# Metric system

The metric system is a decimal system of measurement that was developed in France in the late 18th century. The metric system was refined over the course of history into the International System of Units (SI), the most widely used measurement system in the world today.

## What is the metric system

The metric system is a measurement system that was developed with the goal of standardizing units of measurement in such a way that the system would be adopted universally.

### Who uses the metric system

Most of the world has fully adopted the International System of Units (SI), the modern form of the metric system. Three notable exceptions include the United States, Myanmar, and Liberia. Although these countries have not officially adopted SI, they still use the systems in many areas such as science, industry, and other contexts in which standardization is important.

### Properties of the metric system

The metric system is characterized by the following:

- Base units - The modern form of the metric system, SI, has 7 base units. Each base unit represents some physical quantity (e.g. length, time, mass, temperature) such that no quantity can be expressed in terms of another. For example, we cannot express time in terms of length; there is no way to express a meter in terms of time. Thus, a base unit represents a base quantity, and other quantities within the metric system are expressed in terms of multiples or submultiples of the corresponding base unit.
- Decimal ratios - The metric system is based on multiples of 10. For example, the meter is the base unit of length in the metric system. Other metric units of length are related to the meter by powers of 10. The centimeter is a unit of length smaller than the meter and it is related to the meter by a factor of 1/100. A kilometer is a larger unit of length than the meter and is related by a factor of 1000. In other words, 1 centimeter = 0.01 meters and 1 kilometer = 1,000 meters.
- Derived units - A derived unit is a unit that expresses any other physical quantity that is not a base unit. Derived units are expressed in terms of a product of powers of base units. For example, speed is a derived unit that is expressed in terms of length and time. Specifically, speed has the derived unit meters per second.
- Prefixes for multiples and submultiples - In the metric system, decimal-based prefixes are used to indicate multiplication or division of a base unit by the corresponding power of 10. For example, the prefix "kilo-" indicates multiplication by 1,000 while the prefix "centi-" indicates division by 100. A kilometer is a multiple of a meter while a centigram is a submultiple of a kilogram.
- Coherence - Derived units are directly related to base units without a need for intermediate conversion factors.

These properties make the metric system easy to use and widely applicable, which is why the International System of Units has been adopted by the vast majority of the world.

## Base unit

There are 7 base units in the International System of Units, the modern form of the metric system: meter, kilogram, kelvin, second, ampere, candela, and mole. The following table shows the base units, the physical quantities they measure, and the symbol used to denote each base unit.

Base unit | Physical quantity | Symbol |
---|---|---|

meter | length | m |

kilogram | mass | kg |

kelvin | temperature | K |

second | time | s |

ampere | current | A |

candela | luminous intensity | cd |

mole | amount of substance | mol |

### SI base unit definitions

The modern definitions of the base units are shown below. Note that the definitions are complex and are shown here just for reference.

- meter - the length traveled by light in a vacuum in of a second.
- kilogram - the fixed numerical value of the Planck constant h (6.62607015 × 10
^{-34}) when expressed in units of J·s, which is equal to kg·m^{2}·s^{-1}. - kelvin - the fixed numerical value of the Boltzmann constant k (1.380649 × 10
^{-23}) when expressed in units of J·K^{-1}, which is equal to kg·m^{2}·s^{-2}K^{-1}. - second - the fixed numerical value of the caesium frequency ΔV
_{cs}, 9,192,631,770 when expressed in units of Hz, which is equal to s^{-1}. - ampere - the fixed numerical value of the elementary charge (1.602176634 × 10
^{-19}) when expressed in coulombs, which is equal to A·s. - candela - the candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation 540 × 10
^{12}Hz, K_{cd}, to be 683 when expressed in units of lm·W^{-1}, which is equal to cd·sr·W^{-1}or cd·sr·kg^{-1}·m^{-2}·s^{3}. - mole - the fixed numerical value of the Avogadro Constant (6.02214076 × 10
^{23}) when expressed in units of mol^{-1}.

## Metric prefix

A metric prefix is a prefix (e.g. milli-, centi-) that denotes a decimal multiple or submultiple of the base unit it precedes. The prefix indicates the power of 10 by which the base unit is multiplied or divided. For example, the prefix centi- indicates division by 10^{2}, or 100. Its counterpart, "hecto-", indicates multiplication by 100. Thus, a centimeter is 1/100th of a meter, while a hectometer is 100 times larger than 1 meter. When the metric system was first developed in 1795, there were 8 prefixes. More prefixes were added over the years up through 2022, when 4 more were added making 24 the total number of SI prefixes 24. These prefixes are shown in the table below.

SI Prefixes table | |||
---|---|---|---|

Prefix | Symbol | Factor | Factor name |

quetta | Q | 10^{30} |
nonillion |

ronna | R | 10^{27} |
octillion |

yotta | Y | 10^{24} |
septillion |

zetta | Z | 10^{21} |
sextillion |

exa | E | 10^{18} |
quintillion |

peta | P | 10^{15} |
quadrillion |

tera | T | 10^{12} |
trillion |

giga | G | 10^{9} |
billion |

mega | M | 10^{6} |
million |

kilo | k | 10^{3} |
thousand |

hecto | h | 10^{2} |
hundred |

deka | da | 10^{1} |
ten |

10^{0} |
one | ||

deci | d | 10^{-1} |
tenth |

centi | c | 10^{-2} |
hundredth |

milli | m | 10^{-3} |
thousandth |

micro | μ | 10^{-6} |
millionth |

nano | n | 10^{-9} |
billionth |

pico | p | 10^{-12} |
trillionth |

femto | f | 10^{-15} |
quadrillionth |

atto | a | 10^{-18} |
quintillionth |

zepto | z | 10^{-21} |
sextillionth |

yocto | y | 10^{-24} |
septillionth |

ronto | r | 10^{-27} |
octillionth |

quecto | q | 10^{-30} |
nonillionth |

## Derived units and non-SI units

The table below shows some commonly used SI derived units and non-SI units that are accepted for use within SI. There are many, not all of which are included here.

Name | Symbol | Quantity |
---|---|---|

hertz | Hz | frequency |

radian | rad | angle |

newton | N | force, weight |

pascal | Pa | pressure, stress |

joule | J | energy, work, heat |

watt | W | power, radiant flux |

coulomb | C | electric charge, quantity of electricity |

volt | V | voltage, electrical potential difference, electromotive force |

ohm | Ω | electrical resistance |

degree Celsius | °C | temperature |

lumen | lm | luminous flux |

## History of the metric system

The development of the metric system is widely credited to the French. In 1670, Gabriel Mouton proposed a decimal system of measurement that the French further developed over the course of over a century. In 1790, the national assembly of France called for a system that used a unit of length based on the circumference of the Earth as its basis. This unit became known as the meter, and the standard that it represented was designed to be equal to a fraction of the distance from the North Pole to the equator. The system was also a decimal-based system in which larger and smaller units were arrived at by multiplying or dividing by powers of 10. This was the earliest form of the metric system, and many different versions were developed over the course of history before arriving at the International System of Units (SI), the current global standard. Below is a timeline of some of the milestones in the development of the metric system in use today.

- 1832 - Gauss uses the astronomical second as the base unit in defining the gravitation of the earth. Along with the millimeter and milligram, this was the first system of mechanical units.
- 1860s - The centimetre-gram-second system of units (CGS) was developed and formally promoted by the British Association for Advancement of Science. This was the first coherent metric system. It was characterized by the expression of density in g/cm
^{3}, force in dynes, mechanical energy in ergs, and thermal energy in calories. - 1893 - The 1893 International Electrical Congress defines the international ampere and ohm with definitions based on the metre, kilogram, and second.
- 1901 - Giovanni Giorgi shows that the addition of a fourth base unit, one for electrical charge, resolves the anomalies in various electromagnetic systems. Metric systems such as the metre-kilogram-second-coulomb and metre-kilogram-second-ampere systems were then developed.
- 1960 - The General Conference on Weights and Measures (CGPM) promulgates the International System of Units (SI). SI is based on the metre-kilogram-second-ampere system with the addition of numerous coherent derived units such as watts, lumens, and joules and the addition of three more base units, the kelvin, candela, and mole.

## Metric system vs imperial

The imperial system is a system that was first defined in 1824 in the British Weights and Measures Act 1824. It was further developed over time and is the system from which the US customary system of units is derived. It was predominantly used in the United Kingdom and other Commonwealth countries, but has mostly been replaced by SI. The US customary system is the system still primarily used in day-to-day life in the US, though SI is also used in many contexts.

### Main differences between the metric and imperial systems

Below are some of the key differences between the metric and imperial systems of measurement.

- The metric system is based around the meter. The imperial system (and US customary system) are not based around a specific unit, though its units are exactly defined in relation to metric units.
- Metric units can be easily converted with an understanding of SI prefixes since units are simply multiples or submultiples of a base unit and can be arrived at by multiplying or dividing by the appropriate power of 10. On the other hand, imperial units have no pattern of conversion, and it is necessary to know the appropriate conversion factors to convert between units, even if they measure the same quantity.
- The imperial and US customary systems are not coherent systems of measurement, while SI is since the derived units of the metric system can be directly related to its base units without the need for intermediate conversion factors; this is not true of either the US customary or imperial systems.

### Why doesn't the US use the metric system

The reason that the US has not fully adopted the metric system is because at the time of the development of the US customary system, the metric system was not as widespread as it is today. Since all industries in the US were set up using the US customary system, overhauling its entire infrastructure would be extremely costly and time consuming. Since the US already uses the metric system in areas such as science, the military, and most any context in which standardization is important, at this point it is unlikely that it will overhaul its current infrastructure without a major impetus.

### Metric vs imperial units

The table below provides some comparisons between units used in the metric and US customary systems of measurement.

Measurement | Metric units | US customary units |
---|---|---|

Length | centimeter, meter, kilometer | inch, foot, yard, mile |

Mass/weight | gram, kilogram | ounce, pound, ton |

Volume | liter, cubic centimeter | cup, pint, quart, gallon |

## Metric conversions

Since most countries around the world use the metric system, it is useful to be able to convert between common metric units and US customary or imperial units.

### Metric conversions of length

The following are some conversions from meters to measurements of length in the US customary system of measurement.

1 meter | = 39.3701 inches |

= 3.28084 feet | |

= 1.09361 yards | |

= 0.00062136931818182 miles |

### Metric conversions of mass

The following are some conversions from kilograms to measurements of mass in the US customary system of measurement.

1 kilogram | = 35.274 ounces |

= 2.20462 pounds | |

= 0.001 metric tons |

### Metric conversions of volume

The following are some conversions from cubic meters to other commonly used measurements of volume. Some measures are units accepted for use within SI while others are US customary units of volume.

1 cubic meter | = 264.172 gallons |

= 1056.69 quarts | |

= 33,814 fluid ounces | |

= 1,000 liters (metric unit) | |

= 10,000 milliliters (metric unit) |

### Metric conversions of area

The following are some conversions from square meters to US customary units of area.

1 square meter | = 1550 square inches |

= 10.7639 square feet | |

= 1.19599 square yards | |

= 0.0000003861 square miles | |

= 0.000247105 acres |