# Ground Distance Calculations Used in Map Research, page 2

## Calculating Ground Distance from Historic Map with Lexical 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 properly. If necessary, invert the Representative Fraction (RF) for that purpose. To obtain correct results, use appropriate units in the formula.

1) If I have a map with a lexical scale "1cm represents 500 metres", I use the same procedure as with the RF/Ratio scale. The only difference is that I have to use the units given in the lexical scale (e.g., 1 cm to 500 metres). I would have to measure the map distance in the same units (in this case, centimetres) to make my conversion easy.

The map distance from the homestead to the road junction is 2.5 cm. To find the ground distance, I must use the fraction - expression of lexical scale, 1 cm / 500 metres. Again I invert the fraction, so the units will cancel properly. Once I multiply the map distance by the scale, I obtain the actual ground distance:

The formula for calculating ground distance (expressed in metres) from Map with Lexical Scale looks like this:

if Lexical Scale = "1 cm represents A (meters)", then:

where:
A (meters) - ground distance corresponding to 1 cm on map,
C (cm) - map distance between two objects,
D (meters) - actual ground distance between two objects on the Earth.

2) To determine the ground distance expressed in kilometers, use this formula:

3) To determine the ground distance expressed in miles, use this formula:

4) To determine the ground distance expressed in feet, use this formula:

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