Systems of Units

The most widely used system of units and measures around the world is the Systeme International d'Unites (SI), the modern form of the metric system. This originated in France, where in 1790 the French Academy of Science was commissioned to design a new system of units. They decided that

• The units should be based on unvarying quantities in nature
• Multiples of units should be decimal
• The base units should be used to derive other units

These principles allowed the metric system to evolve and SI units have become the fundamental basis of scientific measurement world-wide.

International system of units (SI)

The Système Internationale d'Unitès was adopted in 1960 as the title for an MKSA system based on (meter, kilogram, second, Ampere).

Basic units

 Physical quantity SI unit Unit symbol Length Meter m Mass Kilogram kg Time Second s Electric current Ampere A Degree of temperature Kelvin K Amount of substance Mole mole Light (luminous) intensity Candela cd

Associated with these basic units are a variety of supplementary derived units which are adopted worldwide.

Derived units

 Derived quantity SI unit Unit symbol Area Square meter m2 Volume Cubic meter m3 Velocity Meter per second m/s Acceleration Meter per second squared m/s2 Density Kilogram per cubic meter kg/m3

Derived units with special names and symbol

 Physical quantity SI unit Unit symbol Force, weight newton N = kg m/s2 Work, energy, quantity of heat joule J =N m Power watt W = J/s Pressure, stress pascal Pa = N/m2 Electric charge coulomb C =A s Electrical potential volt V =W/A Electric capacitance farad F =A s/V Electric resistance ohm Ω = V/A Frequency hertz Hz = s-1

In the Système Interntional d’Unitès, SI, a unit is chosen for a particular purpose and larger and smaller are obtained by applying a prefix to this unite and multiplying or dividing by 10 or power of 10.

Larger units, obtained by multiplying by 1000, etc., are called ‘multiples’, smaller units, obtained by multiplying by 0.01, etc., are termed ‘sub-multiples’.

Multiplying factors

 Factor Prefix Symbol 1 000 000 000          [109] giga G 1 000 000                 [106] mega M 1 000                        [103] kilo k 100                           [102] hecto h 10                             [10 ] deca da 0.1                            [10-1] deci d 0.01                          [10-2] centi c 0.001                        [10-3] milli m 0.000001                  [10-6] micro μ

Units outside the SI that are accepted for use with the SI

 Derived quantity Unit symbol Value Minute min 1 min = 60 s Hour h 1 h = 60 min = 3600 s Day day 1 day = 24 h = 86400 s Degree angle o 1o =  (π/180) rad Liter l, (L) 1 L = 1dm3 = 0.001 m3 Metric ton (tonne) t 1 t = 1000 kg

Other units outside the SI that are currently accepted for use with the SI

 Derived quantity Unit symbol Value Nautical mile 1 nautical mile = 1852 m Knot 1 knot = 1.852 km/h Hectare ha 1 ha = 1 hm2 = 104 m2 Bar bar 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa

SI unit rules and style conventions
-
Unit symbols are placed after the numerical value, leaving a space between the value and the symbol. For example 5 V not 5V.

- Only one prefix can be applied to a unit at a time. For example, 1000 kilonewton must not express 1 kilokilonewton but as meganewton; 0.001 millimeter must not be written as 1 millmillmeter but as 1 micrometer.

-The correct use of upper and lower case letters (capital and small letters) is important. For example m- meter, but M- mega; k- kilo, but K- Kelvin.

- Symbols must not made plural by adding ‘s’ since ’s’ is symbol of second.

-When a prefix is attached to a unit there should be no space between the prefix and the unit; for example, mm- millimeter, kW- kilowatt, MN- meganewton.

-When a complex unit is formed by multiplying two units together, however, the symbol should be separated by a space; for example, N m- newton meter (the unit of torque).

- Abbreviations such as sec, cc, or mps are avoided and only standard unit symbols, prefix symbols, unit names, and prefix names are used, (s, cm3, m/s).

- Unit symbols are generally written in lower case letters, except when the name of the unit is derived from a proper name. (Note that when the name of a unit which is derived from a proper name is written out in full, such as ampere or hertz, the name is not capitalized. The only exception to this is Celsius.)

Imperial unit

The Imperial units or the Imperial system is a collection of English units, first defined in the Weights and Measures Act of 1824, later refined (until 1959) and reduced. The units were introduced in the United Kingdom and its colonies, including Commonwealth countries, but excluding the then already independent United States.

Relation to other systems

The distinction between this imperial system and the U.S. customary units (also called standard units there) or older British/English units/systems and newer additions (foot-pound-second systems) is often not drawn precisely. Most length units are shared among the Imperial and U.S. systems, albeit partially and temporally defined slightly differently. Capacity measures differ the most due to the introduction of the Imperial gallon and the unification of wet and dry measures.

The term imperial should not be applied to English units that were outlawed in Weights and Measures Act of 1824 or earlier, or which had fallen out of use by that time, nor to post-imperial inventions such as the slug or poundal.

Although most of the units are defined in more than one system, some subsidiary units were used to a much greater extent, or for different purposes, in one area rather than the other.

Imperial Units of length
1 inch = 25.4 mm
1 foot = 12 inches = 304.8 mm
1 yard = 3 feet = 36 inches = 914.4 mm
1 mile = 8 furlongs = 1760 yards = 5280 feet = 1.609 344 km
1 league = 3 miles = 5280 yards = 15840 feet = 4.828 032 km

Imperial Units of volume

1 fluid ounce (oz) = 0.028 413 062 5 L

1 pint = 20 oz = 0.568261 L

1 quart = 2 pint = 40 oz = 1.136522 L

1 gallon = 4 quart = 8 pints = 4.54609 L

1barrel = 36 gallon = 163.659 24 L

Imperial Units of weight and mass

1 ounce = 1/16 pound = 28.349 523 125 g

1 pound = 7000 grains = 453.592 37 g

1 ton = 20 hundredweight = 2240 pounds = 1016.046 908 8 kg

The USA ton (also known as the "short ton" is 2000 pounds, the UK ton (also known as the "long ton") is 2240 pounds, and the metric ton is 1000 kg.

# United States customary units

The United States customary system (also called American system or, more rarely, "English units") is the most commonly used system of measurement in the United States. It is similar but not identical to the British Imperial units. The U.S. is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities, although the International System of Units (SI, often referred to as "metric") is universally used in science, and increasingly in medicine, government, and many sectors of industry. The vast majority of U.S. customary units have been defined in terms of the meter and the kilogram since the Mendenhall Order of 1893 (and, in practice, for many years before that date). These definitions were refined in 1959.

The U.S. customary units have common roots with the Imperial units which were used in the British Empire. Many U.S. units are virtually identical to their Imperial counterparts, but the U.S. customary system developed from English units in use before the Imperial system was standardized in 1824, and there are several numerical differences from the Imperial system.

Units of volume

1 teaspoon (tsp) = 4.928921 mL

1 tablespoon (Tbsp) 3 tsp =14.78676 mL

1 US fluid ounce (fl oz) 2 Tbsp = 29.57353 mL

1 (liquid) US gallon (gal) = 3.785412 L

Units of temperature
Degrees Fahrenheit are used in the United States to measure temperatures in most non-scientific contexts. The Rankine scale of absolute temperature also saw some use in thermodynamics.

1 F = 9/5 C + 32