# Ground Distance Calculations Used in Map Research, page 3

## Calculating Ground Distance from Historic & Topographic Maps with Bar 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) Suppose I have a map with a bar scale showing 1 mile in 1/4 mile increments. The distance measurement between two homesteads is 3.5 inches on the map. I have to multiply this measurement by the map's scale to find the real ground distance expressed in miles. To determine the map's scale from the bar scale, I measure one 1/2 mile increment as 1.25 inches on a bar scale, and by using a fraction 1.25" / 0.5 mile, calculate the map 's lexical scale:

or "1 inch represents 0.4 mile"

To find the ground distance between the homesteads on the Earth, I invert the fraction "1 inch / 0.4 mile", so the units will cancel correctly, and multiply it by the map distance of 3.5 inches:

My formula for calculating ground distance (expressed in miles) from Map with Bar Scale looks like this:

where:
A (miles) - value of increment on Bar Scale,
B (inches) - length of incriment on Bar Scale,
C (inches) - map distance between two objects,
D (mile) - actual ground distance between two objects on the Earth.

2) To find the ground distance expressed in feet, use this formula:

3) To find the ground distance expressed in metres, use this formula:

4) To find the ground distance expressed in kilometres, use this formula:

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