# Converting Between Scale Types of Historic & Modern Maps, page 3

## Converting Lexical 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.

### 1) IN ENGLISH UNITS

Converting Lexical Scale "1 inch represents 3.9 miles" to Representative Fraction (RF) & Ratio:

First, I write the lexical scale as a fraction - 1 inch (on the map) / 3.9 miles (on the ground), then I convert the length unit mile to inches because the RF shows how many inches on the ground are represented by 1 inch on a map.

I should round the denominator of the resulting fraction so that it does not imply more accuracy than the original precision warranted. So the resulting fraction is 1/250,000 corresponding to a ratio 1:250,000.

Because 1 mile = 5,280 feet x 12 inches = 63,360 inches, I can write the formula for converting Lexical Scale to the RF/Ratio Scale in English units this way:

if Lexical Scale = "1 inch represents A (miles)", then:

where: A (miles) - distance on the ground represented by 1 inch on a map.

### 2) IN METRIC UNITS

Converting Lexical Scale "6 cm represent 1.5 km" to RF/Ratio:

As in a previous case, I express the lexical expression as a fraction - "6 cm / 1.5 km" and convert kilometres to centimeters, so that the numerator has a "1" in a resulting fraction, and both numerator and denominator have the same units:

By solving this equation, I converted a lexical expression "6 cm represent 1.5 km" to a scale as a RF - 1/25,000, or as a Ratio - 1:25,000.

Knowing that 1 km = 100,000 centimetres, I can express the formula for determining the map scale from just a verbal expression in metric units:

if Lexical Scale = "B (cm) represent C (km)", then:

and:

where:
RF - Representative Fraction Scale of the map,
A (cm) - actual distance - a number of centimetres on the ground, represented by 1 centimetre on a map,
B (cm) - distance on a map,
C (km) - distance on the ground represented by "B" on a map.

And the formula for converting Lexical Scale "1 cm represents A km" to RF & Ratio would look like this:

if "1 cm represents A (km)", then:

where A (km) - distance on the ground represented by 1 cm on a map.

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