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UNIT CONVERSIONS |
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UNIT CONVERSIONS |
Unit systems are built upon the necessity to describe seven fundamental quantities. These quantities are described using base units, units that do not depend on other units for their definition. These base units are combined to form complex or derived units to describe additional phenomena. For example, one unit for speed in the U.S. customary system is feet per second. This is a derived from the fundamental definitions of length and time. In the U.S. customary unit system, the fundamental unit of length is the foot and the fundamental unit of time is the second. The seven fundamental quantities, their unit and their derivation are described below.
The U.S. customary system is what is used primarily in the United States and [very] few other countries today. Since this system is derived from Celtic, Roman, Saxon, and Norse cultures, it is a system full of flaws, contradictions and ambiguities. It is these problems that forced the development of the different metric systems, with the current S.I. system being the 'official' system. What many persons do not know is that much of the U.S. Customary system has legal definitions rooted in the metric system. However, the derivations of the original units is quite fascinating.
| Quantity | Unit | NIST Definition |
| Mass | Pound Mass | pound–mass equals exactly 0.45359237 kilograms. Do not confuse this with pound–force! |
| Length | Foot | The foot is defined as exactly 1/3 of a yard, which in turn is exactly 0.9144 meter. |
| Time | Second | See S.I. table below. |
| Temperature | Rankine | Kelvins multiplied by 1.8. This unit has been virtually abandoned in favor of measuring absolute temperatures in Kelvins. See the S.I. table below. |
| Current | Ampere | See S.I. table below. |
| Luminous Intensity | Lumen | 1 candela steradian.* :See the S.I. table below. |
| Substance | Mole | See S.I. table below. |
The cgs system is a small–unit metric system. It was formally introduced in 1874 in an effort to standardize units across national boundaries and to eliminate the confusion generated by what we now call the U.S. customary system of units. At that time, the same unit had different definitions from region to region. This new system, the cgs system, was well accepted by laboratory research scientists who needed a standard system to measure small quantities. Although considered a subset of the S.I. system of units, it has since been supplanted by the S.I. system. Many of the cgs units are no longer accepted by the S.I. standard.
| Quantity | Unit | Standard |
| Length | Centimeter | Refer to the S.I. table below for appropriate
Standards. It should be noted the original cgs system only included units for Length, Mass and Time. There actually exists several 'unofficial' cgs systems, usually based on how electrical units are defined. Notice the cgs system has units for charge, not current. Shown in the table is the unit of Coulomb to indicate charge. The Coulomb is also defined as an Ampere–second. Refer to the definition of an Ampere in the S.I. table below. In fundamental cgs units, the coulomb is also equal to 3.3356 x 10−10cm3/2g1/2s−1. However, the unit of Franklin is an electrostatic charge unit which can be expressed fundamentally as a cm3/2g1/2s−1. When the unit of Franklin, more commonly referred to as an esu, is used to express the quantity of charge, the system is electrostatic cgs system. However, there also exists a magnetic charge unit defined in fundamental cgs units as a cm1/2 g1/2. When this unit is used to express charge, it is referred to as the electromagnetic cgs system. Note the difference in fundamental units as well as magnitude (in the case of esu vs coulomb) between the charge units of esu, emu and coulomb. Units of current, luminosity and substance are not part of the original cgs system. Even the units for temperature were added after the cgs system was abandoned in favor of the S.I. system. |
| Mass | Gram | |
| Time | Second | |
| Temperature | Kelvins | |
| Charge | Coulomb | |
| Luminous Intensity | Candela | |
| Substance | Mole |
Also known as the metric system, it was introduced in 1889. It was generated for use in commerce, thus was comprised of units describing larger quantities. It was favored in commerce, engineering, and other areas where a more practical system of units was required. The metric system is considered a subset of the S.I. system of units. Howver, the metric system has since been abandoned in favor of the S.I. system of units. Although the metric system has been supplanted by the S.I. system of units, the S.I. system is largely based on the metric system.
| Quantity | Unit | Standard |
| Mass | Kilogram | Refer to the S.I. table below for appropriate
Standards. The mks system does not suffer from the ambiguities of the cgs system related to electrical units. In fact, it is the base upon which an electrical unit was proposed to form, at that time, a four–unit system. The proposal included using either ohm, ampere or volt, and rewriting the equations for electromagnetism. Eventually, the unit of Ampere was selected as the base unit to describe current and the system was renamed the S.I. system. Units of current, luminosity and substance are not part of the original mks system. Even the units for temperature were added after the mks system was abandoned in favor of the S.I. system. |
| Length | Meter | |
| Time | Second | |
| Temperature | Kelvins | |
| Current | Ampere | |
| Luminous Intensity | Candela | |
| Substance | Mole |
Often referred to as the 'Metric System', it is properly named the S.I. system of units. In 1950, there was discomfort amongst users of the cgs and mks (metric) systems and the need to convert between the systems. This was specially true with the derived units used in each of the systems. This necessity to convert went against the ideal of the metric system in general. Thus were the beginnings of the S.I. system. The S.I system of units is a superset of units of which the metric and cgs systems are a member. However, the S.I. system of units has supplanted both the cgs and the metric systems. The SI system of units is largely based on mks definitions for base units, which is probably why it is still referred to as the 'Metric System'. Many of the cgs units are no longer officially recognized as S.I. units. Although the first steps toward the development and adoption of the present S.I. system began in 1799, a key agreement toward the development of this system is 'The Treaty of the Meter'. This agreement was signed in 1875. It should be noted the United States is a charter member having signed the treaty at that time. Forty eight countries have since signed the treaty. The current S.I. system was actually adopted as such in 1960 and continues to evolve even today.
| Quantity | Unit | Standard |
| Mass | Kilogram | The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. The prototype is a platinum–Iridium mass developed in 1889 and maintained by the International Bureau of Weights and Measures under a set of specified conditions. (History) |
| Length | Meter | The meter is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. (History) |
| Time | Second | The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Although accepted for use in and defined by the SI, the second is not an SI unit. (History) |
| Temperature | Kelvins | The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. To properly use this unit, one expresses temperature in Kelvins, not in degrees Kelvin. It is also improper to use the degree symbol when abbreviating the unit. (ie: 300 K, not 300 oK or 300o K. (History) |
| Current | Ampere | The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross–section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10−7 newton per meter of length. (History) |
| Luminous Intensity | Candela | The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian*. (History) |
| Substance | Mole | 1. The mole is the amount of substance of
a system which contains as many elementary
entities as there are atoms in 0.012 kilogram
of carbon 12; its symbol is "mol." 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. (History) |
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* A steradian is a unit of solid angle measurement. It is the solid angle, 'q', with its origin at the center of a sphere such that when it is projected to the surface of the sphere, the subtended portion of the sphere has area r2, where r is the radius of the sphere. |
The SI system approves use of the following 22 derived units
Additional units may be added to this list in the future. For example, the katal was added as a recognized S.I. derived unit in 1999.
The SI permits the use of certain additional units, including:
The SI accepts the use of certain other metric and non–metric units. The continued use of these units is based upon traditional and are required to be defined in relation to accepted SI units. However, their use is discouraged. It is possible for these units to be excluded from the SI system in the future.
As of April 2003
