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Basic Metric
Note that the standard measurment of length in the United States is the meter. What the meter is has been redefined many times. In 1799 the meter was originally defined as one ten millionth of the quadrant of the earth. Later in 1872, thirty prototype meters were made on metal bars with marks to indicate the meter. In 1960 the meter was redefined as as 1650763.73 wavelengths of the orange-red line of krypton-86. And in 1983 the meter was again redefined so that the speed of light was exactly 299729458 meters/second.
In 1964, a liter was defined as one cubic decimeter. One liter of water at maximum density, about 4 degrees Celsius, standard pressure, has a mass very close to 1 kilogram.
Metric Notation
With English unit, we add a sufix to denote very large or very small quantities. For example, "seven million" In the metric system a prefex is added to the unit, as in "seven megabucks" which would be seven million dollars. Similarly a kilobuck would be $1000, a decibuck would be a dime and a centibuck would be one cent. Below is a list of some of the prefixes used by the metric system preceded by their abreviation. Also included for completeness are the numbers shown in Scientific Notation and their English name.
Metric Standard Scientific United
Notation Notation Notation States
(Y) yotta 1000000000000000000000000 1024
(Z) zetta 1000000000000000000000 1021
(E) exa 1000000000000000000 1018 quintillion
(P) peta 1000000000000000 1015 quadrillion
(T) tera 1000000000000 1012 trillion
(G) giga 1000000000 109 billion
(M) mega 1000000 106 million
(k) kilo 1000 103 thousand
(h) hecto 100 102 hundred
(dk) deca 10 10 ten
(d) deci 0.1 10-1 tenth
(c) centi 0.01 10-2 hundredth
(m) milli 0.001 10-3 thousandth
(µ) micro 0.000001 10-6 millionth
(n) nano 0.000000001 10-9 billionth
(p) pico 0.000000000001 10-12 trillionth
(f) femto 0.000000000000001 10-15 quadrillionth
(a) atto 0.000000000000000001 10-18 quintillionth
(z) zepto 0.000000000000000000001 10-21
(y) yocto 0.000000000000000000000001 10-24
Note that "µ" is the Greek letter mu.
Please DO NOT confuse "m" and "M". Asprin is measured in mg (milligram) and a Mg (megagram) is called a metric tonne. A mm is less than .04 inches but a Mm is more than 621.37 miles, about the distance between San Diego and Salt Lake City. Of course the original definition of 10 Mm was the distance from the equator to the North Pole through Paris.
Note that it is improper to mix English notation (thousand, million, billion, etc.) with metric notation. The total electric power generation capability in California is about 43 gigawatts. It is often incorrectly written as 43 thousand megawatts, or 43 million kilowatts. In a desire to keep the digits significant, writing 43,000 megawatts or 43,000,000 kilowatts should be discouraged. Calling a 1 gram tablet of asprin a 1000 mg tablet is also improper advertising hype.
Fundamental Metric Units
The unit of length is the meter (m).
The unit of mass is the gram (g).
The unit of time is the second (s).
The unit of temperature is the Kelvin. (K)
The unit of current is the ampre (A).
The meter (m) is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. [i.e. by definition, light travels 29.9792458 cm in a ns.]
The kilogram (kg) is the unit of mass; it is equal to the mass of the international prototype of the kilogram. [Essentially the mass of a liter of water at 4°C.]
The second (s) 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. [Duration chosen to equal what was a mean solar day divided by 86400.]
The kelvin (K), unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature between the triple point of water and absolute zero. Absolute zero is 0K.
The ampere (A) 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 2 x 10-7 newton per meter of length.
The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Derived Metric Units
The liter (L), a measure of volume, is a cubic decimeter.
The newton (N) is the force needed to accelerate 1 kg at 1 m/sec2. 100000 dynes are equal to 1 Newton. [On the Earth, gravity attracts 1 kg with a force of about 9.8 newtons. This force is the attraction of the 1 kg to all the mass in the universe and is known as the weight of the 1 kg. It varies between the equator and the poles. It also varies with time of day. Standard gravity is defined as 9.80665 m/sec2. ]
Joule (J), a measure of energy, is 1 newton-meter of work. It is also equal to 1 watt-second of energy. There are 3.6 megajoules in a kilowatt-hour. To raise a liter of water one meter is about 9.8 joules of work.
Watt (W), a measure of power, is one joule per second or one newton-meter per second. The power needed to raise a liter of water one meter in one second is about 9.8 watts. One ampere through an electrical resistance of one ohm develops an EMF of one volt and dissipates one watt of power.
Coulomb is the charge of 1 mole of electrons. [About 6.281 x 1018 electrons or 1 ampere-second of charge.]
Ohm is the electrical resistance of a uniform column of mercury at 0°C, 106.4 cm in lenght with a mass of 14.4521 g. A current of 1 ampere though a resistance of 1 ohm disapates a power of 1 watt.
Volt (V) is the electrical potential across a 1 ohm resistance through which flows a current of 1 ampere.
The degree Celcius (°C) [aka centigrade] is the same difference as the degree Kelvin, but zero on the Celcius scale is at the freezing point of water.
Hertz (Hz), a measure of frequency, is the number of times something happens per second. It replaces the old unit 'Cycles per Second' (CPS). The frequency of a periodic function is the reciprical of the period in seconds.
Diopter, a measure of lens power, is the inverse of the lens focal length in meters. Thus a lens with a focal length of 1 m has a power of 1 diopter and a lens with a focal length of 0.25 m has a power of 4.0 diopters. When lenses are used together, the total power is the sum of the powers of each lens.
Bel (B) is a logrithmic measure of power ratio. A power ratio of 10 is 1 B, a power ratio of 100 is 2 B, and a power ratio of 1000 is 3 B. A power ratio of 100.1 [about 1.26] is 0.1 B or 1 dB [decibel].
Relationships between Metric Units
By design, metric units combine to form new units to measure other properties. The following table may prove useful. For all practical purposes:
Volume Volume Mass of Water
cubic meter kiloliter tonne [t]
cubic decimeter liter kilogram [kg]
cubic centimeter milliliter gram [g]
cubic millimeter microliter milligram [mg]
It shows the relationship between volume expressed in cubic meters, and the equivalent volume in liters, and the mass of water, at maximum density which is about 4 degrees centigrade, that will fill that volume. Note that water therefore has a maximum density of about 1 metric ton per cubic meter [kiloliter], and 1 kilogram per liter, and 1 gram per milliliter, and 1 milligram per microliter.
Similiarly, the unit of pressue called a 'pascal' is a newton per square meter, and is equal to a centinewton per square decimeter, and is equal to 100 micronewtons per square centimeter, and is equal to a micronewton per square millimeter.
Algebra on Units
A measurement consists of two parts, the number and the unit. Both are important. If I were to say:
9.806650 = 32.17405 = 21.93685
you would say I was wrong. And I would be wrong. But if I were to say:
1 g=9.806650 m/sec2=32.17405 ft/sec2=21.93685 mph/sec
then I would be right. [more or less, these are approximations] Note that here "g" represents the standard [average] acceration of a mass on the surface of the Earth due to the force of gravity.
If I multiply 30 cm. by 40 cm., the answer is 1200 cm2. Note that the units are subject to the same algebraic manipulation as are the numbers. Acceleration is the rate of change of velocity. Rate of change, also known as a time derivative, has the unit 1/sec. Distance is the area under the velocity versus time plot. This area, also known as a time integral, has the unit sec. Thus the rate of change of distance with time is velocity, the rate of change of velocity is acceleration, and the rate of change of acceleration is jerk. If the distance is in meters and the time in seconds, the corresponding units are:
Distance in m
Velocity in m/sec
Acceleration in m/sec2
Jerk in m/sec3
Velocity will always be in the form of unit distance per unit time. Any other unit is wrong. Knowing how to multiply and divide units is essential to understanding science.
Measurement of Angle
There are four different ways to divide a circle and measure an angle. There are 2 pi radians, 360 degrees, or 400 gradients in a circle. In addition, computers often represent a circle as a fraction between 0 and 1 using Binary Angular Measure or BAMs. The 5 bit Grey coded optical disk shown in Figure 1 is an example of a disk used to encode direction into a computer.
Figure 1
code BAM deg/min/sec radians
00 BBBBB N 0.015625 5° 37' 30" 0.098175
01 BBBBW NNE 0.046875 16° 52' 30" 0.294524
02 BBBWW NNE 0.078125 28° 7' 30" 0.490874
03 BBBWB NE 0.109375 39° 22' 30" 0.687223
04 BBWWB NE 0.140625 50° 37' 30" 0.883573
05 BBWWW ENE 0.171875 61° 52' 30" 1.079922
06 BBWBW ENE 0.203125 73° 7' 30" 1.276272
07 BBWBB E 0.234375 84° 22' 30" 1.472622
08 BWWBB E 0.265625 95° 37' 30" 1.668971
09 BWWBW ESE 0.296875 106° 52' 30" 1.865321
10 BWWWW ESE 0.328125 118° 7' 30" 2.061670
11 BWWWB SE 0.359375 129° 22' 30" 2.258020
12 BWBWB SE 0.390625 140° 37' 30" 2.454369
13 BWBWW SSE 0.421875 151° 52' 30" 2.650719
14 BWBBW SSE 0.453125 163° 7' 30" 2.847068
15 BWBBB S 0.484375 174° 22' 30" 3.043418
16 WWBBB S 0.515625 185° 37' 30" 3.239767
17 WWBBW SSW 0.546875 196° 52' 30" 3.436117
18 WWBWW SSW 0.578125 208° 7' 30" 3.632467
19 WWBWB SW 0.609375 219° 22' 30" 3.828816
20 WWWWB SW 0.640625 230° 37' 30" 4.025166
21 WWWWW WSW 0.671875 241° 52' 30" 4.221515
22 WWWBW WSW 0.703125 253° 7' 30" 4.417865
23 WWWBB W 0.734375 264° 22' 30" 4.614214
24 WBWBB W 0.765625 275° 37' 30" 4.810564
25 WBWBW WNW 0.796875 286° 52' 30" 5.006913
26 WBWWW WNW 0.828125 298° 7' 30" 5.203263
27 WBWWB NW 0.859375 309° 22' 30" 5.399612
28 WBBWB NW 0.890625 320° 37' 30" 5.595962
29 WBBWW NNW 0.921875 331° 52' 30" 5.792314
30 WBBBW NNW 0.953125 343° 7' 30" 5.988661
31 WBBBB N 0.984375 354° 22' 30" 6.185011
The reason for the Grey code is to prevent errors that might occur if two bands were suppose to change at a given angle, but one change was a very small fraction off.
Even though many software programs use BAMs for calculation of angles to describe, for example, direction of travel, computer output is usually converted to degrees and minutes for user display. This is done by multiplying the fractional angle [BAM] by 360 degrees, using the resultant integer as degrees, multiplying the new fraction by 60, then using that integer for minutes. The new fraction could be multiplied by 60 to get the seconds. Unlike this simple example, most encoding disks use 8 or more bits to encode an angle.
Computer Pseudometric
Computers are binary machines. Everytime a bit is added the memory address space, the amount of addressable membory doubles. So the measurement of computer memory is bases on power of 2. To simplify the description of memory size, the term kilobye is applied to the size of memory assable by 10 bits that is 1024 bytes. This was done because 1024 is close to 1000. So when taking about computer memory or disk size, use the following table:
Computer Memory
Metric Standard Computer United
Notation Notation Notation States
(PB) petabyte 1125899906842624 250 quadrillion
(TB) terabyte 1099511627776 240 trillion
(GB) gigabyte 1073741824 230 billion
(MB) megabyte 1048576 220 million
(kB) kilobyte 1024 210 thousand
Metric Review
To summarize, the basic units of the Metric System are the meter [m], kilogram [kg] and the second [s]. 100 inches is the same distance as 2.54 meters. A cubic decimeter [0.1 m or about 3.937" on a side] is a liter [l]. Fill that liter with cold water and the water will have a mass very close to a kilogram [kg]. In Saint Louis, Missouri, that kilogram will have a weight of about 9.8 Newtons [N]. Raise that kilogram up 1 meter and you will have done 9.8 joules [J] of work. Raise that kilogram up 1 meter in 1 second requires a power of 9.8 watts [W]. The pressure at the bottom of that cubic decimeter of water is .98 kilopascal [kP]
Weight of 100 kg
as a function of location
North Pole 983.217 N 221.036 lbf. St. Michael, Alaska 982.192 N 220.806 lbf. Paris, France 980.943 N 220.525 lbf. Standard Gravity 980.665 N 220.46223 lbf. (avoirdupois) New York, New York 980.267 N 220.373 lbf. Key West, Florida 978.970 N 220.081 lbf. Equator 978.039 N 219.872 lbf. Surface of Mars 369.7 N 83.1 lbf. Surface of our Moon 162.7 N 36.5 lbf. Surface of Pluto 65.7 N 14.7 lbf.
Mass & Weight are NOT the same thing. The weight of an object varies with location. But its mass remains the same where ever it is. The mass of an object is measured on a balance scale by comparing it with other masses. Weight is a force and must be measured on a spring scale. The chart above shows how the weight of a 100 kg mass changes with location. Weight even changes with time of day. In the United States, things weigh the least at noon, in June, with a new moon! The difference is not much, but it is enough to cause the tides.
Note that when selling sugar, apples, nuts, etc., 1 lb = .45359237 kg. At the standard gravity of 9.80665 m/sec2, a 1 lb [one pound mass] has a weight of 1 lbf [one pound force].
Sometimes the confusion between mass and force results in the use of the meaningless unit of kg/m2 [kilogram per square meter] being used to measure 'pressure'. Presure must be N/m2 which is Pa [pascal].
Below is a list of common metric unit symbols, the name of of the unit and a short description.
A ampere electric current B bell power ratio C coulomb electric charge cd candela luminous intensity ° degree plane angle °C degree Celsius Temperature F farad electric capacitance Gs gauss magnetic flux density [cgs] g gram mass H henry electric inductance Hz hertz frequency J joule energy, work, quantity of heat kg kilogram mass K kelvin absolute temperature L or l liter volume lm lumen luminous flux lx lux illuminance m meter length mol mole amount of substance N newton force Oe oersted reluctance Ω ohm electric resistance Pa pascal pressure s second time S siemens electric conductance t ton mass [megagram] [metric ton or tonne] T tesla magnetic flux density V volt electric potential difference, EMF W watt power Wb weber magnetic flux
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NIST Handbook 44, the Official U. S. Metric Page
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