Download Commonly used metric system units and symbols

The Metric System
Important dates in the history of the modern
metric system (S.I.):
1670 metric system originated on about this date. Gabriel Mouton, a French vicar
1790 Thomas Jefferson proposed a decimal-based measurement system for the United States.
1792 The U.S. Mint was formed to produce the world's first decimal currency (the U.S. dollar consisting of 100
cents).
1866 The use of the metric system made legal (but not mandatory) in the United States by the Metric Act of
1866 (Public Law 39-183). This law also made it unlawful to refuse to trade or deal in metric quantities.
1975 The Metric Conversion Act of 1975 (Public Law 94-168) passed by Congress. The Act established the
U.S. Metric Board to coordinate and plan the increasing use and voluntary conversion to the metric system.
However, the Act was devoid of any target dates for metric conversion.
1979 BATF requires wine producers and importers to switch to metric bottles in seven standard [liter and
milliliter] sizes.
1983 The meter is redefined in terms of the speed of light by the 17th CGPM, resulting in better precision but
keeping its length the same.
1988 The Omnibus Trade and Competitiveness Act of 1988 amended and strengthened the Metric Conversion
Act of 1975, designating the SI metric system as the preferred measurement system, and requiring each federal
agency to be metric by the end of fiscal year 1992.
1991 President George Bush signed Executive Order 12770, Metric Usage in Federal Government Programs
directing all executive departments and federal agencies implement the use of the metric system. The Executive
Order is also available as an appendix to: Interpretation of the SI for the United States and Federal Government
Metric Conversion Policy
1994 The Fair Packaging and Labeling Act (FPLA) was amended by the Food and Drug and Administration
(FDA) to require the use of dual units (inch-pound AND metric) on all consumer products.
1996 As of July 1996 all surface temperature observations in National Weather Service METAR/TAF reports
are now transmitted in degrees Celsius.
2001 April 09 U.S. Stock Exchanges changed to decimal trading. The Securities and Exchange Commission
has ordered that all stocks must be quoted in dollars and cents rather than fractions by this date. The switch to
decimal trading brought the U.S. in line with the rest of the world's major exchanges. This follows the change of
the Canadian Stock Exchanges to decimal trading in 1996.
One of the principal advantages of the Metric System is its use of only one unit (standard of size) for each
parameter (thing that is being measured). The metric units are interrelated in such a way that only five
fundamental standards are necessary. These fundamental standards are identified with an * in the tables below.
The 5 Standard Metric Units
Second - time
Gram - mass
degrees Kelvin - temperature
Candle - light
Coulomb - electrical charge
MECHANICS
Parameter:
Metric Unit
English Units
Time duration, delay
second * s
second, minute, hour, day
frequency
Hertz 1/s
cycle per second
length
distance, displacement
Meter
1/299 792 458 light sec
m
inch, foot, yard
rod, chain, furlong, mile
velocity, speed
rate of change of position
meter per second
m/s
foot per second
mile per hour, knot
acceleration
rate of change of velocity
meter per second squared
m/s2
foot per second squared
mass
quantity of material
gram *
g
ounce, pound, ton
force
push, pull, or weight
Newton
kg m/s2
pound-force
impulse
force times time
newton second
kg m/s
pound-force second
momentum
mass times velocity
kilogram meter per second
kg m/s
pound foot per second
work, energy
force times distance
joule (pronounced "jewel")
= one newton meter
kg m2/s2
foot pound-force
power
rate of doing work
Watt
= one joule per second
kg m2/s3
foot pound-force per second
horsepower
area
size of a surface
square meter
m2
square foot, square yard
acre, square mile
pressure
force per unit area
Pascal
newton per square meter kg/m s2
pound-force per square inch
volume, capacity
cubic meter (stere)
m3
pint, quart, gallon
cubic foot, cubic yard
density, heaviness
grams per cubic centimeter
g/cm3
pounds per cubic foot
HEAT
Parameter:
Metric Heat Unit
English Heat Unit
heat energy
joule, calorie, Calorie
1 cal = 4.186 joules
1 Cal = 4186 joules
British Thermal Unit
temperature change
kelvin *
Fahrenheit degree
temperature
degrees kelvin
degrees Fahrenheit
LIGHT
Parameter:
Metric Light Unit
luminous intensity
candle *
luminous flux
lumen
one candle produces 4 pi lumens
illumination
lux
lumen per square meter
focus
diopter
reciprocal meters
astronomical distance
parsec
ELECTRICITY & MAGNETISM (There are no English electrical units)
Parameter:
Metric Electrical Unit
electric charge
coulomb *
96,500 coul = 1 faraday = 1 mole of electrons
electromotive force (EMF)
volt (joule per coulomb)
capacitance
farad (coulomb per volt)
electric current
ampere (coulomb per second)
electric energy
joule (watt second) -- (newton meter)
KWH = 3,600,000 joules
electric power
watt (joule per second)
electrical resistance
ohm (volt per ampere)
electrical conductivity
siemens (coulomb per joule)
(ampere per volt)
electrical field strength
electromagnetic inductance
volts per meter
henry (pl. henrys)
magnetic field intensity
oersted (formerly the gauss)
magnetic flux
weber (108 maxwells)
magnetic flux density
tesla weber per square meter
magnetomotive force
gilbert
Each physical quantity (length, mass, volume, etc.) is represented by a specific SI unit. That unit is made larger
or smaller by addition of a prefix to the stem unit.
Commonly used metric system units and symbols:
Type of Measurement
Unit Name
Symbol
length, width, distance, thickness, girth, etc.
meter
m
mass (often called weight)
kilogram*
kg
mass (larger)
metric ton
t
time
second
s
temperature
degree Celsius**
°C
area
square meter
m2
area (land)
hectare
ha
volume (liquid or other)
liter
L***
volume (larger)
cubic meter
m3
density
kilogram per cubic meter
kg/m3
velocity
meter per second
m/s
velocity (autos)
kilometer per hour
km/h
force
newton
N
pressure, stress
kilopascal
kPa
energy
kilojoule
kJ
power
watt
W
*The gram (g) is the stem unit to which other prefixes are added.
**The kelvin (K) is the SI base unit of thermodynamic temperature.
***The capital el (L) is preferred as the symbol for liter in the USA; however the lower case el (l) also is
correct and is used in many metric countries.
Derived Units
Force
Newton
N
kg m s-2
Energy
joule
J
kg m2 s-2
Power
watt
W
kg m2 s-3
Frequency
hertz
Hz
s-1
Charge
coulomb
C
As
Capacitance
farad
F
C2 s2 kg-1 m-2
Magnetic Induction tesla
T
kg A-1 s-2
The Metric Prefixes
Prefix: Symbol: Magnitude:
Meaning (multiply by):
24
Yotta- Y
10
1 000 000 000 000 000 000 000 000
Zetta- Z
1021
18
1 000 000 000 000 000 000 000
Exa-
E
10
1 000 000 000 000 000 000
Peta-
P
1015
1 000 000 000 000 000
Tera-
T
10
12
1 000 000 000 000
Giga-
G
109
1 000 000 000
Mega- M
6
1 000 000
4
10
myria- my
10
10 000 (this is now obsolete)
kilo-
k
103
1000
hecto- h
10
2
100
deka-
da
10
10
-
-
-
-
deci-
d
10-1
c
-2
0.01
10
-3
0.001
10-6
0.000 001
centimilli-
m
micro- u (mu)
10
-9
0.1
nano-
n
10
0.000 000 001
pico-
p
10-12
0.000 000 000 001
femto- f
10
-15
0.000 000 000 000 001
atto-
a
10-18
0.000 000 000 000 000 001
zepto- z
-21
0.000 000 000 000 000 000 001
-24
0.000 000 000 000 000 000 000 001
yocto- y
10
10
Commonly used metric prefixes
Prefix Name Prefix Symbol
Prefix Value
giga
G
1 000 000 000
109
mega
M
1 million or 1 000 000
106
kilo
k
1 thousand or 1000
103
hecto
h
100
102
deka
da
10
10
deci
d
1/10 or 0.1
10-1
centi
c
1/100 or 0.01
10-2
milli
m
1/1000 or 0.001
10-3
micro
µ
1/1 000 000 or 0.000 001
10-6
nano
N
1/1 000 000 000 or 0.000 000 001 10-9
Some special relationships:




1 milliliter = 1 cubic centimeter
1 milliliter of water has a mass of approximately 1 gram
1 liter of water has a mass of approximately 1 kilogram
1 cubic meter of water has a mass of approximately 1 metric ton
Legal/official (exact) definitions of inch-pound units as set by U.S.
law:



1 inch = 25.4 millimeters
1 pound = 453.592 37 grams
1 gallon = 3.785 411 784 liters
Note: In Canada the inch and the pound are defined identically, but 1 Canadian gallon = 4.546 09 liters.
Approximate conversion factors between inch-pound units and the
International System of Units (SI):







Multiply inches by 2.54 to get centimeters (this conversion factor is exact)
Multiply feet by 0.305 to get meters
Multiply miles by 1.6 to get kilometers
Divide pounds by 2.2 to get kilograms
Multiply ounces by 28 to get grams
Multiply fluid ounces by 30 to get milliliters
Multiply gallons by 3.8 to get liters
Some baseline temperatures in the three temperature scales
temperature
kelvins degrees Celsius degrees Fahrenheit
symbol
°K
°C
°F
boiling point of water
373.15
100.
212.
average human body temperature
37.
98.6
average room temperature
20. to 25.
68. to 77.
freezing / melting point of water / ice
273.15
0.
32.
absolute zero
0.
-273.15
-459.67
Temperature conversions between the three temperature scales:
kelvin / degree Celsius conversions (exact):


kelvins = degrees Celsius + 273.15
degrees Celsius = kelvins - 273.15
degree Fahrenheit / degree Celsius conversions (exact):


degrees F = degrees C x 1.8 + 32.
degrees C = (degrees F - 32.) / 1.8
A degree Celsius memory device:
There are several memory aids that can be used to help the novice understand the degree Celsius temperature
scale.
One such nemoic is:
When it's zero it's freezing,
when it's 10 it's not,
when it's 20 it's warm,
when it's 30 it's hot!
Or, another one to remember:
30's hot
20's nice
10's cold
zero's ice
Examples of everyday item equivalences for metric units of length, mass, volume, and
temperature
(Drawings excerpted from the book, Quick Guide to the Metric System, by Valerie Antoine, USMA Executive
Director)
Length:
1 meter (1 m)
1 centimeter (1 cm)
1 kilometer (1 km)
Mass:
1 kilogram (1 kg)
1 gram (1 g)
Volume:
1 liter (1 L or 1 l)
1 milliliter (1 mL or
1 ml)
Temperature:
degree Celsius (°C)
Scientific Notation
Learn how to write numbers in scientific notation
http://www.nyu.edu/pages/mathmol/textbook/scinot.html
More info
http://dbhs.wvusd.k12.ca.us/SigFigs/Scientific-Notation.html
Temperature conversions (°C <--> °F)
Sources:
http://lamar.colostate.edu/~hillger/
http://users.aol.com/tspquinn/units.html
http://www.essex1.com/people/speer/metric.html
http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl
http://www.nyu.edu/pages/mathmol/textbook/scinot.html
http://dbhs.wvusd.k12.ca.us/SigFigs/Scientific-Notation.html