CONDENSED GUIDE TO SI UNITS AND STANDARDS
\n By Drew Daniels<\/p>\n
The following is a highly condensed guide to SI units, standard usage and
\nnumerical notation for the benefit of people who have occasion to write
\nspecifications or technical literature of any kind.
\n The abominable disregard for (literary and verbal) communication
\nstandards even among engineers and highly skilled technicians makes for
\nneedless confusion, ambiguity and duplication of effort.
\n Let’s review the world standard means and methods for expressing the
\nterms we use and use them to codify our jargon and simplify our
\ncommunications.<\/p>\n
SI UNITS, STANDARDS AND NOTATION <\/p>\n
All the way back in 1866, the Metric System of units was legalized by
\nthe U.S. Government for trade in the United States.
\n In 1960 the international “General Conference on Weights and Measures”
\nmet in Paris and named the metric system of units (based on the meter,
\nkilogram, second, ampere, kelvin and candela) the “International System of
\nUnits”. The Conference also established the abbreviation “SI” as the official
\nabbreviation, to be used in all languages.
\n The SI units are used to derive units of measurement for all physical
\nquantities and phenomena. There are only seven basic SI “base units”, these
\nare: <\/p>\n
NAME SYMBOL QUANTITY
\n————————————————-
\nampere A electric current
\ncandela cd luminous intensity
\nmeter m length
\nkelvin K thermodynamic temperature
\nkilogram kg mass
\nmole mol amount of substance
\nsecond s time<\/p>\n
The SI derived units and supplementary units are listed here with applicable
\nderivative equations:<\/p>\n
NAME SYMBOL QUANTITY DERIVED BY
\n——————————————————————
\ncoulomb C quantity of electricity A*s
\nfarad F capacitance A*s\/V
\nhenry H inductance V*s\/A
\nhertz Hz frequency s^-
\njoule J energy or work N*m
\nlumen lm luminous flux cd*sr
\nlux lx illuminance lm\/m^2
\nnewton N force kg*m\/s^2
\nohm (upper case omega) electric resistance V\/A
\npascal Pa pressure N\/m^2
\nradian rad plane angle
\nsteradian sr solid angle
\ntesla T magnetic flux density Wb\/m^2
\nvolt V potential difference W\/A
\nwatt W power J\/s
\nweber Wb magnetic flux V*s<\/p>\n
NAME SYMBOL QUANTITY
\n——————————————————————–
\nampere per meter A\/m magnetic field strength
\ncandela per square meter cd\/m^2 luminance
\njoule per kelvin J\/K entropy
\njoule per kilogram kelvin J\/(kg*K) specific heat capacity
\nkilogram per cubic meter kg\/m^3 mass density (density)
\nmeter per second m\/s speed, velocity
\nmeter per second per second m\/s^2 acceleration
\nsquare meter m^2 area
\ncubic meter m^3 volume
\nsquare meter per second m^2\/s kinematic viscosity
\nnewton-second per square meter N*s\/m^2 dynamic viscosity
\n1 per second s^- radioactivity
\nradian per second rad\/s angular velocity
\nradian per second per second rad\/s^2 angular acceleration
\nvolt per meter V\/m electric field strength
\nwatt per meter kelvin W\/(m*K) thermal conductivity
\nwatt per steradian W\/sr radiant intensity<\/p>\n
DEFINITIONS OF SI UNITS <\/p>\n
(The wording used by the Conference may seem a bit stilted, but it is
\ncarefully chosen for semantic clarity to make the definitions unambiguous.)<\/p>\n
The ampere is that constant current which, if maintained in two straight
\nparallel conductors of infinite length, of negligible circular cross section,
\nand placed 1 meter apart in vacuum, would produce between these conductors a
\nforce equal to 2E-7 newton per meter of length.<\/p>\n
The candela is the luminous intensity, in the perpendicular direction, of a
\nsurface of 1\/600,000 square meter of a blackbody at the temperature of
\nfreezing platinum under a pressure of 101,325 newtons per square meter.<\/p>\n
The coulomb is the quantity of electricity transported in 1 second by the
\ncurrent of 1 ampere.<\/p>\n
The farad is the capacitance of a capacitor between the plates of which
\nthere appears a difference of potential of 1 volt when it is charged by a
\nquantity of electricity equal to 1 coulomb.<\/p>\n
The henry is the inductance of a closed circuit in which an electromotive
\nforce of 1 volt is produced when the electric current in the circuit varies
\nuniformly at a rate of 1 ampere per second.<\/p>\n
The joule is the work done when the point of application of 1 newton is
\ndisplaced a distance of 1 meter in the direction of the force.<\/p>\n
The kelvin , the unit of thermodynamic temperature, is the fraction 1\/273.16
\nof the thermodynamic temperature of the triple point of water.<\/p>\n
The kilogram is the unit of mass; it is equal to the mass of the
\ninternational prototype of the kilogram. (The international prototype of the
\nkilogram is a particular cylinder of platinum-irridium alloy which is
\npreserved in a vault at Sevres, France, by the International Bureau of Weights
\nand Measures.)<\/p>\n
The lumen is the luminous flux emitted in a solid angle of 1 steradian by a
\nuniform point source having an intensity of 1 candela.<\/p>\n
The meter is the length equal to 1,650,763.73 wavelengths in vacuum of the
\nradiation corresponding to the transition between the levels 2p sub 10, and 5d
\nsub 5 of the krypton-86 atom.<\/p>\n
The mole is the amount of substance of a system which contains as many
\nelementary entities as there are carbon atoms in 12 grams of carbon 12. The
\nelementary entities must be specified and may be atoms, molecules, ions,
\nelectrons, other particles or specified groups of such particles.<\/p>\n
The newton is that force which gives to a mass of 1 kilogram an acceleration
\nof 1 meter per second per second.<\/p>\n
The ohm is the electric resistance between two points of a conductor when a
\nconstant difference of potential of 1 volt, applied between these two points,
\nproduces in this conductor a current of 1 ampere, this conductor not being the
\nsource of any electromotive force.<\/p>\n
The radian is the plane angle between two radii of a circle which cut off on
\nthe circumference an arc equal in length to the radius.<\/p>\n
The second is the duration of 9,192,631,770 periods of the radiation
\ncorresponding to the transition between the two hyperfine levels of the ground
\nstate of the cesium-133 atom.<\/p>\n
The steradian is the solid angle which, having its vertex in the center of a
\nsphere, cuts off an area of the surface of the sphere equal to that of a
\nsquare with sides of length equal to the radius of the sphere.<\/p>\n
The volt is the difference of electric potential between two points of a
\nconducting wire carrying a constant current of 1 ampere, when the power
\ndissipated between these points is equal to 1 watt.<\/p>\n
The watt is the power which gives rise to the production of energy at the
\nrate of 1 joule per second.<\/p>\n
The weber is the magnetic flux which, linking a circuit of one turn,
\nproduces in it an electromotive force of 1 volt as it is reduced to zero at a
\nuniform rate in 1 second.<\/p>\n
SI PREFIXES
\n The names of multiples and submultiples of any SI unit are formed by
\napplication of the prefixes:<\/p>\n
MULTIPLIER PREFIX SYMBOL TIMES 1, IS EQUAL TO:
\n———- —— —— ————————–
\n10^18 exa E 1 000 000 000 000 000 000
\n10^15 peta P 1 000 000 000 000 000
\n10^12 tera T 1 000 000 000 000
\n10^9 giga G 1 000 000 000
\n10^6 mega M 1 000 000
\n10^3 kilo k 1 000
\n10^2 hecto h 100
\n10 deka da 10
\n0 — — 1 (unity)
\n10^-1 deci d .1
\n10^-2 centi c .01
\n10^-3 milli m .001
\n10^-6 micro u .000 001
\n10^-9 nano n .000 000 001
\n10^-12 pico p .000 000 000 001
\n10^-15 femto f .000 000 000 000 001
\n10^-18 atto a .000 000 000 000 000 001<\/p>\n
Some examples: ten-thousand grams is written; 10 kg, 20,000 cycles per
\nsecond is written; 20 kHz, 10-million hertz is written; 10 MHz, and 250
\nbillionths of a weber per meter of magnetic flux is written; 250 nWb\/m.
\nAlways use less than 1000 units with an SI prefix; “1000 MGS” is advertizing
\nhyperbole and should be written ” 1 g ” only.
\n SI prefixes and units should be written together and then set off by a
\nspace (single space in print) from their numerators. For example; use the
\nform ” 35 mm ” instead of ” 35mm ” and ” 1 kHz ” instead of ” 1k Hz “.
\n When writing use standard SI formats and be consistent. You should
\nconsult National Bureau of Standards publication 330, (1977) for details on
\nusage.
\n Never combine SI prefixes directly, that is, write 10^-10 farads as 100
\npF instead of 0.1 micro-microfarads (uuF). Keep in mind that whenever you
\nwrite out a unit name longhand, the rule is that the name is all lower case,
\nbut when abbreviating, the first letter is upper case if the unit is named
\nafter a person and lower case if it is not; examples: V = volt for Volta, F =
\nfarad for Faraday, T = tesla for Tesla, and so on. Letter m = meter, s =
\nsecond, rad = radian, and so on. Revolutions per minute may be written only
\nas r\/min, miles per hour may be written only as mi.\/hr, and inches per second
\nmay be written only as in.\/s and so on.<\/p>\n
In addition to the correct upper and lower case, prefixes and
\ncombinations, there is also a conventional text spacing for SI units and
\nabbreviations. Write 20 Hz, rather than 20Hz. Write 20 kHz, rather than
\n20k Hz, and so on. Always separate the numerator of a unit from its prefix
\nand\/or unit name, but do not separate the prefix and name. <\/p>\n
SCIENTIFIC AND ENGINEERING NOTATION
\n(NOTE: “E” stands for power of 10 exponent.)
\n Scientific notation is used to make big and small numbers easy to handle.
\nEngineering notation is similar to scientific notation except that it uses
\nthousands exclusively, rather than tens like scientific notation.<\/p>\n
The number 100 could be written 1E2 (1*10^2) or 10^2 in scientific
\nnotation, but would be written only as 100 in engineering notation. The
\nnumber 12,000 would be written 1.2E4 (1.2*10^4) in scientific, and written
\n12E3 (12*10^3) in engineering notation. Here is a partial listing of possible
\nScientific and Engineering notation prefixes:<\/p>\n
SCIENTIFIC ENGINEERING SCIENTIFIC ENGINEERING
\n———- ———– ———- ———–
\n10^-18 = 1 a 10^1 = 10
\n10^-17 = 10 a 10^2 = 100
\n10^-16 = 100 a 10^3 = 1 k
\n10^-15 = 1 f 10^4 = 10 k
\n10^-14 = 10 f 10^5 = 100 k
\n10^-13 = 100 f 10^6 = 1 M
\n10^-12 = 1 p 10^7 = 10 M
\n10^-11 = 10 p 10^8 = 100 M
\n10^-10 = 100 p 10^9 = 1 G
\n10^-9 = 1 n 10^10 = 10 G
\n10^-8 = 10 n 10^11 = 100 G
\n10^-7 = 100 n 10^12 = 1 T
\n10^-6 = 1 u 10^13 = 10 T
\n10^-5 = 10 u 10^14 = 100 T
\n10^-4 = 100 u 10^15 = 1 P
\n10^-3 = 1 m 10^16 = 10 P
\n10^-2 = 10 m 10^17 = 100 P
\n10^-1 = 100 m 10^18 = 1 E
\n10^0 = 1 10^19 = 10 E
\n 10^20 = 100 E<\/p>\n
Engineering notation is used by default when we speak because the
\nnumerical values of the spoken names of SI prefixes run in increments of
\nthousands such as; kilohertz, microfarads, millihenrys and megaohms
\n(pronounced “megohms”). The spoken term “20 kilohertz” is already in
\nengineering notation, and would be written on paper as 20E3 (20*10^3) hertz in
\nstrict engineering notation and as 2E4 (2*10^4) in scientific notation if it
\nwere not written in the more familiar form, 20 kHz.<\/p>\n
In either case, scientific or engineering, the rule is: for numbers
\ngreater than 1, the En part of the figure indicates the number of decimal
\nplaces to the right that zeros will be added to the original number. For
\nnumbers smaller than 1, the E-n part of the figure indicates the number of
\ndecimal places to the left of the original number that the decimal point
\nitself should be moved. The small “n” and “-n” here stand for the digits in
\nthe exponent itself.<\/p>\n
A definitive phamphlet describing SI units, conversions between SI units,
\nolder CGS and MKS units and units outside the SI system of units is available
\nin the form of NASA Publication SP-7012, (1973). Inquire to the U.S.
\nGovernment Printing Office in Pueblo, Colorado or in Washington, D.C. for this
\nand other publications about SI units, their use and history.<\/p>\n
END<\/p>\n
