Converting Between Scale Types of Historic & Topographic Maps, page 1

Converting Bar Scale to Representative Fraction (RF)/Ratio Scale

English and Metric Measures of Length to use:

1 inch (in) = 2.54 centimeters
1 centimeter (cm) = 0.39 inch
1 foot (ft) = 12 inches = 30.5 centimeters = 0.3 meter
1 yard (yd) = 36 inches = 3 feet = 91.44 centimeters = 0.9 meter
1 meter (m) = 100 centimeters = 39.37 inches = 3.28 feet = 1.09 yards
1 mile (mi) = 63,360 inches = 5,280 feet = 1,760 yards = 1.609 kilometers
1 nautical mile = 1,852 meters = 1.852 kilometers
1 kilometer (km) = 1,000 m = 100,000 cm = 1,094 yards = 0.6 mile

NOTE: When you carry out any calculation with fractions, make sure that all units in equation are cancelled correctly. If necessary, invert the RF for that purpose.

If the map that I am going to use for my research has a Bar Scale, I can easily determine the map's scale expressed in small units.

Historic Bar Scale with Compass

First, I take a measurement from the bar scale to determine the map distance that corresponds to a ground distance. By measuring with a compass or just a ruler, I find that 10 kilometers measures 2.5 cm.

Bar Scale in Kilometers & Miles

I use this relationship (2.5 cm to 10 km) for determining the map's scale which will show how many centimeters on the ground are represented by one cm on the map:

Convert Bar Scale to Representative Fraction (RF) of Map

or 1:400,000

1) A simple formula for converting Bar Scale to RF Scale in Metric units looks like this:

step 1:

Formula for Converting Bar Scale to Representative Fraction (RF) Scale of Map

step 2:

Formula for RF

where:
RF - Representative Fraction Scale of the map,
A (cm) - actual distance - a number of centimetres on the ground surface, represented by 1 centimetre (1 cm) on a map,
B (km) - value of one small incriment of a Bar Scale,
C (cm) - length of the "B" incriment measured on a Bar Scale.

2) A similar formula for converting Bar Scale to RF Scale in English units looks like this:

step 1:

Formula for Converting Bar Scale to RF Scale in English units

step 2:

Formula for RF in Inches

where:
RF - Representative Fraction Scale of the map,
A (inches) - actual distance - a number of inches on the ground surface, represented by 1 inch (or 1") on a map,
B (miles) - value of one small incriment of a Bar Scale,
C (inches) - length of the "B" incriment taken from a Bar Scale.



| Converting Bar Scale to RF/Ratio Scale | Converting RF/Ratio Scale to Lexical Scale |
| Converting Lexical Scale to RF/Ratio Scale | Next >

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