# Ground Distance Calculations Used in Map Research, page 1

## Calculating Ground Distance from Topographic Map with 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 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 scale of 1:50,000. On this map, I measure the distance from the homestead to the road junction as 2.5 cm. To find the ground distance in the real world, I must use the map's Rate scale to convert map distance to ground distance. I invert the Rate scale, so the units will cancel properly. Once I multiply the map distance by the scale, I convert the ground distance to units suitable for ground measurement from centimeters to meters.

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

if

then:

where:
RF - Representative Fraction scale of the map,
A (cm) - ground distance corresponding to 1 cm on a 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:

| Calculating Ground Distance from Map with RF/Ratio Scale | Calculating Ground Distance from Map with Lexical Scale |
| Calculating Ground Distance from Map with Bar Scale | Next >

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