the metric system applies to waves. Though it is primarily used for sonic and electromagnetic waves, it may also apply to water waves, or indeed any other wave. The standard metric unit and SI unit of frequency is the wave per second, or Hertz (Hz) . 1Hz means one wave passes a fixed point every second. Other frequently used measurements of frequency are kilohertz (kHz) and megahertz (MHz).

Another unit of light and sound is intensity. This is determined by the amplitude, or height of the crest of the wave. The greater the intensity, the brighter the light or the louder the sound.

The SI unit of sound intensity is the watt per metre squared (W m^-2) and the standard metric unit is the bel (b), though this is technically a measurement of power. The most commonly used unit is the decibel (db), which is officially defined as the unit of power output expressed by the ratio of the amounts of power emitted by two sources and equal to 10 times the common logarithm of the ratio. In simple terms, 1db is the lowest sound a human can hear, and 130db is the loudest.

Radioactivity Decay

The standard metric unit of radioactive decay is the becquerel (Bq). 1Bq is equal to one radioactive atom decaying per second.

Conversions

Metric to Imperial

1 metre = 1.094 yards

1 centimetre = 0.3937 inches

1 kilometre = 0.6214 miles

1m² = 1.962 sq yards

1 ha = 2.471 acres

1 km² = 0.3861 sq miles

1 cm² = 0.155 sq inches

1m³ = 1.308 cubic yards

1cc = 0.06102 cubic inches

1 litre = 1.760 pints

1 kilogramme = 2.205 pounds

1 tonne = 0.9842 tons

0°Celsius = 32°Fahrenheit

100°C = 212°F

-273°C = -491.6°F

Imperial to Metric

1 yard = 0.9144m

1 inch = 2.54cm

1 mile = 1.609 km.

1 sq yard = 0.8361m²
1 acre = 0.4047 ha

1 sq mile = 2.59 km²
1 sq inch = 6.452 cm²

1 cubic yard = 0.7646m²
1 cubic inch = 16.39 cm²
1 pint = 0.5682 l

1 pound = 0.4536kg

1 ton = 1.016 tonnes.