Units of Measure A. Measurement Magnitudes of measurements are typically given in terms of a specific unit. In surveying, the most commonly used units define quantities of length (or distance), area, volume, and horizontal or vertical angles. The two systems used for specifying units of measure are the English and metric systems. Units in the English system are historical units of measurement used in medieval England which evolved from the Anglo-Saxon and Roman systems. The metric system is a decimalized system of measurement developed in France in late 18th century. Since the metric system is almost universally used, it is often referred to as the International System of Units and abbreviated SI. 1. Length a. English Units The basic units for length or distance measurements in the English system are the inch, foot, yard, and mile. Other units of length also include the rod, furlong, and chain.

b. Metric Units The basic unit of length in the SI system is the meter. The meter was originally intended to be one ten-millionth of the distance from the Equator to the North Pole (at sea level). The meter has since been redefined as the distance travelled by light in a vacuum in 1/299,792,458 seconds (i.e. the speed of light in a vacuum is 299,792,458 m/sec). Subdivisions of the meter are the millimeter, centimeter, and the decimeter, while multiples of meters include the decameter, hectometer, and kilometer.

Units of Measurement c. English to Metric Conversions There are two different conversions to relate the foot and the meter. In 1893, the United States officially defined a meter as 39.37 inches. Under this standard, the foot was equal to 12/39.37 m (approximately 0.3048 m). In 1959, a new standard was adopted that defined an inch equal to 2.54 cm. Under this standard, the foot was equal to exactly 0.3048 m. The older standard is now referred to as the U.S. survey foot, while the new standard is referred to as the international foot. All WYDOT surveys use the U.S. survey foot definition.

2. Area a. English Units In the English system, areas are typically given in square feet or square yards. For larger area measurements, the acre or square mile may be used. Historically, the acre was originally established as an area one furlong in length and four rods in width. Laying out ten of these acres side by side is a square furlong (10 acres). Since a mile is eight furlongs in length, there are exactly 640 acres in a square mile. A survey township is a square unit of land six miles on a side that conforms to meridians and parallels. Each township is further divided into 36 one-square mile sections. Because some of the townships have boundaries designed to correct for the convergence of meridian lines, not all townships and their sections are exactly square.

G-2

Revised November, 2011

Appendix F b. Metric Units Areas in the metric system are given is square meters while larger measurements are given in hectares.

c. English to Metric Conversions

3. Volume a. English Units Volumes in the English system are typically given in cubic feet or cubic yards. For larger volumes, such as the quantity of water in a reservoir, the acre-foot unit is used. It is equivalent to the area of an acre having a depth of 1 foot.

b. Metric Units Volumes in the metric system are given in cubic meters.

c. English to Metric Conversions

4. Mass The mass of an object is often referred to as its weight though these are different concepts and quantities. Mass refers to the amount of matter in an object, whereas weight refers to the Revised November, 2011

G-3

Units of Measurement force experienced by an object due to gravity. In other words, an object with a specific mass will weigh more on the Earth than the moon. a. English Units The avoirdupois pound is the primary unit of mass in the English system. Avoirdupois is a system of weight based on the 16 ounces per pound rather than the 12 ounces per pound in the troy system of weight.

b. Metric Units The kilogram is the unit of mass in the metric system.

c. English to Metric Conversions The avoirdupois pound is defined as exactly 0.45359237 kg.

5. Angular Measurement In geometry, any horizontal or vertical angle is measured in degrees. These angles may be given in decimal degrees or degrees, minutes, and seconds.

The radian is another unit of measure for angles. By definition, a full circle has 2 or 360 degrees.

G-4

radians

Revised November, 2011

Appendix F 6. Temperature a. English Units The Fahrenheit scale, or degrees Fahrenheit (°F), is used in the United States to measure temperature. On the Fahrenheit scale, the freezing point of water is 32°F while the boiling point is 212°F at standard atmospheric pressure. The boiling and freezing points of water are exactly 180 degrees apart, making each degree Fahrenheit 1/180 of the interval between the two points. b. Metric Units The Celsius scale, or degrees Celsius (°C), is used the metric system to measure temperature. On the Celsius scale, the freezing point of water is 0°C while the boiling point is 100°C at standard atmospheric pressure. The boiling and freezing points of water are exactly 100 degrees apart, making each degree Celsius 1/100 of the interval between the two points. The Fahrenheit and Celsius scales converge at -40° (i.e. -40°F and -40°C are the same temperature).

c. English to Metric Conversions

7. Pressure Atmospheric pressure is the force per unit area exerted against a surface by the weight of the Earth’s atmosphere above that surface. Because there is less overlying atmospheric mass as elevation increases, pressure decreases with increasing elevation. The standard atmosphere (atm) is an international reference for pressure. a. English Units In the English system, air pressure is typically measured in inches mercury (inHg).

b. Metric Units Air pressure is measured in millimeters mercury (mmHg) or millibars (mbars) in the metric system, but may also be measured in pascals or kilopascals.

Revised November, 2011

G-5

Units of Measurement c. English to Metric Conversions

G-6

Revised November, 2011