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CONDENSED GUIDE TO SI UNITS AND STANDARDS
By Drew Daniels
The following is a highly condensed guide to SI units, standard usage and
numerical notation for the benefit of people who have occasion to write
specifications or technical literature of any kind.
The abominable disregard for (literary and verbal) communication
standards even among engineers and highly skilled technicians makes for
needless confusion, ambiguity and duplication of effort.
Let's review the world standard means and methods for expressing the
terms we use and use them to codify our jargon and simplify our
communications.
SI UNITS, STANDARDS AND NOTATION
All the way back in 1866, the Metric System of units was legalized by
the U.S. Government for trade in the United States.
In 1960 the international "General Conference on Weights and Measures"
met in Paris and named the metric system of units (based on the meter,
kilogram, second, ampere, kelvin and candela) the "International System of
Units". The Conference also established the abbreviation "SI" as the official
abbreviation, to be used in all languages.
The SI units are used to derive units of measurement for all physical
quantities and phenomena. There are only seven basic SI "base units", these
are:
NAME SYMBOL QUANTITY
-------------------------------------------------
ampere A electric current
candela cd luminous intensity
meter m length
kelvin K thermodynamic temperature
kilogram kg mass
mole mol amount of substance
second s time
The SI derived units and supplementary units are listed here with applicable
derivative equations:
NAME SYMBOL QUANTITY DERIVED BY
------------------------------------------------------------------
coulomb C quantity of electricity A*s
farad F capacitance A*s/V
henry H inductance V*s/A
hertz Hz frequency s^-
joule J energy or work N*m
lumen lm luminous flux cd*sr
lux lx illuminance lm/m^2
newton N force kg*m/s^2
ohm (upper case omega) electric resistance V/A
pascal Pa pressure N/m^2
radian rad plane angle
steradian sr solid angle
tesla T magnetic flux density Wb/m^2
volt V potential difference W/A
watt W power J/s
weber Wb magnetic flux V*s
NAME SYMBOL QUANTITY
--------------------------------------------------------------------
ampere per meter A/m magnetic field strength
candela per square meter cd/m^2 luminance
joule per kelvin J/K entropy
joule per kilogram kelvin J/(kg*K) specific heat capacity
kilogram per cubic meter kg/m^3 mass density (density)
meter per second m/s speed, velocity
meter per second per second m/s^2 acceleration
square meter m^2 area
cubic meter m^3 volume
square meter per second m^2/s kinematic viscosity
newton-second per square meter N*s/m^2 dynamic viscosity
1 per second s^- radioactivity
radian per second rad/s angular velocity
radian per second per second rad/s^2 angular acceleration
volt per meter V/m electric field strength
watt per meter kelvin W/(m*K) thermal conductivity
watt per steradian W/sr radiant intensity
DEFINITIONS OF SI UNITS
(The wording used by the Conference may seem a bit stilted, but it is
carefully chosen for semantic clarity to make the definitions unambiguous.)
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 2E-7 newton per meter of length.
The candela is the luminous intensity, in the perpendicular direction, of a
surface of 1/600,000 square meter of a blackbody at the temperature of
freezing platinum under a pressure of 101,325 newtons per square meter.
The coulomb is the quantity of electricity transported in 1 second by the
current of 1 ampere.
The farad is the capacitance of a capacitor between the plates of which
there appears a difference of potential of 1 volt when it is charged by a
quantity of electricity equal to 1 coulomb.
The henry is the inductance of a closed circuit in which an electromotive
force of 1 volt is produced when the electric current in the circuit varies
uniformly at a rate of 1 ampere per second.
The joule is the work done when the point of application of 1 newton is
displaced a distance of 1 meter in the direction of the force.
The kelvin , the unit of thermodynamic temperature, is the fraction 1/273.16
of the thermodynamic temperature of the triple point of water.
The kilogram is the unit of mass; it is equal to the mass of the
international prototype of the kilogram. (The international prototype of the
kilogram is a particular cylinder of platinum-irridium alloy which is
preserved in a vault at Sevres, France, by the International Bureau of Weights
and Measures.)
The lumen is the luminous flux emitted in a solid angle of 1 steradian by a
uniform point source having an intensity of 1 candela.
The meter is the length equal to 1,650,763.73 wavelengths in vacuum of the
radiation corresponding to the transition between the levels 2p sub 10, and 5d
sub 5 of the krypton-86 atom.
The mole is the amount of substance of a system which contains as many
elementary entities as there are carbon atoms in 12 grams of carbon 12. The
elementary entities must be specified and may be atoms, molecules, ions,
electrons, other particles or specified groups of such particles.
The newton is that force which gives to a mass of 1 kilogram an acceleration
of 1 meter per second per second.
The ohm is the electric resistance between two points of a conductor when a
constant difference of potential of 1 volt, applied between these two points,
produces in this conductor a current of 1 ampere, this conductor not being the
source of any electromotive force.
The radian is the plane angle between two radii of a circle which cut off on
the circumference an arc equal in length to the radius.
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.
The steradian is the solid angle which, having its vertex in the center of a
sphere, cuts off an area of the surface of the sphere equal to that of a
square with sides of length equal to the radius of the sphere.
The volt is the difference of electric potential between two points of a
conducting wire carrying a constant current of 1 ampere, when the power
dissipated between these points is equal to 1 watt.
The watt is the power which gives rise to the production of energy at the
rate of 1 joule per second.
The weber is the magnetic flux which, linking a circuit of one turn,
produces in it an electromotive force of 1 volt as it is reduced to zero at a
uniform rate in 1 second.
SI PREFIXES
The names of multiples and submultiples of any SI unit are formed by
application of the prefixes:
MULTIPLIER PREFIX SYMBOL TIMES 1, IS EQUAL TO:
---------- ------ ------ --------------------------
10^18 exa E 1 000 000 000 000 000 000
10^15 peta P 1 000 000 000 000 000
10^12 tera T 1 000 000 000 000
10^9 giga G 1 000 000 000
10^6 mega M 1 000 000
10^3 kilo k 1 000
10^2 hecto h 100
10 deka da 10
0 -- -- 1 (unity)
10^-1 deci d .1
10^-2 centi c .01
10^-3 milli m .001
10^-6 micro u .000 001
10^-9 nano n .000 000 001
10^-12 pico p .000 000 000 001
10^-15 femto f .000 000 000 000 001
10^-18 atto a .000 000 000 000 000 001
Some examples: ten-thousand grams is written; 10 kg, 20,000 cycles per
second is written; 20 kHz, 10-million hertz is written; 10 MHz, and 250
billionths of a weber per meter of magnetic flux is written; 250 nWb/m.
Always use less than 1000 units with an SI prefix; "1000 MGS" is advertizing
hyperbole and should be written " 1 g " only.
SI prefixes and units should be written together and then set off by a
space (single space in print) from their numerators. For example; use the
form " 35 mm " instead of " 35mm " and " 1 kHz " instead of " 1k Hz ".
When writing use standard SI formats and be consistent. You should
consult National Bureau of Standards publication 330, (1977) for details on
usage.
Never combine SI prefixes directly, that is, write 10^-10 farads as 100
pF instead of 0.1 micro-microfarads (uuF). Keep in mind that whenever you
write out a unit name longhand, the rule is that the name is all lower case,
but when abbreviating, the first letter is upper case if the unit is named
after a person and lower case if it is not; examples: V = volt for Volta, F =
farad for Faraday, T = tesla for Tesla, and so on. Letter m = meter, s =
second, rad = radian, and so on. Revolutions per minute may be written only
as r/min, miles per hour may be written only as mi./hr, and inches per second
may be written only as in./s and so on.
In addition to the correct upper and lower case, prefixes and
combinations, there is also a conventional text spacing for SI units and
abbreviations. Write 20 Hz, rather than 20Hz. Write 20 kHz, rather than
20k Hz, and so on. Always separate the numerator of a unit from its prefix
and/or unit name, but do not separate the prefix and name.
SCIENTIFIC AND ENGINEERING NOTATION
(NOTE: "E" stands for power of 10 exponent.)
Scientific notation is used to make big and small numbers easy to handle.
Engineering notation is similar to scientific notation except that it uses
thousands exclusively, rather than tens like scientific notation.
The number 100 could be written 1E2 (1*10^2) or 10^2 in scientific
notation, but would be written only as 100 in engineering notation. The
number 12,000 would be written 1.2E4 (1.2*10^4) in scientific, and written
12E3 (12*10^3) in engineering notation. Here is a partial listing of possible
Scientific and Engineering notation prefixes:
SCIENTIFIC ENGINEERING SCIENTIFIC ENGINEERING
---------- ----------- ---------- -----------
10^-18 = 1 a 10^1 = 10
10^-17 = 10 a 10^2 = 100
10^-16 = 100 a 10^3 = 1 k
10^-15 = 1 f 10^4 = 10 k
10^-14 = 10 f 10^5 = 100 k
10^-13 = 100 f 10^6 = 1 M
10^-12 = 1 p 10^7 = 10 M
10^-11 = 10 p 10^8 = 100 M
10^-10 = 100 p 10^9 = 1 G
10^-9 = 1 n 10^10 = 10 G
10^-8 = 10 n 10^11 = 100 G
10^-7 = 100 n 10^12 = 1 T
10^-6 = 1 u 10^13 = 10 T
10^-5 = 10 u 10^14 = 100 T
10^-4 = 100 u 10^15 = 1 P
10^-3 = 1 m 10^16 = 10 P
10^-2 = 10 m 10^17 = 100 P
10^-1 = 100 m 10^18 = 1 E
10^0 = 1 10^19 = 10 E
10^20 = 100 E
Engineering notation is used by default when we speak because the
numerical values of the spoken names of SI prefixes run in increments of
thousands such as; kilohertz, microfarads, millihenrys and megaohms
(pronounced "megohms"). The spoken term "20 kilohertz" is already in
engineering notation, and would be written on paper as 20E3 (20*10^3) hertz in
strict engineering notation and as 2E4 (2*10^4) in scientific notation if it
were not written in the more familiar form, 20 kHz.
In either case, scientific or engineering, the rule is: for numbers
greater than 1, the En part of the figure indicates the number of decimal
places to the right that zeros will be added to the original number. For
numbers smaller than 1, the E-n part of the figure indicates the number of
decimal places to the left of the original number that the decimal point
itself should be moved. The small "n" and "-n" here stand for the digits in
the exponent itself.
A definitive phamphlet describing SI units, conversions between SI units,
older CGS and MKS units and units outside the SI system of units is available
in the form of NASA Publication SP-7012, (1973). Inquire to the U.S.
Government Printing Office in Pueblo, Colorado or in Washington, D.C. for this
and other publications about SI units, their use and history.
END