There are two widely used measurement systems. Most of the world uses a system known as the metric system, or the International System, abbreviated SI, from Système Internationale, its name in French. The United States continues to use a system called U.S. customary measure, which derives from (and differs from) the British imperial series of weights and measures. From time to time, our government has taken steps to change from the customary system to the International System, but these efforts have had limited success. Metric measure is legal in the United States, but nearly everyone continues to use the customary system in everyday life. The International System is generally used in scientific pursuits and increasingly in international trade.
Length or Distance
U.S. customary system
| 1 foot (ft.) | = | 12 inches |
| 1 yard (yd.) | = | 3 feet = 36 inches |
| 1 rod (rd.) | = | 5.5 yards = 16.5 feet |
| 1 furlong (fur.) | = | 40 rods = 220 yards |
| = | 660 feet | |
| 1 mile (mi.) | = | 8 furlongs =1,760 yards |
| = | 5,280 feet |
An international nautical mile is 6,076.1155 feet.
International System The basic unit of length is the meter, which is slightly longer than the yard. Other units of length are decimal subdivisions or multiples of the meter.
| 1 decimeter (dm) | = | 10 | centimeters |
| = | 0 .1 | meter | |
| 1 centimeter (cm) | = | 0 .01 | meter |
| 1 millimeter (mm) | = | 0 .1 | centimeter |
| = | 0 .001 | meter | |
| 1 micrometer (µm) | = | 0 .001 | millimeter |
| = | 0 .0001 | centimeter | |
| = | 0 .000001 | meter | |
| 1 angstrom (Å) | = | 0 .0001 | micrometers |
| = | 0 .0000001 | milimeter | |
| 1 dekameter (dam) | = | 10 | meters |
| 1 hectometer (hm) | = | 10 | dekameters |
| = | 100 | meters | |
| 1 kilometer (km) | = | 10 | hectometers |
| = | 100 | dekameters | |
| = | 1,000 | meters |
Conversions In 1959 the relationship between between customary and international measures of length was officially defined as follows:
| 0.0254 meter (exactly) | = | 1 inch |
| 0.0245 meter x 12 | = | 0.3048 meter |
| = | 1 international foot |
This definition, which makes many conversions simple, defines a foot that is shorter (by about 6 parts in 10 million) than the survey foot, which had earlier been defined as exactly 1200/3937, or 0.3048006, meter.
Following the international foot standard, the major equivalents are as listed below:
| 1 in. | = | 2.54 cm = 0.0254 m |
| 1 ft. | = | 30.48 cm = .3048 m |
| 1 yd. | = | 91.44 cm = 0.9144 m |
| 1 mi. | = | 1,609.344 m = 1.609344 km |
| 1 cm | = | 0.3937 in. |
| 1 m | = | 1.093613 yd. = 3.28084 ft. |
| 1 km | = | 0.62137 mi. |
Area
U.S. customary system Areas are derived from lengths as follows:
| 1 square foot | = | 144 square inches |
| 1 square yard | = | 9 sq. ft. |
| 1 square rod (rd.2) | = | 30.25 square yards |
| = | 272.25 square feet | |
| 1 acre | = | 160 square rods |
| = | 4,840 square yards | |
| = | 43,560 sq. ft. | |
| 1 square mile | = | 640 acres |
| 1 section | = | 1 mile square |
| 1 township | = | 6 miles square |
| = | 36 square miles |
International System
| 1 sq. millimeter (mm2) | = | 1,000,000 sq. micrometers |
| 1 sq. centimeter (cm2) | = | 100 mm2 |
| 1 sq. decimeter (dm2) | = | 100 cm2 |
| 1 sq. meter (m2) | = | 10,000 cm2 |
| 1 are (a) | = | 100 m2 |
| 1 hectare (ha) | = | 100 ares |
| = | 10,000 m2 | |
| 1 sq kilometer (km2) | = | 100 hectares |
| = | 1,000,000 m2 |
Conversions 2
| 1 square inch | = | 6.4516 cm2 |
| 1 square foot | = | 929.0304 cm2 |
| = | 0.09290304 m2 | |
| 1 square yard | = | 8,361.2736 cm2 |
| = | 0.83612736 m2 | |
| 1 acre | = | 4,046.8564 m2 |
| = | 0.40468564 hectares | |
| 1 square mile | = | 2,589,988.11 m2 |
| = | 258.998811 hectares | |
| = | 2.58998811 km2 | |
| 1 cm 2 | = | 0.1550003 sq. in. |
| 1 m2 | = | 1,550.003 sq. in. |
| = | 10.763 91 sq. ft. | |
| = | 1.195990 sq. yds. | |
| 1 hectare | = | 107,639.1 sq. ft. |
| = | 11,959.90 sq. yd. | |
| = | 2.4710538 acres | |
| 1 km2 | = | 247.10538 acres |
| = | 0.3861006 sq. mi |
Cubic Measure
U.S. customary system
| 1 cu foot (ft.3) | = | 1,728 cubic inches (in.3) |
| 1 cubic yard (yd.3) | = | 27 cubic feet (ft.3) |
International System
| 1 cubic centimeter (cm3) | = | 1,000 cubic |
| millimeters (mm3) | ||
| 1 cubic decimeter (dm3) | = | 1,000 cubic |
| centimeters (cm3) | ||
| 1 cubic meter (m3) | = | 1,000 cubic |
| decimeters (dm3) | ||
| = | 1,000,000 cubic | |
| centimeters (cm3) |
Cubic centimeter is sometimes abbreviated cc and is used in fluid measure interchangeably with milliliter (ml).
Conversions
| 1 in.3 | = | 16.387064 cm3 |
| 1 ft. 3 | = | 28.316846592 cm3 |
| = | 0.028316847 cm3 | |
| 1 yd.3 | = | 764,554.857984 cm3 |
| = | 0.764554858 m3 | |
| 1 cm3 | = | 0.06102374 in.3 |
| 1 m3 | = | 61,023.74 in.3 |
| = | 35.31467 ft.3 | |
| = | 1.3 07951 yd.3 |
Fluid Volume
U.S. customary system A gallon is equal to 231 cubic inches of liquid or capacity.
| 1 tablespoon (tbs.) | = | 3 teaspoons (tsp.) |
| = | 0.5 fluid ounce (fl. oz). | |
| 1 cup | = | 8 fl. oz. |
| 1 pint (pt.) | = | 2 cups = 16 fl. oz. |
| 1 quart (qt.) | = | 2 pt.= 4 cups |
| = | 32 fl. oz. | |
| 1 gallon (gal.) | = | 4 qt. = 8 pt. = 16 cups |
| 1 bushel (bu.) | = | 8 gal. = 32 qt. |
International System Fluid-volume measurements are directly tied to cubic measure. One milliliter of fluid occupies a volume of 1 cubic centimeter. A liter of fluid (slightly more than the customary quart) occupies a volume of 1 cubic decimeter, or 1,000 cubic centimeters.
| 1 centiliter (cL) | = | 10 mililiters (mL) |
| 1 deciliter | = | 10 cL = 100 mL |
| 1 liter (L) | = | 10 dL = 1,000 mL |
| 1 dekaliter (daL) | = | 10 L |
| 1 hectoliter (hL) | = | 10 daL = 100 L |
| 1 kiloliter (kL) | = | 10 hL = 1,000 L |
Conversions
| 1 fluid ounce | = | 29.573528 mL = 0.02957 L |
| 1 cup | = | 236.588 mL = 0.236588 L |
| 1 pint | = | 473.176 mL = 0.473176 L |
| 1 quart | = | 946.3529 mL = 0.9463529 L |
| 1 gallon | = | 3,785.41 mL = 3.78541 L |
| 1 milliliter | = | 0.0338 fluid ounce |
| 1 liter | = | 33.814 fluid ounces |
| = | 4.2268 cups = 2.113 pints | |
| = | 1.0567 quarts = 0.264 gallon |
Mass and Weight
Mass is a measure of the quantity of matter in an object and does not vary with changes in altitude or in gravitational force (as on the moon or another planet). Weight, on the other hand, is a measure of the force of gravity on an object and so does change with altitude or gravitational force.
U.S. customary system In customary measure it is more common to measure weight than mass. The most common customary system of weight is avoirdupois:
| 1 pound (lb.) | = | 16 ounces (oz.) |
| 1 (short) hundred-weight (cwt.) | = | 100 lb. |
| 1 (short) ton | = | 20 hundredweight |
| = | 2,000 lb. | |
| 1 long hundred-weight | = | 112 lb. |
| 1 long ton | = | 2,240 lb. |
A different system called troy weight is used to weigh precious metals. In troy weight the ounce is slightly larger than in avoirdupois, but there are only 12 ounces to the troy pound.
International System Instead of weight, the International System uses measures of mass. The original basic unit was the gram, which was defined as the mass of 1 milliliter (= 1 cm3) of water at 4 degrees Celsius (about 39°F). Today the official measure of mass is a specific metal object defined as the standard kilogram.
| 1 centigram (cg) | = | 10 milligrams (mg) |
| 1 decigram (dg) | = | 10 cg = 100 mg |
| 1 gram (g) | = | 10 dg = 100 cg = 1,000 mg |
| 1 kilogram (kg) | = | 10 hectograms (hg) |
| = | 100 dekagrams (dag) | |
| = | 1,000 grams | |
| 1 metric ton (t) | = | 1,000 kg |
Conversions Since mass and weight are identical at standard conditions (sea level on Earth), grams and other International System units of mass are often used as measures of weight or converted into customary units of weight. Under standard conditions:
| 1 ounce | = | 28.3495 grams |
| 1 pound | = | 453.59 grams |
| = | 0.45359 kilogram | |
| 1 short ton | = | 907.18 kilograms |
| = | 0.907 metric ton | |
| 1 milligram | = | 0.000035 ounce |
| 1 gram | = | 0.03527 ounce |
| 1 kilogram | = | 35.27 ounces |
| = | 2.2046 pounds | |
| 1 metric ton | = | 2,204.6 pounds |
| = | 1.1023 short tons |
Temperature
U.S. customary system In the U.S, temperature is usually measured in degrees Fahrenheit: water freezes at 32°F and boils at 212°F. The basis of the Fahrenheit scale was 0°F, the coldest temperature that its originator, G. D. Fahrenheit (1686–1736), could obtain under laboratory conditions.
International System The Swedish astronomer Anders Celsius (1701–44) devised the temperature scale that bears his name in 1742. On the Celsius scale, water freezes at 0°C and boils at 100°C. Very low temperatures are measured on the kelvin scale, named for William Thomson, Baron Kelvin (1824–1907). It is also called the absolute scale because absolute zero—0°K (–273.15° C)—is the temperature at which no body can give up heat. The interval of a kelvin equals the interval of a degree Celsius.
Conversions
Fahrenheit to Celsius: Subtract 32 from the temperature and multiply the difference by 5; then divide the product by 9. The formula is: C = 
(F–32)
(F–32)Celsius to Fahrenheit: Multiply the temperature by 1.8 (or 
), then add 32. The formula is: F = 
C + 32
), then add 32. The formula is: F = C + 32Celsius to Kelvin: Add 273.15 to the temperature. The formula is: K= C + 273.15
Force, Work/Energy, Power
U.S. customary system The foot/pound/second system of reckoning includes the following units:
slug = mass to which a force of 1 poundal will give an acceleration of 1 foot per second per second (= approximately 32.17 lb.)
poundal = fundamental unit of force
foot-pound = work done when a force of 1 poundal produces a movement of 1 foot
foot-pound/second = unit of power equal to 1 foot/pound per second
Another common unit of power is horsepower, which is equal to 550 foot-pounds per second.
Thermal work or energy is often measured in British thermal units (Btu). One Btu is defined as the energy required to increase the temperature of 1 pound of water by 1 degree Fahrenheit. The Btu is equal to about 0.778 foot-pound.
International System In physics, compound measurements of force, work or energy, and power are essential. There are two parallel systems using International System units: the centimeter/gram/second system (cgs) is used for small measurements, and the meter/kilogram/second system (mks) is used for larger measurements. The mks system is the official one for SI. They are described below. Measurement of force
| cgs unit | dyne (dy) | Force required to accelerate a mass of 1 g 1 cm/s2 (cm/s2 means “centimeter per second per second”) |
| mks unit | newton (N) | Force required to accelerate a mass of 1 kg l m/s2 |
Measurement of work or energy
| cgs unit | erg | Dyne-centimeter, i.e., work done when a force of 1 dy produces a movement of 1 cm |
| mks unit | joule (j) | Newton-meter, i.e., work done when a force of 1 N produces a movement of 1 m (10,000,000 ergs) |
Heat energy is also measured using the calorie (cal), which is
defined as the energy required to increase the temperature of 1 cubic centimeter (1 ml) of water by 1 degree C. One calorie is equal to about 4.184 joules. The kilocalorie (Kcal or Cal) is equal to 1,000 calories and is the unit in which the energy values of food are measured. This more familiar unit, also commonly referred to as a Calorie, is equal to about 4,184 joules. Measurement of power
| cgs unit | erg/second | Rate of 1 erg per second |
| mks unit | watt (W) | Joule/second, i.e., a rate of 1 joule per second |
Conversions
Measurement of force
| 1 poundal | = | 13,889 dynes |
| = | 0.13889 newton | |
| 1 dyne | = | 0.000072 poundal |
| 1 newton | = | 7.2 poundals |
Measurement of work or energy
| 1 foot-pound | = | 1,356 joules |
| British thermal unit | = | 1,055 joules |
| = | 252 calories | |
| 1 joule | = | 0.0007374 ft.-lbs. |
| 1 calorie | = | 0.003968 Btu |
| 1 Kilocalorie | = | 3.968 Btu |
Measurement of power
| 1 foot-pound/second | = | 1.3564 watts |
| 1 horsepower | = | 746 watts |
| = | 0.746 kilowatt | |
| 1 watt | = | 0.73725 ft.-lb/sec. |
| = | 0.00134 horsepower | |
| 1 kilowatt | = | 737.25 ft.-lb./sec. |
| = | 1.34 horsepower |
Electrical Measure
Originally, the basic unit of quantity in electricity was the coulomb. A coulomb is equal to the passage of 6.25 x 1018 electrons past a given point in an electrical system.
The unit of electrical flow is the ampere, which is equal to a coulomb/second, i.e., the flow of 1 coulomb per second. The ampere is analogous in electrical measure to a unit of flow such as gallons-per-minute in physical measure. In SI, the ampere is taken as the basic unit.
The unit for measuring electrical potential energy is the volt, which is defined as 1 joule/ coulomb, i.e., 1 joule of energy per coulomb of electricity. The volt is analogous to a measure of pressure in a water system.
The unit for measuring electrical power is the watt as defined in the previous section. Power in watts (P) is the product of the electrical flow in amperes (I) and the potential electrical energy in volts (E):
P=IE
Since the watt is such a small unit for practical applications, the kilowatt (= 1,000 watts) is often used. A kilowatt-hour is the power of 1,000 watts over an hour’s time.
The unit for measuring electrical resistance is the ohm, which is the resistance offered by a circuit to the flow of 1 ampere being driven by the force of 1 volt. It is derived from Ohm’s law, which defines the relationship between flow or current (amperes), potential energy (volts), and resistance (ohms). It states that the current in amperes (I) is proportional to potential energy in volts (E) and inversely proportional to resistance in ohms (R). Thus, when voltage and resistance are known, amperage can be calculated by the simple formula
Roman Numerals
Invented by the ancient Romans as a mathematical system of representation in which the Roman letters I, V, X, L, C, D and M represent the numbers 1, 5, 10, 50, 100, 500 and 1000. A letter placed after another of equal or greater value increases the value of the letter, and a letter placed before another of greater value subtracts from the letter’s value, so that VI equals 6 and IV equals 4. A bar placed over a letter indicates that the value is multiplied by 1000. The number zero does not exist in the Roman method of counting. Roman numerals were commonly used in Europe until the 1200’s, when the system of Arabic numerals and mathematics which is now employed became the preferred scholarly method of counting.
| I = 1 | X = 10 | C = 100 |
| II = 2 | XX = 20 | CC = 200 |
| III = 3 | XXX = 30 | CCC= 300 |
| IV = 4 | XL = 40 | CD = 400 |
| V = 5 | L = 50 | D = 500 |
| VI = 6 | LX = 60 | DC = 600 |
| VII = 7 | LXX = 70 | DCC= 700 |
| VIII = 8 | LXXX = 80 | M = 1000 |
| IX = 9 | XC = 90 | MMD= 2,500 |
| X = 10 | C = 100 | XV=15,000 |