# Calculate the scale of a map in which the distance between two features

Calculate the scale of a map in which the distance between two

features

Coordinate Systems and Location.

Question 3: What continent is found at grid cell 35N?

A. The continent of Africa

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B. The continent of Australia

C. The continent of Europe

D. The continent of South America

Question 4: Looking at the map layers above, which layers would be most

likely acquired through the use of radar and satellites?

A. States and cities

B. Countries and Territories

C. Background

Collapse and uncheck INTRODUCTION.

GLOBAL PERSPECTIVE

Latitude and Longitude form a grid on the Earth’s surface, enabling us to determine

an absolute location for any given place or phenomenon.

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Expand GLOBAL PERSPECTIVE.

Turn on the latitude and longitude grid by selecting View > Grid, or by using

the keyboard shortcut CTRL + L. Mac users click + L.

Lines of latitude, or parallels, divide the globe at the Equator, and run parallel in

both the Northern and Southern Hemispheres (Figure 1). Locations in the Northern

Hemisphere are denoted with an N (or a positive number), while locations in the

Southern Hemisphere are denoted with an S (or a negative number). The parallel at

the Equator is 0°N or 0°S, and increases to 90°N (or +90) at the North Pole, and

90°S (or -90) at the South Pole.

Latitude (parallels)

Longitude (meridians)

Figure 1. Lines of latitude (parallels) and longitude (meridians) (Arbogast)

Double-click and select Prime Meridian.

Lines of longitude, or meridians, run from pole to pole. Along the Prime Meridian

(which runs through Greenwich, UK), the Earth is divided into Eastern and Western

Hemispheres. Locations in the Eastern Hemisphere are denoted with an E (or a

positive number), while locations in the Western Hemisphere are denoted with a W

(or a negative number). The Prime Meridian is 0°E or 0°W, and increases to toward

180°E (or +180) or 180°W (or -180).

Latitude and longitude are measured in degrees, minutes, and seconds. Similar to a

clock, where one hour equals 60 minutes, and one minute equals 60 seconds, each

degree of latitude or longitude can be divided into 60 minutes (60’) and each

minute of latitude or longitude can be further subdivided into 60 seconds (60”). For

example, the White House in Washington, DC is located at 38° 53’ 51” N, 77° 02’

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11” W. Latitude and longitude can also be measured in decimal degrees, or degrees

and decimal minutes, by converting the minutes and/or seconds into decimal

fractions. Cardinal directions (North, East, South and West) are replaced with

positive or negative signs. Therefore, the absolute location of the White House in

decimal degrees would be 38.8976, -77.0365.

Click Exit Street View in the top right corner of the Google Earth 3D viewer.

Change your units to degrees, minute and seconds. (Refer to the GETTING

STARTED lab module for directions on how to change latitude and longitude

units).

Double-click and select Location A.

Question 5: What are the latitude and longitude coordinates for Location A?

A. 51N, 114E

B. 114S, 51 E

C. 51S, 114W

D. 51N, 114W

Double-click and select Location B.

Question 6: What are the latitude and longitude coordinates for Location B?

A. 53N 6E

B. 6N, 53E

C. 53S, 6W

D. 53N, 6W

Question 7: Which is closer – the distance between Location A and the

Equator or the distance between Location B and the Equator?

A. Location A and the Equator

B. Location B and the Equator

C. Locations A and B are the same distance from the Equator

D. Cannot discern from the information provided

Question 8: Which is closer – the distance between Location A and the

Prime Meridian or the distance between Location B and the Prime Meridian?

A. Location A and the Prime Meridian

B. Location B and the Prime Meridian

C. Locations A and B are the same distance from the Prime Meridian

D. Cannot discern from the information provided

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Double-click and select Location C.

Question 9: What are the latitude and longitude coordinates for Location C?

A. 50N, 68S

B. 50N, 68W

C. 50S, 68E

D. 50S, 68W

Question 10: Which is farther– the distance between Location B and the

Equator or the distance between Location C and the Equator?

A. Location B and the Equator

B. Location C and the Equator

C. Locations B and C are the same distance from the Equator

D. Cannot discern from the information provided

Question 11: Which is farther – the distance between Location A and the

Prime Meridian or the distance between Location C and the Prime Meridian?

A. Location A and the Prime Meridian

B. Location C and the Prime Meridian

C. Locations A and C are the same distance from the Prime Meridian

D. Cannot discern from the information provided

Collapse and uncheck GLOBAL PERSPECTIVE.

Turn off the latitude/longitude grid. Press CTRL + L. Mac users press + L.

MAP SCALES

Map scale (or scale) is the ratio of the distance between two features or absolute

locations on the map and the distance between the same two features or absolute

locations on the ground. Maps should provide a scale to the user; typically, map

scales are shown in the bottom margin of the map.

Map scales are expressed in the following ways:

 Ratio  Representative fraction  Verbal scale (also called a lexical scale)

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 Bar scale (also called a scale bar, graphic scale, or graphical scale).

An example of each of these map scales is illustrated below.

Scale Expression

Ratio 1:12,000

Representative Fraction (RF) 1/12,000

Verbal 1 inch equals 1,000 feet

Scale Bar

Expand MAP SCALES and then double-click and select Boothbay Harbor

(Note: The topographic map might take a few seconds to display). To close the

citation, click the X in the top right corner of the window.

Question 12: How is the scale on this map expressed or presented (Hint:

look toward the bottom of the map image)?

A. Scale bar and RF

B. RF and Verbal

C. Verbal and Ratio

D. Scale Bar and Ratio

If you enlarge (zoom in) or reduce (zoom out) of the map, the scale of the image

changes, but the scales found the map do not. It is important to note only a bar

scale can be used to make distance calculations to a map that is enlarged or

reduced because it is the only map scale that remains correct if the map size

changes.

If a bar scale is not provided, it is important to know how to calculate distance. In

between two (or more) points.

To calculate scale, we will use the equation

S =

where:

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 S = scale

 d = distance between two features on the map

 D = distance between two feature on the ground

Whether using the metric system or the British/Imperial system, make sure that

you know the conversions between the units.

Metric Units

1 m = 100 cm

1 km = 1000 m

1 km = 100,000 cm

British/Imperial Units

1 ft = 12 in

1 mile = 5,280 ft

1 mile = 63,360 in

Now for an example that will use the scale equation (S =

) and British/Imperial

units.

Example 1: Two buildings are 8 inches apart on a map (d). The same buildings

are 16,000 feet apart on the ground (D). Calculate the scale of the map.

To calculate the scale, first let’s make sure that are units are the same. Currently,

the map units (d) are in inches and the ground units (D) are in feet. Therefore, we

will convert feet to inches.

We know there are 12 inches in a foot, so we can multiply D by 12 to convert the

distance on the ground from feet (ft) to inches (in).

D = 16,000 ft.

D = 16,000 ft. x 12 inches/ft. = 192,000 inches

Now we can use the equation

S =

S =

Because we are dividing the same unit in the numerator as the denominator, the

units (inches) cancel out.

S =

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Now we need to simplify the equation so that our numerator is a 1. We can do this

by dividing both the numerator and the denominator by 8.

S =

S =

This ratio can also be written as 1:24,000.

Example 2: Calculate the scale of a map in which the distance between two

features is 6” on the map (d) and 12 miles on the ground (D).

Again, to calculate the scale, we first need to convert distances into the same units.

There are 63,360 inches in a mile. If we multiply 12 miles by 63,360 we can

convert D into inches

D = 12 miles
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