Converting Between Scale Types of Historic and 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.
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.
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:
or 1:400,000
1) A simple formula for converting Bar Scale to RF Scale in Metric units looks like this:
step 1:
step 2:
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:
step 2:
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.
