**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

Content

- SI Units, Standards and Notation
- Definition of SI Units
- SI Prefixes
- Scientific and Engineering Notation

**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 | 1/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^-1 | 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 |

(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-iridium 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.

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 advertising 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 pamphlet 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.