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.

1792The U.S. Mint was formed to produce the world's first decimal currency (the U.S. dollar consisting of 100 cents).

1866The 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.

1975The 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.

1979BATF requires wine producers and importers to switch to metric bottles in seven standard [liter and milliliter] sizes.

1983The meter is redefined in terms of the speed of light by the 17th CGPM, resulting in better precision but keeping its length the same.

1988The 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.

1991President 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

1994The 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.

1996As of July 1996 all surface temperature observations in National Weather Service METAR/TAF reports are now transmitted in degrees Celsius.

2001 April 09U.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 / volts per meter
electromagnetic inductance / 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 / A s
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):
Yotta- / Y / 1024 / 1 000 000 000 000 000 000 000 000
Zetta- / Z / 1021 / 1 000 000 000 000 000 000 000
Exa- / E / 1018 / 1 000 000 000 000 000 000
Peta- / P / 1015 / 1 000 000 000 000 000
Tera- / T / 1012 / 1 000 000 000 000
Giga- / G / 109 / 1 000 000 000
Mega- / M / 106 / 1 000 000
myria- / my / 104 / 10 000 (this is now obsolete)
kilo- / k / 103 / 1000
hecto- / h / 102 / 100
deka- / da / 10 / 10
- / - / - / -
deci- / d / 10-1 / 0.1
centi- / c / 10-2 / 0.01
milli- / m / 10-3 / 0.001
micro- / u (mu) / 10-6 / 0.000 001
nano- / n / 10-9 / 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 / 10-21 / 0.000 000 000 000 000 000 001
yocto- / y / 10-24 / 0.000 000 000 000 000 000 000 001

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 temperaturesin 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

More info

Temperature conversions (°C <--> °F)

Sources: