Posts Tagged ‘formulas’

Map Scale Calculator Tools? (Kelso)

Monday, December 15th, 2008

Do you know of any good tools for converting a map’s graphic scale bar measurement to a representational fraction (RF)? Please share them! We often think of maps as 1:24,000 or 1:1,000,000 natural scale but more often than not a scale bar is the only indication of scale we have on a map. How to convert that back to the more familiar representational fraction?

What are the features and interface you’d like to see for such a tool?

The best that I’ve been able to dig up is:

From Oregon State University Library
http://oregonstate.edu/~reeset/html/scale.html

Type in the number of units per distance (or distance per unit) and it’ll return the relational fraction. It does not do a very good job allowing you to type in both the units and the distance as variable. I hardly ever find scale bars on maps that are exactly an inch long. So involves some pre-math to get this tool to work.

Screenshots below:

This University of Texas site does the opposite:
http://www.beg.utexas.edu/GIS/tools/scale2.htm

Enter the representational fraction of the map and get “1 inch = X miles” verbal statements where the left and right terms do not have the same units.

Then there is the general problem of converting between map units.

Google provides the most ready answer:
Type in “convert 12 miles to km” and it will return the conversion.

The same OSU site also has a version:

Read more about map scales.

Some example map scales and worked formula examples from Richard Layton (source).

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

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
10 in = 395 mi
10 in = 395 mi x 63360 in/mi
10 in [d] 10 = 25027200 in [d] 10
1 in = 2502720 in
1:2,502,720

East-west
7.5 in = 340 mi
7.5 in = 340 mi x 63360 in/mi
7.5 in [d] 7.5 = 21542400 in [d] 7.5
1 in = 2872320 in
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 an 8 1/2 x 11 inch sheet of paper.

Scale

Miles/inch

Line
Width on Ground*

Examples

1:2,000,000

~32

2000’

USGS
Nation-wide maps

1:1,000,000

~16

1000’

National and
state maps

1:500,000

~8

500’

State or
regional maps

1:250,000

~4

250’

US Army Map
Series

1:100,000

~1.6

100’

USGS 30′
quads

1:62,500

5208 feet

62.5’

USGS 15′
quads

1:24,000

2000 feet

24’

USGS 7′
quads

1:15,840

1320 feet

15.84’

Soils

1:9,600

800 feet

Aerial
photos

*Approximate real width on ground of a pencil line on a map – harder pencils give a finer line

1:2,000,000 to about 1:250,000 are SMALL-scale maps. Items on these maps appear small (e.g. a county on a 1:2,000,000 map is much smaller than on a 1:100,000 map).

1:24,000 on towards 1:9,600 are LARGE-scale maps. Items on these maps appear larger. 1:100,000 are
pretty much in the middle – intermediate scale.