SI STANDARD AND MEASUREMENT
The International System (SI) of Weights and Measures
From the extremely small to the extremely large:
SCALES OF MEASUREMENT
Metric prefixes applied to the meter, the gram, the second, and the unit, with examples
ABOUT METRIC PREFIXES
name  prefix  10^{x}  number 
U.S.  Short Scale  Europe  Long Scale 
Metric Prefix Etymology 
yocto  y  24 
0.000,000,000,000,000,000,000,001  Septillionth  Quadrillionth 
Greek letter iota, "octo" 
zepto  z  21 
0.000,000,000,000,000,000,001  Sextillionth  Trilliardth 
Greek letter zeta, "septo" 
atto  a  18 
0.000,000,000,000,000,001  Quintillionth  Trillionth 
Norwegian for "18" 
femto  f  15 
0.000,000,000,000,001  Quadrillionth  Billiardth 
Norwegian for "15" 
pico  p  12 
0.000,000,000,001  Trillionth  Billionth 
Spanish for "beak" or "little bit" 
nano  n  9 
0.000,000,001  Billionth  Milliardth 
Greek for "dwarf" 
micro  μ, u  6 
0.000,001  Millionth  Millionth 
Greek for "small" 
milli  m  3 
0.001  Thousandth  Thousandth 
Latin for "1000" 
centi  c  2 
0.01  Hundredth  Hundredth 
Latin for "100" 
deci  d  1 
0.1  Tenth  Tenth 
Latin for "tenth" 
(unit) 
 0 
1  One  One 

deka  D or dk  1 
10  Ten  Ten 
Greek for "10" 
hecto  H  2 
100  Hundred  Hundred 
Greek for "100" 
kilo  K  3 
1,000  Thousand  Thousand 
Greek for "1000" 
myria  (My)  4 
10,000  Tenthousand  Tenthousand 
Greek for "10000" 
mega  M  6 
1,000,000  Million  Million 
Greek for "mighty" 
giga  G  9 
1,000,000,000  Billion  Milliard 
Greek for "giant" 
tera  T  12 
1,000,000,000,000  Trillion  Billion 
Greek for "monster" 
peta  P  15 
1,000,000,000,000,000  Quadrillion  Billiard 
Greek for "5", n removed 
exa  E  18 
1,000,000,000,000,000,000  Quintillion  Trillion 
Greek for "6", h removed 
zetta  Z  21 
1,000,000,000,000,000,000,000  Sextillion  Trilliard 
Greek letter zeta, Italian "setta" 
yotta  Y  24 
1,000,000,000,000,000,000,000,000  Septillion  Quadrillion 
Greek letter iota, Italian "otta" 
A note on the naming of numbers over 999,999,999 and numbers less than .000,001:
 The Long Scale was first, originating in France. The major names occur every power of one
million (6 digits).
 Britain adopted the Long Scale by the early 1600s. Dots were placed every 6 digits.
 In the mid1600s, France and Italy started placing commas every 3 digits.
 At nearly the same time, French usage changed to the Short Scale. Major names occur every
power of one thousand (3 digits).
 The French brought the Short Scale to the American colonies. The US always used the Short
Scale.
 Most European, Spanish Speaking, and PortugueseSpeaking countries adopted the Long
Scale.
 In 1961, the French Government changed all French speaking nations to the Long Scale.
 In 1974, the British Government changed to the Short Scale.
 Most EnglishSpeaking and Arab countries, Brazil, and Russia now use the Short Scale.
 Canada, South Africa, Namibia, and Antarctica use both scales, depending on the language
spoken.
 Other than the UK, the European Union uses the long scale.
 East and Southeast Asia, and Greenland have languages with numbers not based on powers of
one thousand. Some use myriads.
 Metric prefixes always denote the same actual number, not being affected by whether the
Long Scale or the Short Scale is used.
BASE UNITS
var  QUANTITY  UNIT  SYMBOL  FORMULA 
l  length  meter  m 
distance traveled by light in absolute vacuum in 1/299,792,458 s. 
m  mass  kilogram  Kg 
1 cubic decimeter of water @ 277K 
t  time  second  s 
9,192,631,770 periods of two hyperfine levels, ground state Cs133, at rest, 0 K, zero
magnetic field. 
I  electric current  ampere  A 
current producing 200 nN between two straight  conductors 1 m apart in vacuum 
T  temperature  kelvin  K 
absolute 0, 273.16 K = triple point of water 
 luminous intensity  candela  cd 
radiation of frequency 540 * 10^{12} Hz of 1/683 W/sr 
θ  plane angle  radian  rad 
circle / 2 / pi 
ψ  solid angle  steradian  sr 
1 / 4 / pi sphere 
c  lightspeed  light second  m / s 
lightspeed in vacuum 
DERIVED UNITS
var  QUANTITY  UNIT  SYMBOL  FORMULA 
f  frequency  hertz  Hz  1/s 
F  force  newton  N  Kg * m / s^{2}; F = m * a 
p  pressure  pascal  Pa  Kg * m / s 
E  energy, work, heat  joule  J  N * m 
P  power, radiant flux  watt  W  J / s 
Q  charge  coulomb  C  A * s 
V  electromotive force  volt  V  W / A 
C  capacitance  farad  F  C / V 
 elastance  daraf  F^{1}  1 / F 
I  inductance  henry  H  V * s / A = Wb / A 
 reluctance  yrneh  H^{1}  1 / H 
R  resistance  ohm  Ω  V / A 
X  reactance  ohm  Ω  V / A, 90 degree phase 
Z  impedance  ohm  Ω  V / A, any angle 
G  conductance  siemens (mho)  S  A / V 
B  susceptance  siemens  S  A / V, 90 degree phase 
Y  admittance  siemens  S  A / V, any angle 
M  magnetic flux  weber  Wb  V * s 
B  magnetic flux density  tesla  T  Wb / m^{2} 
 luminous flux  lumen  lm  cd * sr 
i  illuminance  lux  lx  lm / m^{2} 
r  activity (radiation)  becquerel  Bq  counts / s 
d  dose  gray  Gy  J / Kg 
λ  wavelength  meter  m  lambda = c / f 
t  time  minute  min  60 s 
t  time  hour  h  60 min = 3600 s 
t  time  day  min  24 h = 86400 s 
θ  angle  degree  deg or ^{o}  pi / 180 * rad 
θ  angle  minute  '  1 / 60 * deg 
θ  angle  second  "  1 / 3600 * deg 
θ  angle  gradient  grad  pi / 200 * rad 
v  volume  liter  l  (dm)^{3} 
m  mass  tonne  t  1 Mg 
A  area  are  a  100 m^{2} 
A  area  hectare  Ha  10000 m^{2} 
 chemical amount  mole  mol  1 g * AMU 
DERIVED VALUES
var  QUANTITY  FORMULA 
a  acceleration  m / s^{2} 
α  angular acceleration  rad / s^{2} 
ν  angular velocity  rad / s^{2} 
A  area  m^{2} 
C  concentration  mol / m^{3} 
dI  current density  A / m^{2} 
d  density (mass)  Kg / m^{3} 
dQ  charge density  C / m^{3} 
e  electric field strength  V / m 
η  electric flux density  C / m^{2} 
dE  energy density  J / m^{2} 
Η  entropy, heat capacity  J / K 
ι  irradiance, heat flux density  W / m^{2} 
L  luminance  cd / m^{2} 
m  magnetic field strength  A / m 
E_{mol}  molar energy  J / mol 
Η_{mol}α  molar heat capacity, entropy  J / mol / K 
m  momentum  N * m / s 
μ  permeability  H / m 
p  permittivity  F / m 
r  radiance  W / m^{2} / sr 
I  radiant intensity  W / sr 
H  specific heat capacity  J / Kg / K 
E_{sp}  specific energy  J / Kg 
H  specific entropy  J / Kg / K 
V_{sp}  specific volume  m^{3} / Kg 
T  surface tension  N / m 
T  temperature  ^{o}C: T  273.15 (from K) 
T  temperature  ^{o}F: 1.8 * T  459.67 (from K) 
tc  thermal conductivity  W / m / K 
Τ  torque  N * m 
v  velocity  m / s> 
 dynamic viscosity  Pa * s 
 kinematic viscosity  m^{2} / s 
V  volume  m^{3} 
n  wave number  1 / m 
PROPER USE OF UNITS OF MEASURE
COMMON MISTAKES
 Converting to or from SI units in the wrong direction
 Confusing mass and weight, and the units for each
 Mixing up Short Scale numbering with Long Scale numbering
 Confusing milli, micro, and mega
 Confusing force with pressure
 Confusing heat with temperature
 Using nonSI units
 Forgetting to square or cube the units when squaring or cubing the amount
 Confusing similar units in magnetism, light, and radiant energy
Units of measure are often used wrong. Here are tips on using them right:
Pronouncing the prefixes right:
deka  like the company Decca 
 deci  as in decimal 
hecto  hecktoe 
 centi  as in sentiment 
kilo  killo (not keelo) 
 milli  as in military 
mega  as in megaphone 
 micro  as in microphone 
giga  jigga (not gigga) 
 nano  nanno (a as in ant) 
tera  as in terrace 
 pico  peeko 
peta  as in petal 
 femto  femtoe (as in feminine) 
exa  exuh 
 atto  as in anatomy 
zetta  zettuh 
 zepto  zeptoe (think of a Marx brother) 
yotta  rhymes with gotta 
 yocto  yocktoe 
Some people just can't get straight the difference between mass, weight, force, and
pressure. Here are the correct uses and some examples of incorrect use:
 Mass is the amount of matter in something. Mass must not be confused with weight.
Weight is the force gravity places on a mass. The two are very different. A space shuttle
always has mass, but in space, it has no weight. On the moon, the mass of an 86 Kg man
is 86 Kg, but that 190 lb man weighs only 31 pounds on the moon.
 Confusion comes from the fact that the mass unit (kilogram) is commonly used in the
metric system, but the force unit is more common in the English system. Conversion factors
between the two are good only at sea level on the surface of the earth. At any other
altitude, or on any other planet, the published conversion factors are wrong.
 The gram is the metric unit of mass. It measures the amount of matter in something.
The gram must never be used to indicate weight, force, or pressure. The
kilogram is the MKS (MeterKilogramSecond) standard unit of mass.
 The newton is the MKS unit of force. It is used for weight, force, and tension.
It must never be used for mass or pressure. At sea level on the surface of the earth, one
kilogram weighs 9.8 newtons.
 The dyne is the CGS (CentimeterGramSecond) unit of force. It is equal to one
hundredthousandth of a newton.
 The unit of pressure in the MKS system is the pascal. It is one newton per square
meter. Pressure is measured as force distributed over an area.
 The unit of mass in the English FPS (FootPoundSecond) system is the slug. It is
not used very often. One slug is 14.59 kilograms.
 The pound is the FPS unit of force. It is often mistakenly used as a unit of mass.
At sea level on the surface of the earth, one slug weighs 32.174 pounds.
 The pound per square foot is the FPS unit of pressure. Divide this by 144 to get
pounds per square inch, the more common unit used.
 Many experimenters confuse mass and weight. I once "repaired" a program that asked
for body mass in pounds.
 Makers of record players used to talk of stylus pressure in grams. They made two
errors. First of all, they were not talking about pressure, but force. Second, they
reported the force in grams, a unit reserved for mass. The gram is never a unit of force.
The force should be measured in millinewtons.
An alternative is the use of the gramequivalent or the pfund. Both are the amount
of force exerted by earth gravity on a mass of 1 gram.
 Many makers of exercise equipment calibrate the tension dial in pounds, then put a
kilogram scale alongside. Again, the newton is the correct unit.
 Postal scales are calibrated in kilograms and pounds. The slug should be the FPS
measure for mass, but it is mostly unheard of. (Do they charge by mass, or weight?)
 The following are units of pressure, with the number of pascals in each:
 An atmosphere is 101.325 kilopascals.
 A bar is exactly 100 kilopascals.
 A dyne per square centimeter is .1 pascal.
 A millibar is 100 pascals.
 One pound per square foot is 47.88 pascals.
 One pound per square inch is 6.895 kilopascals.
 A torr is 133.322 pascals.
 One cm of water at 293 K is 97.891 pascals.
 One inch of water at 293 K is 248.64 pascals.
 One foot of water at 293 K is 2.98368 kilopascals.
 One millimeter of mercury at 273 K is 133.322 pascals.
 One centimeter of mercury at 273 K is 1.33322 kilopascals.
 One inch of mercury at 273 K is 3.38639 kilopascals.
 One foot of sea water is 3.0702 kilopascals.
Units of energy are the most misunderstood, because there are so many different forms
of energy. Here are a few, with the differences between them, and proper uses:
 The joule is the MKS unit of energy, work, and heat. It is one newton meter.
 The watt is not a unit of energy, but power. Power is the rate at which energy is
produced or used. A watt is one joule per second.
 The erg is the CGS unit of energy. It is one tenmillionth of a joule.
 A kilowatt hour is exactly 3,600,000 joules (3.6 megajoules).
 A foot pound is 1.356 joules.
 A BTU (British Thermal Unit) is 1.0548 kilojoules.
 A gram calorie is 4.185 joules.
 A kilogram calorie is 4.185 kilojoules. (These are the food calories)
 A horsepower second is 746 joules.
 A horsepower hour is 2.686 megajoules.
 A metric horsepower hour is 2.723 megajoules.
 I don't know what to do with the quad (1 quadrillion barrels of oil). Which
quadrillion is it: Long Scale or Short Scale?
 Do we have too many units here? Let's stick with the joule.
Another question is: What happens to units of measure when mathematical operations
are performed on the measurements? Here is a list of what can be done:
 When adding or subtracting two values, the units of measure must be the same, and
the result will be in the same units as the original measurements.
 When multiplying two values with different units, the result will be in the product
of the two units, or a derivation of the same. Example: Work=force*distance. Force is
in newtons, and distance is in meters, so work is in newtonmeters. Since a newtonmeter
is a joule, the work is expressed in a derivation, joules.
 When multiplying two values in like units, square the units of the answer. Example:
Area=length*height. 10 meters * 2 meters = 20 square meters.
 When multiplying by a value without units (e.g. number of tanks) the resulting units
of measure are unchanged. 20 cylinders, each massing 10 Kg is a mass of 200 Kg.
 When dividing two values, divide the units in the dividend by the units in the
divisor. Units appearing in both of them are canceled out.
 When raising a value to a power, raise the units to that power.
 A mean or standard deviation has the same units of measure as the raw data do.
 A variance should be reported in the square of the units the raw data are sampled in.
 When integrating a measurement over time, multiply the unit of time by the
measurement's units.
 When integrating a measurement over another variable, multiply its unit by the
measurement's units.
 When differentiating a measurement with respect to time, divide the measurement's
units by the unit of time.
 When differentiating a measurement with respect to another variable, divide the
measurement's units by those of the other variable.
 When multiplying by a conversion factor, substitute the new unit of measure for
the old one.
 When performing a transform (e.g. Fourier) replace the old unit by the new unit the
transform produces.
Temperature and heat are two quantities that are confused. Heat is the amount of
energy (measured in joules or gram calories) in a certain amount of substance. Temperature
is the energy in a quantity of material, divided by the mass of the material, then divided
by the specific heat of that material. Therefore:
 The change in temperature of a quantity of matter depends on the change in heat
energy stored in the matter, the mass of the matter, and the substance it is made out of.
 The amount of energy required to effect a desired temperature change depends on
the specific heat of the matter to be heated or cooled, and the mass of that matter.
 Heat is measured using the measures of energy given in another section above.
There are 4 temperature scales. Here are their properties:
property  Fahrenheit  Rankine  Kelvin  Celsius 
Zero point (base value)  coldest day  absolute 0  absolute 0 
water freezes 
100 offset point  hottest day 

 water boils 
degree size  100 offset  Fahrenheit degree  Celsius degree 
100 offset point 
purpose  weather  proportion  metric proportion  water standard 
conversion  T_{F} = T_{R}  459.67 
T_{R} = T_{F} + 459.67 
T_{K} = T_{C} + 273.1 
T_{C} = T_{K}  273.1 
 T_{F} = 9 / 5 * T_{C} + 32 
T_{R} = 9 / 5 * T_{K} 
T_{K} = 5 / 9 * T_{R} 
T_{C} = 5 * (T_{F}  32) / 9 
Here is a list of obsolete measures (minus the ones already mentioned), and
standard equivalents:
 1 angstrom = 100 picometers
 1 carat (metric) = 200 milligrams
 1 curie = 37 gigabecquerels
 1 electron volt = 6.24 exajoules
 1 faraday = 96.48 kilocoulombs
 1 fermi = 1 femtometer
 1 foot = 304.8 millimeters
 1 footcandle = 10.764 lux
 1 footlambert = 3.4263 candelas per square meter
 1 gamma = 1 picotesla
 1 gauss = 100 microteslas
 1 gilbert = .7958 ampere turns
 1 horsepower = 746 watts
 1 horsepower (metric) = 735.5 watts (What's a standard horse?)
 1 inch = 25.4 millimeters
 1 lambert = .3183 candelas per square centimeter
 1 maxwell = 10 nanowebers
 1 mho = 1 siemens
 1 micron = 1 micrometer
 1 neper = 8.686 decibels
 1 oersted = 79.577 amperes per meter
 1 pound = 4.4482 newtons
 1 roentgen = 258 microcoulombs per kilogram
 1 slug = 14.59 kilograms
 1 stere = 1 cubic meter
 1 yard = 914.4 millimeters
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