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Guide to Map Scale

Three Forms of Scale Large & Small Scale How to Convert Scale Common Scales Determining Scale for Paper Size Finding Maps at a Particular Scale Arizona Topographical Maps

Background

This guide has been prepared to help the users of the Map Collection in understanding the concept of scale in cartography. Scale is defined as the ratio of the distance on a map to the corresponding distance on the surface the map represents.

Three forms of Scale (Scale is shown on maps in three ways):

Verbal Scale:

1 inch equals 16 miles

This example tells us that 1 inch on the map represents 16 miles on the surface of the Earth. This is the easiest scale to understand because it generally uses familiar units.

Graphic or Bar Scale:

______________________________________
_____16________0________16_________32_ miles

The Bar Scale is particularly important when enlarging or reducing maps by photocopy techniques because it changes with the map. If the Bar Scale is included in the photocopy, you will have an indication of the new scale.

Representative Fraction (RF) or Natural Scale:

1:1,000,000 (this is the same as 1/1,000,000)

The RF says that 1 of any measurement on the map equals 1 million of the same measurement on the original surface; for the example above 1 foot equals 1 million feet or 1 cm. equals 1,000,000 cm. This is the form of scale commonly used in the Map Collection. A good quality map should have both the RF and Bar Scales.

Large & Small Scale:

When we speak of large scale maps we are saying the RF is large, i.e. the RF's denominator is small. 1:10,000 and 1:62,500 maps are large scale. Small scale maps have a small RF. 1:500,000 and 1:1,000,000 maps are small scale.

How to Convert from one Form of Scale to Another:

Often when using cartographic materials it is useful to convert from one form of scale to another. If you have a good understanding of the concept of scale, the techniques are fairly simple. Here is an example of converting from Verbal Scale to RF. Remember, the RF has the same unit of measurement on both sides of the colon.

1 inch equals 10 miles 1 inch = 10 miles 1 inch = 10 miles x 12 inches/foot x 5280 feet/mile 1 inch = 10 x 63360 inches = 633,600 inches 1:633,600

To convert from RF to Verbal Scale you convert the fraction to familiar units of measurements; for example:

1:250,000 1 inch = 250,000 inches 1 inch = 250,000 inches [d] 12 inches/foot = 20,833.3 feet 1 inch = 20,833.3 feet [d] 5280 feet/mile = 4 miles or 1 inch = 250,000 [d] 63360 inches/mile = 4 miles 1 inch equals 4 miles

[Note: [d] = divided by]

Some Common Scales

Here is a list of RF scales commonly used in the Map Collection and their equivalent Verbal Scales.

  • 1:24,000 - 1 in. = .379 mi.
  • 1:250,000 - 1 in. = 4 mi.
  • 1:62,500 - 1 in. = .986 mi.
  • 1:500,000 - 1 in. = 7.891 mi.
  • 1:100,000 - 1 in. = 1.578 mi.
  • 1:1,000,000 - 1 in. = 15.783 mi.

How to Determine which Scale Map will fit on a Particular Size of Paper

At times map users need to calculate the scale of a map that will fit on a particular size of paper. To do this you first need to determine the dimensions of the area you want on the map and then relate that to the dimensions of the new sheet.

For example you want a map of Arizona on a 8 1/2 x 11 inch piece of paper. To allow for 1/2 inch margins the new sheet will then be 7 1/2 x 10 inches. Since Arizona's north-south dimension, 395 miles, is slightly longer than its east-west dimension, 340 miles, we will place the longer north-south dimension along the longer 10 inch dimension of the paper. The next step is to compute the scales for both dimensions of the State. The smaller of the two scales will be the one we need.

North-south East-west 10 in = 395 mi 7.5 in = 340 mi 10 in = 395 mi x 63360 in/mi 7.5 in = 340 mi x 63360 in/mi 10 in [d] 10 = 25027200 in [d] 10 7.5 in [d] 7.5 = 21542400 in [d] 7.5 1 in = 2502720 in 1 in = 2872320 in 1:2,502,720 1:2,872,320

[Note: [d] = divided by]

We therefore need a map of Arizona at a scale of 1:2,872,320 or less to place it on a 8 1/2 x 11 inch sheet of paper.

How to Find Maps at a Particular Scale

Maps cannot be located in the online catalog directly by scale. You need to look under the geographic area or under a thematic subject heading to see what maps are available. Map scales are given in the catalog in the RF form. A map series for a larger area may include the area you are interested in; so be sure to check for maps of larger areas such as countries or continents. For example, the entry for the 1:100,000 series topographic maps for Arizona may be found only under the heading "United States-maps, topographic". If you need assistance in locating a map at a particular scale please ask a staff member at the reference desk.

Topographic Maps for Arizona

Here is a list, from the largest scale to the smallest, of the various series of topographic maps available for Arizona.  Unless indicated, maps are located in the Map Collection.

  • 1:24,000. 7.5 Minute Series (Topographic). Reston, VA: U. S. Geological Survey, 1945 to present, app. 1971 sheets.
  • G4331s C2 1882 U6 (located on left side of compact shelving, row 1)
  • 1:50,000. Arizona 1:50,000 [15 Minute Series (Topographic)]. Washington, DC: Army Map Service and Defense Mapping Agency, 1947 to present, currently 72 sheets, coverage incomplete.  
  • G4330s 50 U5
  • 1:50,000. Arizona 1:50,000 [15 Minute Series (Topographic)]. Washington, DC: USGS and Defense Mapping Agency, 1978 to present, currently 63 sheets, coverage incomplete.
  • G4330s 50 G4
  • 1:62,500. 15 Minute Series (Topographic). Reston: USGS, 1910 to 1968, 306 sheets, coverage incomplete.
  • G4331s.C2 1882.U6 (located on left side of compact shelving, row 1)
  • 1:100,000. 30 x 60 Minute Series (Topographic). Reston: USGS, 1980 to present, 68 sheets.
  • G3700s.100.U5
  • 1:125,000. 30 Minute Series (Topographic). Reston: USGS, 1901 to 1939, 23 sheets, only partial coverage.
  • G4331s.C2 1882.U6 Special Colln.
  • 1:250,000. 60 Minute Series (Topographic). Reston, USGS, 1896 to 1900, 16 sheets, only partial coverage.
  • G4331s.C2 1882.U6 Special Colln.
  • 1:250,000. 1 x 2 Degree Series (Topographic). Reston: USGS, 1953 to present, 22 sheets, periodically revised.
  • G4050s.250.U5
  • 1:550,000. Arizona. Medford, OR: Allen Cartography, 1987, 1 sheet.
  • G4330. 1987.A4
  • 1:1,000,000. World (North America) 1:1,000,000. Reston: USGS, 1952, 4 sheets. G3200s.1,000.U51