Map Scale and Distance Calculations: Practical Examples
Map Scale and Distance Calculations
On a map with a scale of 1:200,000, the distance between two points is 87 mm. Calculate the actual distance on the ground:
1 mm —-> 200,000 mm
87 mm —-> x
x = 87 * 200,000 = 17,400,000 mm = 17.4 km
Expressed as a fraction, a 5 cm scale is equivalent to 20 km:
5 cm —-> 20 km
5 cm —-> 2,000,000 cm
1 cm —-> 400,000 cm. Therefore, the RSL (Representative Scale) is 1:400,000
Expressed as a fraction of English units, one inch on the scale equals 47 miles, where 63,360 inches are measured as one mile:
47 miles —-> x inches
1 mile —-> 63,360 inches
x = 47 * 63,360 = 2,977,920 inches. E = 1 inch / 2,977,920. RSL in inches.
The surface area of a farm on a plane at 1:5,000 is 40 mm2. Calculate the actual area expressed in hectares:
1 mm —-> 5 m
1 mm2 —-> 25 m2
40 mm2 —-> 1,000 m2. RSL = 0.1 ha
Calculate the surface area of a rectangular plot whose dimensions on a map at 1:8,000 are 5 mm and 8 mm:
1 —-> 8,000
5 —-> x
x = 5 * 8,000 mm = 40,000 mm = 40 m
1 —-> 8,000
8 —-> x
x = 8 * 8,000 mm = 64,000 mm = 64 m. S = l × L = 40 m * 64 m = 2,560 m2
On one level, there is a rectangle of 23 mm x 52 mm, representing a plot of 4,784 ca. Calculate E (the scale):
23 mm * 52 mm = 1,196 mm2 —-> 4,784 m2
1 mm2 —-> 4 m2
1 mm —-> 2 m. E = 1 / 2,000
On one level, there is a plot of 7,500 m2, represented by a figure whose surface area measures 300 cm2. Calculate E:
300 cm2 —-> 7,500 m2
1 cm2 —-> 25 m2
1 cm —-> 5 m. E = 1 / 500
On a scale of 1:2,000, there is a rectangular plot with legs measuring 23 mm and 52 mm. Calculate the actual area:
1 mm —-> 2,000 mm
1 mm —-> 2 m
23 mm —-> 46 m
52 mm —-> 104 m. S = 46 m * 104 m = 4,784 m2
On one level, there is a right triangle with legs measuring 56 mm and 81.5 mm. Calculate and draw the scale bar knowing that the triangle in 5,705 actually measures:
S = (81.5 mm * 56 mm) / 2 = 2,282 mm2
2,282 mm2 —-> 5,705 m2
1 mm2 —-> 2.5 m2
1 mm —-> 5 m. E = 1 / 5,000
The heights of two points are 638.7 m and 612.4 m. The slope between them is 25%. You want to know the distance between their representations on a plane at 1:2,000:
Difference in height = 638.7 m – 612.4 m = 26.3 m
100 —-> 25
x ——> 26.3
x = (26.3 * 100) / 25 = 105.2 m
1 mm —-> 2 m
x ——> 105.2 m. RSL x = 105.2 m / 2 m/mm = 52.6 mm
A slope has an inclination of 30°. Calculate the separation of their contours on a plane at 1:40,000 of equidistance 20 m:
tan(30°) = 20 / D, D = 20 * cot(30°) = 20 * √3 ≈ 34.6 m
1 mm —-> 40 m
x ———> 34.6 m; RSL = 34.6 m / 40 m/mm ≈ 0.87 mm
Calculate the slope between two points in two consecutive contours on a 1:25,000 scale map and equidistance 10 m, knowing that the distance between points is 14 mm:
1 mm —-> 25,000 mm
1 mm —-> 25 m
14 mm —> 14 * 25 m = 350 m
Slope calculation:
(Difference in height / Horizontal distance) * 100
(10 / 350) * 100 = 2.86%
Contours of a plane with dimensions 150 m and 162 m are separated by 48 mm in an area where the uniform slope of the terrain is 4%. Calculate the scale:
Difference in height = 162 m – 150 m = 12 m
4 —-> 100
12 —> x, x = (12 * 100) / 4 = 300 m
1 mm —-> z
48 mm —> 300 m, z = 300 m / 48 mm = 6.25 m/mm
1 mm —-> 6.25 m
1 mm —-> 6,250 mm, E = 1 / 6,250
In a plane with equal distance between contours of 10 m, the separation between two immediate contours is 5 mm. Calculate the scale:
Slope = (Vertical distance / Horizontal distance) * 100
x ——-> 10, x = (100 * 10) / 100 = 100
1 mm —-> z
5 mm —-> 100 m, z = 100 m / 5 mm = 20 m/mm
1 mm —-> 20 m
1 mm —-> 20,000 mm, E = 1 / 20,000
Calculate the equidistance curves on a 1:15,000 scale map with a separation between two consecutive curves of 8 mm, with the slope of 2.5%:
1 mm —-> 15,000 mm
1 mm —-> 15 m
8 mm —-> x, x = 8 * 15 m = 120 m
100 —-> 2.5
120 —-> RSL, RSL = (120 * 2.5) / 100 = 3 m