eLivermore.com - By Bill Nale

Contents
of this
Page

 Bill's Conversion Spreadsheet An Excel Spreadsheet Units of Measurement List of units of measure and their definition / equivalence. Prefixes Metric prefixes and symbols Unit Systems Brief description of several systems of units, including computer data Roman Numerals Explanation of Roman Numerals, and examples Notes References and links Conversion references and calculators.

Excel Spreadsheet to convert between units of:
Length, Area, Volume, Dry Volume, Mass/Weight, Power, Energy, Force, Temperature, Velocity/Speed, Acceleration, Time, and Data.

Most conversions are exact.  Conversion factors that are not exact are listed to around 15 significant digits in most cases.  The formulas are written in such a way as to make the conversion method and assumptions easily understood.  The conversion formulas may be copied from the spreadsheet for use elsewhere.  Excel has some conversion factors built in, but these are NOT used, so as to make the formula's generic, with known assumptions.

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Please let us know what you think / how you use this conversions page!!

Units of Measurement

 Length Area Volume Dry Volume Mass Power Energy Force Temperature Velocity Acceleration Time Data

Length

 Unit Equivalence Comments mil 0.001 inches 25.4 microns "milli-inch", or one one-thousandths of an inch. inch 1000 mils 1/12 foot 25.4 millimeters (2.54 centimeters) (exact) In 1959 the inch was set to be exactly 2.54 centimeters.  Prior to that, it was set at 39.37 inches per meter. The difference is only 0.0002%, or 2 parts per million.  The new definition is slightly smaller than the old definition.  See "US Survey" unit description below. foot 12 inches.  3 feet per yard, 5280 feet per mile yard 36 inches. mile 5280 feet 1.609344 kilometers (exact) Also called Statute mile nautical mile 1852 meters (exact) 6076.11549 feet  (approx) 1.150779448 miles (aprox) Used for air and sea travel. Average length of one minute of arc on a great circle of the earth. Note that this entry was corrected on 3/22/05 Furlong 1/8 mile, 220 yards 1/8 mile.  Normally used in horse racing. rod, pole, or perch 16.5 US Survey feet.  1/4 chain Used in Surveying chain, Gunter's Chain 66 US Survey feet Used in Surveying link 0.66 US Survey feet Used in Surveying Fathom 6.0 US Survey feet Used in Surveying Micron 1/1000,000 meter.  25.4 microns per mil Micro (10e-6) meters. Commonly used to measure features on a silicon chip millimeter 1/1000 meter.  25.4 millimeters per inch. centimeter 1/100 meter.  2.54 centimeters per inch.  39.37... inches (1000 / 25.4 is exact) Used where the inch is used in the English system.  Most rulers are labeled in centimeters, with millimeter marks between. meter 1000 millimeters, 100 centimeters. Standard unit of measure of the metric system.  Used where foot or yard is used in the English system. kilometer 1000 meters Metric equivalent of mile. light year 5.88333.. trillion miles 9.4683... trillion kilometers The distance that light travels in a year.  The exact value varies slightly mainly due to the definition of the year.  Some use 365.25 days, some use the more exact 365 days, 5 hours, 48 minutes and 46 seconds (used here) cubit 18 inches (common conversion) Biblical measurement, as the length from the elbow to the tip of the longest finger.  Generally considered about 18 inches. web reference: World English Bible Dictionary point Since 1886, the point has been defined as 0.3514598 millimeters, or about 1/72 inch. Used in typesetting and now very commonly used for computer text sizes. First used in 1737.

Area

 Unit Equivalence Comments Square Mils One 1,000,000th of a square inch (A mil is a 1000th of an inch). 645.16 Sq Microns (25.4 squared) Commonly used to measure silicon die are in an integrated circuit Square Inches 144 per squire foot 645.16 square millimeters (25.4 squared) Square Feet 144 square inches, 9 per square yard Square Yards 9 square feet. Sq Miles 27,878,400 square feet (5280*5280) 2.58998811 square kilometers Acres 640 acres per US Survey Square mile 43,560 US Survey Square Feet. See "US Survey" unit description below. Sq Microns One 1,000,000th of a square millimeter 0.001550003 Square Mils: 1 / (25.4 squared) Commonly used to measure silicon features on an integrated circuit Sq Millimeters One 1,000,000th of a square meter Sq Centimeters One 10,000th of a square meter Sq Meters 1,000,000 square millimeters 10.76391042 square feet (1000 / 25.4 / 12)^2) 1.195990046 square yards Sq Kilometers 1,000,000 square meters 0.386102159 square miles Hectares 10,000 square meters 2.47104393 acres Metric equivalent of acres.

Volume
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments Cubic Inches (ci) 16.387064 cubit centimeters (2.54 to the third) 1/1728 cubit feet The volume of 1 inch x 1 inch x 1 inch.  Commonly used to measure the displacement of automobile engines. Cubic Feet 1728 cubic inches 7.480519481 gallons 1/27 cubic yards 0.028316847 cubic meters The volume of 1 foot x 1 foot x 1 foot. Cubic Yards 27 cubic feet 0.764554858 cubit meters The volume of 1 yard x 1 yard x 1 yard. drop 76 drops per teaspoon Used in cooking dash 6 drops per dash Used in cooking teaspoon (tsp) 1/3 table spoon 1/6 fluid ounce Commonly used in cooking. tablespoon (tbsp) 3 teaspoons 1/2 fluid ounce Commonly used in cooking. Fluid Ounce 1/8 cup. 29.57352956 milliliters The fluid ounce is a unit of volume, not weight.  It is equal to 1/128 of a gallon.  Note that a fluid ounce of water does not weigh an ounce at standard temperature and pressure.  It weighs 1.04125 ounces. cup 8 fluid ounces 1/2 pint 1/4 quart Common liquid measure pint (liquid) 16 fluid ounces, 2 cups 1/2 quart, 1/8 gallon The volume of 1 pound of water. quart (liquid) 32 fluid ounces, 4 cups 2 pints, 1/4 gallon 0.946352946 liters Conversion factors to metric commonly use 231 cubic inches per gallon. gallon (US) 4 quarts 3.785411784 liters 231 cubic inches All calculations in and out of the English Fluid section are based on exactly 231 cubic inches per gallon.  It was based on the wine gallon.  A gallon of water weighs about 8.333 pounds at standard temperature and pressure. Imperial Gallon 4.54609 liters exactly 1.2009499..Gallons (US) Used in Canada and the UK. acre foot 325,853.3837 gallons Used to measure the water contained in a reservoir.  It is the amount of water which would be contained in one acre, one foot deep.  This calculation uses US Survey measurements for both the acre and the foot. cubic millimeter 1/1000 cc cubic centimeter (cc) 1000 cubic millimeters 1 milliliter 1/1000 liters 1/1,000,000 cubic meter 0.061023744 cubic inches cubic meter 1000 liters 1,000,000 cubic centimeters 35.31466672 cubic feet 1.307950619 cubic yards The volume of 1 meter x 1 meter x 1 meter. milliliters (ml) 1 cubic centimeter 1/1000 liter liters 1000 cubic centimeters 61.02374409 cubic inches 1.056688298 quarts 0.264172052 gallons equal to a cubic decimeter.

All calculations in and out of the English Fluid section are based on exactly 231 cubic inches per gallon.  This includes teaspoon, tablespoon, fluid ounce, cup, pint, quart, and gallon.

Dry Volume
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments pint (dry) 1.163647186 pints (fluid) (approx) 1/2 quart (dry) 33.6003125 cubic inches (exact) Used for produce, such as blueberries or strawberries quart (dry) 1.163647186 quarts (fluid) (approx) 2 pints (dry) 67.200625 cubic inches (exact) peck 8 quarts (dry) 1/4 bushel 537.605 cubic inches (exact) Not commonly used.  Made famous by pickled peppers. bushel 32 quarts (dry) 2150.42 cubic inches (exact) 35.23907 liters (approx) Used for produce, such as peaches. liter 1.816165874 pints (dry) 0.908082937 quarts (dry) The liter has the same definition for fluid and dry.

Mass
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments Grain 7000 grains per pound.  5760 grains per troy pound 0.06479891 grams Smallest unit in the English system. Ounce (av) 1/16 pound 28.349523125 grams Pound (lb) (av) 16 ounces.  7000 grains 453.59237 grams Ton 2000 pounds about 907.18474 kilograms Also called a short ton. Troy Ounce 1/12 troy pound, 1.097142857 ounces (av) 31.1034768 grams Used for measuring precious metals Troy Pound 12 troy ounces.  0.822857143 pounds (av) 373.2417216 grams Used for measuring precious metals milligram 1/1000 grams commonly used in nutrition. gram 1000 milligrams 1/1000 kilograms 0.035273962 ounces kilogram 1000 grams 2.204622622 pounds (av) Base unit in the SI system for mass.  The Kilogram is based on the international prototype of the kilogram. metric ton 1000 kilograms 1.102311311 tons (english)

av = avoirdupois

Power
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments watt 1/1000 Kilowatt Electrical equations:  W = E*I = E2/R = I2*R, where W = Watts, E = Volts, I = Current in Amps, and R = Resistance in ohms. kilowatt (KW) 1000 watts Horsepower (550ft-lb) 550 ft-lb per second 745.6998716 watts Originally defined by James Watt by determining that a horse would do 22,000 foot pounds of work per minute.  The horsepower was set at 1.5 times that, which is 33,000 foot pounds per minute, or 550 ft-lb per second. Horsepower (electric) 746 watts The current horsepower is generally defined to be 746 watts, exactly.  This is about 0.04% different than the 550ft-lb definition. BTUs per hour 0.29307107 watts 0.000392857 horsepower (electric) Common rating for furnaces and air conditioning. foot-pounds per second 1/550 Horsepower 1.355817948 watts The power required to lift one pound at one foot per second. ton (air conditioning) 12,000 BTUs per hour Used to measure air conditioning cooling capacity.  The amount of power required to melt a ton of ice in 24 hours.

Energy
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments erg 1/10,000,000 joule Used for very small energy meaurements. 1 dyne of mass moving through 1 cm. newton-meter 1 joule The energy required to cause a mass of one kilogram to move one meter. joule 1 watt second 1 newton-meter 0.238845897 calories (heat) watt-second 1 joule 1/3600 watt hours 1 watt for one second. watt hour 3600 joules 3.412141633 BTUs 1 watt for one hour. kilowatt hour (kWh) 1000 watt hours Used by utility companies to measure electrical energy consumed. Energy used by a 100 watt light bulb in 10 hours. calorie (heat) 4.1868 joules (exact) Energy required to raise one gram of water one degree Celsius. calorie (food) 1000 heat calories Used to measure energy in food. BTU 1055.055853 joules British Thermal Unit. therm (US) 100,000 BTU (BTU 59F for US) 29.30011111 kilowatt hours 105,480,400 joules A therm is defined as 100,000 BTUs, but the EC, US, and UK use slightly different BTU definitions. Used by natural gas industry.  It is equal to approximately the energy content of 100 cubic feet of natural gas. foot-pound 1.355817948 Joules Energy required to lift one pound by one foot

Force
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments ounce-force 1/16 pound-force Force experienced by one ounce mass at 1G (32.174 feet per second per second) pound-force 4.4482216152605 newtons (exact) 16 ounce-force Force experienced by one pound mass at 1G (32.174 feet per second per second) poundal 1 / 32.17404856 pounds-force Force required to accelerate one pound of mass at one foot per second per second dyne 1 / 100,000 newton newton 100,000 dynes 1 / 4.4482216152605 pound-force SI derived unit of force. Force required to accelerate one kilogram of mass at 1 meter per second per second. kilogram-force 9.80665 newtons (exact) Force experienced by one kilogram mass at 1G (9.80665 meters per second per second)

Temperature
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments Kelvin DegreesC + 273.15 0 = Absolute Zero.  273.15 = freezing point of water.  373.15 = boiling point of water.  Triple Point of water is 273.16. Degrees Celsius (DegreesF-32) / 9 * 5 K - 273.15 0 = Freezing point of water, 100 = boiling point of water.  Absolute Zero = -273.15   Triple Point of water is 0.01 Degrees Fahrenheit DegreesC / 5 * 9 + 32 32 = Freezing point of water, 212 = boiling point of water.  Absolute Zero = -459.67

Velocity
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments inches per second (ips) 1 / 12 feet per second 25.4 millimeters per second commonly used for tape speeds in tape recorders feet per second (fps) 12 inches per second 0.3048 meters per second (12*25.4/1000) miles per second 5280 feet per second. miles per hour (MPH) 1,4666667 feet per second 1 / 3600 miles per second 1.609344 kilometers per hour knot 1.150757576 miles per hour 1 nautical mile per hour Used in aircraft and ship speed, as well as wind speed. Furlongs per fortnight 1 / 2688 miles per hour 1 / 152.72727 inches per second Furlong = 1/8 mile, fortnight = 14 days This unit is quoted in jest when one is purposely being obscure. 1 Furlong per fortnight is approximately a snail's pace. meters per second 3.280839895. feet per second.  1 / 1000 kilometers per second 3.6 kilometers per hour kilometers per second 1000 meters per second 0.621371192 miles per second kilometers per hour 0.621371192 miles per hour c (speed of light) 299,792,458 meters per second exactly 186,282.3971 miles per second The meter is defined by this number

Acceleration
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments inches per second per second 1/12 feet per second per second .0254 meters per second per second feet per second per second 12 inches per second per second 0.681818182 miles per hour per second (3600 / 5280) miles per hour per second 1.466666667 feet per second per second (5280 / 3600) meters per second per second 1/1000 kilometers per second per second 3.280839895 feet per second per second. SI "Derived" unit. kilometers per second per second 1000 meters per second per second 0.621271192 miles per second per second kilometers per hour per second 1/3600 kilometers per second per second 0.621271192 miles per hour per second G (gravitational pull) 9.80665 meters per second per second (exact) 32.17404856 feet per second per second Gravitational pull on earth.

Time
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments picosecond (pS) 1 / 1,000,000,000,000 seconds (10-12) 1 / 1,000 nanoseconds common unit of time used to measure the delay of an electronic circuit in an IC. nanosecond (nS) 1 / 1,000,000,000 seconds (10-9) 1 / 1,000 microseconds microsecond (uS) 1 / 1,000,000 seconds (10-6) 1 / 1,000 milliseconds millisecond (mS) 1 / 1,000 seconds second 1/60th minute SI base unit of time. minute 60 seconds hour 60 minutes 3600 seconds day 24 hours week 7 days fortnight 14 days month 1/12 year.  Varies in length from 28 to 31 days. year normal year: 365 days, leap year, 366 days, average year: 365 days, 5 hours, 48 minutes, 46 seconds. Average year is sometimes listed as 365.25 days, but this is less accurate.

Data
Formulas for converting between each of these units can be found in Bill's Conversion Spreadsheet.

 Unit Equivalence Comments bit (b) 1/8 byte, 1/4 nibble A single "binary digit", taking on a value of 0 or 1. nibble 4 bits 4 bits.  A common grouping representing one hexadecimal digit. byte (B) 8 bits A byte is capable of holding a single text character.  It is the unit in which memory is generally measured. word varies, but often 16 bits A word is used in various ways.  In general it represents the natural size of the data used by a particular machine.  With this definition, it can be any size. A "word" often represents 16 bits (2 bytes).  "Quadword" is sometimes used for an 8 byte quantity.  Most memory DIMMs produce a quadword at a time. The term is not generally used to describe quantities of memory.  It is used more to describe data widths. kilobyte (kB) 1024 bytes 210. See note on memory below. megabyte (MB) 1,048,576 bytes 220 or 1024 * 1024 gigabyte (GB) 1,073,741,824 230 or 1024 * 1024 * 1024.  Disk drives define a gigabyte as 1,000,000,000 bytes.  See note below on this. terabyte (TB) 1,099,511,627,776 240 or 1024 * 1024 * 1024 * 1024

Binary vs. Decimal.  The same metric prefixes are used for data quantities as for other units, with slightly different meanings as can be seen above.  This often leads to a ton of confusion.  The decimal units are actually "official", but the binary units are used by convention.  The International System of Units (SI) downright frowns on the usage of the prefixes for binary units.  It suggested alternatives, which are borderline silly.

Memory chips are generally built in quantities of powers of 2 because that is the most efficient way for computers to address them.  When you buy a 256MB memory DIMM, the actual quantity of data is 256*220, or 256 x 1024 x 1024 bytes.  When a new technology of memory arrives, it is generally 2 or 4 times the size of the previous generation.  In-between sizes are not convenient, and not supported by computers.

Disk Drives:  There is no particular reason to build disk drives in powers of 2 quantities of data.  An individual sector on the disk is generally a power of 2, such as 1024 bytes, but the number of sectors on the disk has no particular need for any alignment.  In fact, on modern high density disks, the number of sectors per track varies, with more being on the outer tracks than the inner tracks.

Disk drives, by convention, use base 10 when specifying the data size.  Undoubtedly this convention was initiated by the marketing department.  An 80GB drive is 80,000,000,000 bytes (approximately) and not 85,899,345,920 bytes (80*1024*1024*1024).  The manufacturer would call the latter an 85G drive.  85G looks better on the box than 80G.

Microsoft Windows (including XP) uses the binary sizes when specifying file sizes and disk sizes.  I.E. 1KB=1024 bytes, 1MB = 1024*1024 bytes.  When displaying the properties of a disk drive, both the decimal and binary numbers are displayed, with the decimal being fully listed without prefixes.  For example a drive advertised as 60GB might be listed as:
Capacity:  60,003,868,672 bytes    55.8 GB.
The decimal number is the exact number of bytes.  It is slightly over 60 billion since they rarely are built to an exact decimal value.  The 55.8GB would be 55.8 * 230.  It is rounded to 3 significant digits.

This is why your 60G drive only shows up as 55.8GB.

Flash Memory is actually semiconductor memory, but often used like a disk drive.  It is commonly used by digital cameras, MP3 players, and USB "Flash Disks".  By convention, these use decimal sizes.  Compact Flash, Smart Media, Memory Stick, and Secure Digital are examples of flash memory cards.  Six more are probably being dreamed up as I type this.

Prefixes

 Factor Name Prefix Symbol Factor Name Prefix Symbol 1024 =  (103)8 septillion yotta Y 10-1 tenths deci d 1021 =  (103)7 sextillion zetta Z 10-2 hundreths centi c 1018 =  (103)6 quintillion exa E 10-3 =  (10-3)1 thousandths milli m 1015 =  (103)5 quadrillion peta P 10-6 =  (10-3)2 millionths micro µ 1012 =  (103)4 trillions tera T 10-9 =  (10-3)3 billionths nano n 109 =  (103)3 billions giga G 10-12 =  (10-3)4 trillionths pico p 106 =  (103)2 millions mega M 10-15 =  (10-3)5 quadrillionths femto f 103 =  (103)1 thousands kilo k 10-18 =  (10-3)6 quintillionths atto a 102 hundreds hecto h 10-21 =  (10-3)7 sextillionths zepto z 101 tens deka da 10-24 =  (10-3)8 septillionths yocto y

Symbols from yotta (Y) through mega (M) should be capitalized.  From Kilo (k) to yocto (y) are lower case.  Note that several (m, p, z, and y) have different meaning when upper vs lower case.
The symbol for micro is the greek letter "µ" (pronounced Mew).  Often a lower case "u" in used instead for simplicity.

Information for this table taken from the Guide for the use of the International System of Units from the National Institute of Standards and Technology.

See reference below for powers of ten far in excess of this list.

Unit systems

International System of Units (SI)

SI is the modern metric system, used throughout the world.  It is the official unit system for the United States, and required for use by federal agencies.  Details of this system can be found in the National Institute of Standards and Technology web site.  Reference below take you directly to the document.  The abbreviation is SI.

The system defines 7 base units, and additional derived units.  The base unites are:

 Base Quantity Name Symbol length meter m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K amount of a substance mole mol luminous intensity candela cd

MKS

The MKS system is what is used by SI.  It stands for meter, kilogram, second, as base units

CGS

Stands for centimeter, gram, second.  Generally used where small quantities are measured.

English System

The system in common use in the United States, but pretty much nowhere else.  Some of the units include:

 Base Quantity Name length inch, foot, yard, mile mass ounce, pound volume Fluid ounce, pint, quart, gallon power horsepower, BTU/hr time second, minute, hour temperature degrees Fahrenheit

avoirdupois

A system of weights used in the English system.  The common usage of ounce and pound uses avoirdupois measurements.

Troy

A system of weights used in the English system, generally for precious metals.

Roman Numerals

 Symbol Value I 1 V 5 X 10 L 50 C 100 D 500 M 1000 M 1000,000

 Decimal Roman Decimal Roman Decimal Roman Decimal Roman 1000 M 100 C 10 X 1 I 2000 MM 200 CC 20 XX 2 II 3000 MMM 300 CCC 30 XXX 3 III 400 CD 40 XL 4 IV 1800 MDCCC 500 D 50 L 5 V 1900 MCM 600 DC 60 LX 6 VI 1980 MCMLXXX 700 DCC 70 LXX 7 VII 1990 MCMXC 800 DCCC 80 LXXX 8 VIII 2004 MMIV 900 CM 90 XC 9 IX

I, X, C, and M are used in multiples, up to 3.
A lower denomination in front of a higher denomination subtracts the value.  I.E. IX subtracts 1 from 10.
An overbar multiplies by 1000.  Two overbars multiplies by 1,000,000

Notes

US Survey units.

In 1959 the inch was set to be exactly 2.54 centimeters.  Prior to that, it was set at 39.37 inches per meter. The difference is only 0.0002%, or 2 parts per million, with the new definition being slightly smaller.  The "US Survey" numbers are still officially used where measurements are derived by "geodetic surveys" within the United States.  Presumably this was done to avoid having the definition of land owned and traded change with the unit change, even though the difference amounts to 111 square feet per square mile, or 25 square inches per acre.

The International inch, foot, mile, etc. are used unless "US Survey" is specifically listed.

The Acre is only used as a unit of land, and is only defined in terms of "US Survey" measurements, being 43560 square US Survey feet, or 640 acres per US Survey Square mile.