Common Unit Systems

International System of Units

The International System of Units (SI) is the modern form of the metric system and is composed of seven base units that our society and its profession deem most important. By defining a set of base units, all other units of measurement can be derived, known as derived units. The SI is an evolving system; in 2019, the SI was redefined in terms of fundamental physical constants, rather than artifact standards, making it more accurate and universal.

SI base units

• ampere (symbol: A) – unit of electric current
• kelvin (symbol: K) – unit of temperature
• second (symbol: s) – unit of time
• metre (symbol: m) – unit of length
• kilogram (symbol: kg) – unit of mass
• candela (symbol: cd) – unit of luminous intensity
• mole (symbol: mol) – unit reflecting amount of a substance

Metric prefixes

SI derived units

In addition, SI also includes 22 units of measurement that are derived from the 7 SI base units. These units are either dimensionless or are expressed as a product of one or more of the base units. Some examples of these include:

• radian (symbol: rad) – unit of angle
• newton (symbol: N) – unit of force and weight
• watt (symbol: W) – unit of power
• volt (symbol: V) – unit of voltage, electrical potential difference, and electromotive force
• degree Celsius (symbol: °C) – unit of temperature

Non-SI units accepted for use with SI

There are also some units that are accepted for use with SI that are not considered SI units in the derived units. Some of the more commonly used include:

• minute (min), hour (h), day (d) – units of time
• degree (°), minute (′), second (″) – units of angle
• hectare (ha) – unit of area
• litre (symbol: l or L) – unit of volume
• bar (symbol: bar) – unit of pressure
• tonne (symbol: t) – unit of mass

History of SI

The International System of Units (SI) is the most widely used unit system in the world. It has its roots in the meter-kilogram-second system which was developed over time with contributions from many international bodies and standards organizations.

• 1795 – The metric system was officially adopted by the French government following the French Revolution, standardizing measurements across France.
• 1832 – Carl Friedrich Gauss proposed using the metric system as the basis for a coherent system of units in physics.
• 1862 – The British Association for the Advancement of Science (BAAS) began promoting the adoption of a coherent system of units based on the metric system.
• 1875 – The Metre Convention (Treaty of the Metre) was signed by 17 nations, establishing the General Conference on Weights and Measures (CGPM) to oversee the metric system.
• 1889 – The International Prototype of the Kilogram and the International Prototype of the Metre were sanctioned for use.
• 1901 – Giovanni Giorgi proposed a four-dimensional system based on the metre, kilogram, second, and one electrical unit.
• 1948 – The CGPM instructed the International Committee for Weights and Measures (CIPM) to conduct a study of measurement needs.
• 1954 – Six base units were chosen: metre, kilogram, second, ampere, kelvin, and candela.
• 1960 – The 11th CGPM formally adopted the name "International System of Units" (SI).
• 1971 – The mole was added as the seventh base unit.
• 2019 – The SI was redefined based on fixed numerical values of fundamental constants.

United States Customary Units

United States customary units (USC) are a system of measurements commonly used in the United States. The U.S. is one of the few countries that still primarily uses this system rather than the metric system for everyday measurements. USC developed from English units which were in use in the British Empire before the U.S. became an independent country.

History

• 1832 – The U.S. Treasury Department created standards for measurement based on the customary system.
• 1866 – An act of Congress made it lawful to use the metric system in the United States, but it was not mandatory.
• 1893 – The Mendenhall Order officially defined U.S. customary units in terms of metric units.
• 1959 – The international yard and pound agreement of 1959 further refined the relationship between U.S. customary and metric units.
• 1975 – The Metric Conversion Act of 1975 was passed, making the metric system "the preferred system of weights and measures for U.S. trade and commerce."

Common US customary units

Below are some US customary units that are in everyday use, along with their SI equivalents where noted.

Units of length

• inch (symbol: in) = 0.0254 meters
• foot (symbol: ft) = 0.3048 meters
• yard (symbol: yd) = 0.9144 meters
• mile (symbol: mi) = 1,609.344 meters
• nautical mile = 1,852 meters

Units of area

• acre = 4,046.8564224 square meters
• square foot (ft²) = 0.09290304 square meters
• square mile (mi²) = 2,589,988.110336 square meters

Units of volume

USC uses many different measurements of volume. It uses some general units of measurement such as the cubic inch, cubic foot, and cubic yard, but also uses some more specific units. Note that US customary volume units differ from Imperial volume units.

• cubic inch (in³) = 0.000016387064 meters³
• cubic foot (ft³) = 0.028316846592 meters³
• cubic yard (yd³) = 0.764554857984 meters³
• US fluid ounce (fl oz) = 29.5735295625 millilitres
• US cup = 236.5882365 millilitres
• US pint (pt) = 473.176473 millilitres
• US quart (qt) = 946.352946 millilitres
• US gallon (gal) = 3,785.411784 millilitres

Approximate volume equivalents

• 1 teaspoon (symbol: tsp) = 4.929 millilitres
• 1 tablespoon (symbol: tbsp) = 14.787 millilitres
• 1 fluid ounce (symbol: fl oz) = 29.574 millilitres
• 1 cup (symbol: cp) = 236.588 millilitres
• 1 pint (symbol: pt) = 473.176 millilitres
• 1 quart (symbol: qt) = 946.353 millilitres
• 1 gallon (symbol: gal) = 3,785.41 millilitres

Approximate dry volume

• 1 dry pint (symbol: pt) = 550.610 millilitres
• 1 dry quart (symbol: qt) = 1,101.221 millilitres
• 1 peck = 8,809.768 millilitres
• 1 bushel = 35,239.070 millilitres

Units of weight and mass

The most commonly used system of mass in the United States is avoirdupois weight, which is used for most applications. The international avoirdupois pound, which was defined in 1959 as exactly 453.59237 grams, is the basis for the US system. This pound is sometimes used in body weight, along with the associated ounce.

• grain (symbol: gr) = 64.79891 milligrams
• dram (symbol: dr) = 1.771845195 grams
• ounce (symbol: oz) = 28.349523125 grams
• pound (symbol: lb) = 453.59237 grams
• hundredweight (short) = 45.359237 kilograms
• ton (short) (symbol: t) = 907.18474 kilograms

Units of temperature

The Fahrenheit scale is still commonly used to measure temperature for everyday purposes. Like most of the rest of the world, however, USC uses degrees Celsius and kelvins for scientific applications.

Imperial System

The Imperial system of measurements, also known as British Imperial, was defined in 1824, replacing the previous English units known as the Winchester Standards, which had been in use since 1588. The Imperial system was the primary measurement system used in Great Britain and the countries of the former British Empire (the British Commonwealth). The Imperial system is also still in use in Canada as well as other countries that were previously under the rule of the British Empire.

History

• 1824 – The Weights and Measures Act was passed by the British Parliament, creating a single unified system of British Imperial measurements.
• 1864 – Adoption of the Imperial system as part of the Weights and Measures Act throughout the British Empire, making it mandatory.
• 1897 – Certain industries and government agencies enforced its use in the United Kingdom and its colonies.
• 1965 – The UK officially began a policy to support metrication. Specifically, the policy was intended to support voluntary metrication with some government promotion.
• 1969 – The Metrication Board was founded to promote and coordinate metrication.
• 1978 – The government began mandating metrication in certain sectors.
• 1980 – The Metrication Board was abolished.
• 1985 – Government policy shifted again back to preference for voluntary metrication.
• 1995 – UK completed its official partial transition to the metric system. This does not apply to road signs, beer, cider, and bottled milk, all of which still use Imperial measurements.

Below are some of the various units of the Imperial system, and their approximate metric equivalents. Many of these are similar to units in the US customary system.

Units of length

• inch (symbol: in) = 0.0254 meters
• foot (symbol: ft) = 0.3048 meters
• yard (symbol: yd) = 0.9144 meters
• chain (symbol: ch) = 20.1168 meters
• furlong = 201.168 meters
• mile (symbol: mi) = 1,609.344 meters
• league (symbol: lea) = 4,828.032 meters
• nautical mile = 1,852 meters

Units of area

• perch = 25.292 square meters
• rood = 1,011.714 square meters
• acre = 4,046.856 square meters

Units of volume

While these units have the same names as US customary units, their values are different (except for some, which are the same).

• fluid ounce (symbol: fl oz) = 28.413 millilitres
• gill (symbol: gi) = 142.065 millilitres
• pint (symbol: pt) = 568.261 millilitres
• quart (symbol: qt) = 1,136.523 millilitres
• gallon (symbol: gal) = 4,546.09 millilitres

Units of weight and mass

The Imperial and US customary units of weight are nearly identical, with the exception of the ton. The Imperial ton (2,240 pounds), commonly referred to as the long ton in the US, is much heavier than the US short ton (2,000 pounds).

• grain (symbol: gr) = 64.799 milligrams
• drachm (symbol: dr) = 1.772 grams
• ounce (symbol: oz) = 28.350 grams
• pound (symbol: lb) = 453.592 grams
• stone (symbol: st) = 6.350 kilograms
• quarter = 12.701 kilograms
• hundredweight (symbol: cwt) = 50.802 kilograms
• ton (long) = 1,016.047 kilograms