The International System (SI) of Weights and Measures

From the extremely small to the extremely large:


Metric prefixes applied to the meter, the gram, the second, and the unit, with examples


nameprefix10xnumber U.S. - Short ScaleEurope - Long Scale Metric Prefix Etymology
yoctoy-24 0.000,000,000,000,000,000,000,001SeptillionthQuadrillionth Greek letter iota, "octo"
zeptoz-21 0.000,000,000,000,000,000,001SextillionthTrilliardth Greek letter zeta, "septo"
attoa-18 0.000,000,000,000,000,001QuintillionthTrillionth Norwegian for "18"
femtof-15 0.000,000,000,000,001QuadrillionthBilliardth Norwegian for "15"
picop-12 0.000,000,000,001TrillionthBillionth Spanish for "beak" or "little bit"
nanon-9 0.000,000,001BillionthMilliardth Greek for "dwarf"
microμ, u-6 0.000,001MillionthMillionth Greek for "small"
millim-3 0.001ThousandthThousandth Latin for "1000"
centic-2 0.01HundredthHundredth Latin for "100"
decid-1 0.1TenthTenth Latin for "tenth"
0 1OneOne
dekaD or dk1 10TenTen Greek for "10"
hectoH2 100HundredHundred Greek for "100"
kiloK3 1,000ThousandThousand Greek for "1000"
myria(My)4 10,000Ten-thousandTen-thousand Greek for "10000"
megaM6 1,000,000MillionMillion Greek for "mighty"
gigaG9 1,000,000,000BillionMilliard Greek for "giant"
teraT12 1,000,000,000,000TrillionBillion Greek for "monster"
petaP15 1,000,000,000,000,000QuadrillionBilliard Greek for "5", n removed
exaE18 1,000,000,000,000,000,000QuintillionTrillion Greek for "6", h removed
zettaZ21 1,000,000,000,000,000,000,000SextillionTrilliard Greek letter zeta, Italian "setta"
yottaY24 1,000,000,000,000,000,000,000,000SeptillionQuadrillion Greek letter iota, Italian "otta"

A note on the naming of numbers over 999,999,999 and numbers less than .000,001:


llengthmeterm distance traveled by light in absolute vacuum in 1/299,792,458 s.
mmasskilogramKg 1 cubic decimeter of water @ 277K
ttimeseconds 9,192,631,770 periods of two hyperfine levels, ground state Cs-133, at rest, 0 K, zero magnetic field.
Ielectric currentampereA current producing 200 nN between two straight || conductors 1 m apart in vacuum
TtemperaturekelvinK absolute 0, 273.16 K = triple point of water

luminous intensitycandelacd radiation of frequency 540 * 1012 Hz of 1/683 W/sr
θplane angleradianrad circle / 2 / pi
ψsolid anglesteradiansr 1 / 4 / pi sphere
clightspeedlight secondm / s lightspeed in vacuum


FforcenewtonNKg * m / s2; F = m * a
ppressurepascalPaKg * m / s
Eenergy, work, heatjouleJN * m
Ppower, radiant fluxwattWJ / s
QchargecoulombCA * s
Velectromotive forcevoltVW / A
CcapacitancefaradFC / V

elastancedarafF-11 / F
IinductancehenryHV * s / A = Wb / A

reluctanceyrnehH-11 / H
RresistanceohmΩV / A
XreactanceohmΩV / A, 90 degree phase
ZimpedanceohmΩV / A, any angle
Gconductancesiemens (mho)SA / V
BsusceptancesiemensSA / V, 90 degree phase
YadmittancesiemensSA / V, any angle
Mmagnetic fluxweberWbV * s
Bmagnetic flux densityteslaTWb / m2

luminous fluxlumenlmcd * sr
iilluminanceluxlxlm / m2
ractivity (radiation)becquerelBqcounts / s
ddosegrayGyJ / Kg
λwavelengthmetermlambda = c / f
ttimeminutemin60 s
ttimehourh60 min = 3600 s
ttimedaymin24 h = 86400 s
θangledegreedeg or o pi / 180 * rad
θangleminute'1 / 60 * deg
θanglesecond"1 / 3600 * deg
θanglegradientgrad pi / 200 * rad
mmasstonnet1 Mg
Aareaarea100 m2
AareahectareHa10000 m2

chemical amountmolemol1 g * AMU


aaccelerationm / s2
αangular accelerationrad / s2
νangular velocityrad / s2
Cconcentrationmol / m3
dIcurrent densityA / m2
ddensity (mass)Kg / m3
dQcharge densityC / m3
eelectric field strengthV / m
ηelectric flux densityC / m2
dEenergy densityJ / m2
Ηentropy, heat capacityJ / K
ιirradiance, heat flux densityW / m2
Lluminancecd / m2
mmagnetic field strengthA / m
Emolmolar energyJ / mol
Ηmolαmolar heat capacity, entropyJ / mol / K
mmomentumN * m / s
μpermeabilityH / m
ppermittivityF / m
rradianceW / m2 / sr
Iradiant intensityW / sr
Hspecific heat capacityJ / Kg / K
Espspecific energyJ / Kg
Hspecific entropyJ / Kg / K
Vspspecific volumem3 / Kg
Tsurface tensionN / m
TtemperatureoC: T - 273.15 (from K)
TtemperatureoF: 1.8 * T - 459.67 (from K)
tcthermal conductivityW / m / K
ΤtorqueN * m
vvelocitym / s>

dynamic viscosityPa * s

kinematic viscositym2 / s
nwave number1 / m



  1. Converting to or from SI units in the wrong direction
  2. Confusing mass and weight, and the units for each
  3. Mixing up Short Scale numbering with Long Scale numbering
  4. Confusing milli, micro, and mega
  5. Confusing force with pressure
  6. Confusing heat with temperature
  7. Using non-SI units
  8. Forgetting to square or cube the units when squaring or cubing the amount
  9. 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:

dekalike the company Decca
decias in decimal
centias in sentiment
kilokill-o (not keel-o)
millias in military
megaas in megaphone
microas in microphone
gigajigga (not gigga)
nanonan-no (a as in ant)
teraas in terrace
petaas in petal
femtofem-toe (as in feminine)
attoas in anatomy
zeptozep-toe (think of a Marx brother)
yottarhymes with gotta

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:

  1. 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.
  2. 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.
  3. 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 (Meter-Kilogram-Second) standard unit of mass.
  4. 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.
  5. The dyne is the CGS (Centimeter-Gram-Second) unit of force. It is equal to one hundred-thousandth of a newton.
  6. 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.
  7. The unit of mass in the English FPS (Foot-Pound-Second) system is the slug. It is not used very often. One slug is 14.59 kilograms.
  8. 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.
  9. 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.
  10. Many experimenters confuse mass and weight. I once "repaired" a program that asked for body mass in pounds.
  11. 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 gram-equivalent or the pfund. Both are the amount of force exerted by earth gravity on a mass of 1 gram.

  12. Many makers of exercise equipment calibrate the tension dial in pounds, then put a kilogram scale alongside. Again, the newton is the correct unit.
  13. 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?)
  14. The following are units of pressure, with the number of pascals in each:

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:

  1. The joule is the MKS unit of energy, work, and heat. It is one newton meter.
  2. 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.
  3. The erg is the CGS unit of energy. It is one ten-millionth of a joule.
  4. A kilowatt hour is exactly 3,600,000 joules (3.6 megajoules).
  5. A foot pound is 1.356 joules.
  6. A BTU (British Thermal Unit) is 1.0548 kilojoules.
  7. A gram calorie is 4.185 joules.
  8. A kilogram calorie is 4.185 kilojoules. (These are the food calories)
  9. A horsepower second is 746 joules.
  10. A horsepower hour is 2.686 megajoules.
  11. A metric horsepower hour is 2.723 megajoules.
  12. I don't know what to do with the quad (1 quadrillion barrels of oil). Which quadrillion is it: Long Scale or Short Scale?
  13. 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:

  1. 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.
  2. 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 newton-meters. Since a newton-meter is a joule, the work is expressed in a derivation, joules.
  3. When multiplying two values in like units, square the units of the answer. Example: Area=length*height. 10 meters * 2 meters = 20 square meters.
  4. 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.
  5. 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.
  6. When raising a value to a power, raise the units to that power.
  7. A mean or standard deviation has the same units of measure as the raw data do.
  8. A variance should be reported in the square of the units the raw data are sampled in.
  9. When integrating a measurement over time, multiply the unit of time by the measurement's units.
  10. When integrating a measurement over another variable, multiply its unit by the measurement's units.
  11. When differentiating a measurement with respect to time, divide the measurement's units by the unit of time.
  12. When differentiating a measurement with respect to another variable, divide the measurement's units by those of the other variable.
  13. When multiplying by a conversion factor, substitute the new unit of measure for the old one.
  14. 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:

  1. 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.
  2. 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.
  3. Heat is measured using the measures of energy given in another section above.

There are 4 temperature scales. Here are their properties:

Zero point (base value)coldest dayabsolute 0absolute 0 water freezes
100 offset pointhottest day

water boils
degree size100 offsetFahrenheit degreeCelsius degree 100 offset point
purposeweatherproportionmetric proportionwater standard
conversionTF = TR - 459.67 TR = TF + 459.67 TK = TC + 273.1 TC = TK - 273.1

TF = 9 / 5 * TC + 32 TR = 9 / 5 * TK TK = 5 / 9 * TR TC = 5 * (TF - 32) / 9

Here is a list of obsolete measures (minus the ones already mentioned), and standard equivalents: