# Calculations Used in Map Research, page 3

## Calculating Area from Maps with RF/Ratio Scale

### English and Metric Area Measures to use:

1 square inch (sq in, in²) = 6.45 square centimetres (cm²)
1 square centimeter (cm²) = 0.15 in²
1 square foot (sq ft, ft²) = 144 in² = 930.25 cm² = 0.0929 m² = 1/9 sq yd (yd²)
1 square yard (sq yd, yd²) = 1,296 in² = 9 ft² = 8,361.27 cm² = 0.836 m²
1 square meter (m²) = 10,000 cm² = 1,550.003 in² = 10.763 911 ft² = 1.195 990 sq yd (yd²)
1 acre (ac) = 4,842 yd² = 43,560 ft² (66 feet × 660 feet) = 0.0015625 mi² = 0.40468 ha = 4,046.87261 m²
1 hectare (ha) = 10,000 m² = 2.47 acres
1 square chain (sq ch, ch²) = 66 ft(US) × 66 ft(US) = 4,356 ft² = 1/10 ac
1 square mile (sq mi, mi²) = 640 acres = 4,014,489,600 in² = 27,878,400 ft² = 3,097,600 yd² = 2,56 km²
1 square kilometre (km²) = 1,000,000 m² = 100 ha = 0.38610 sq mi

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 following equations.

Area must be expressed either in areal units - hectare (ha) and acre (ac), or in distance units squared - square inches (in²), square yards (yd²), cm², mi², and so on. One must therefore use squared conversion factors when determining area from map measurements.

### In English Units

For example, a rectangular piece of property on a map is measured 1.5 inches by 2 inches. The map is at a scale of 1:25,000. The area of the parcel on the map is

1.5 in x 2 in = 3 in²

on the ground.

Since this is a large number, you might want to convert it to other units. As there are 4,842 yd² per acre, the area is also

As there are 3,097,600 square yards (yd²) per square mile (mi²), the area is also

### In Metric Units

For example, a rectangular piece of property on a map is measured 2 cm by 3 cm. The map is at a scale of 1:25,000. The area of the parcel on the map is

2 cm x 3 cm = 6 cm²

on the ground.

Since this is a large number, you might want to convert it to other units. As there are (1,000 m)² = 1,000,000 m² per square kilometer (km²), the area is also

As there are 10,000 m² per hectare (ha), the area is also

Another way to determine the area from map measurements is to convert the distance dimensions to real-world distances first, and then multiply them to find the area.

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