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EARTH CURVATURE CALCULATOR

by Eldøy Projects

Accurately calculate the curvature you are supposed to see on the ball Earth.

Distance: Kilometers Miles Calculate


Distance Curvature 1 km 0.00008 km = 0.08 meters 2 km 0.00031 km = 0.31 meters 5
km 0.00196 km = 1.96 meters 10 km 0.00785 km = 7.85 meters 20 km 0.03139 km =
31.39 meters 50 km 0.19620 km = 196.20 meters 100 km 0.78479 km = 784.79 meters
200 km 3.13897 km = 3138.97 meters 500 km 19.6101 km = 19610.09 meters 1000 km
78.3196 km = 78319.62 meters

Distance Curvature 1 mile 0.00013 miles = 0.67 feet 2 miles 0.00051 miles = 2.67
feet 5 miles 0.00316 miles = 16.67 feet 10 miles 0.01263 miles = 66.69 feet 20
miles 0.05052 miles = 266.75 feet 50 miles 0.31575 miles = 1667.17 feet 100
miles 1.26296 miles = 6668.41 feet 200 miles 5.05102 miles = 26669.37 feet 500
miles 31.5336 miles = 166497.53 feet 1000 miles 125.632 miles = 663337.65 feet


EXPLANATION:

The Earth's radius (r) is 6371 km or 3959 miles, based on numbers from
Wikipedia,
which gives a circumference (c)of c = 2 * π * r = 40 030 km

We wish to find the height (h) which is the drop in curvature over the distance
(d)

Using the circumference we find that 1 kilometer has the angle
360° / 40 030 km = 0.009°. The angle (a) is then a = 0.009° * distance (d)

The derived formula h = r * (1 - cos a) is accurate for any distance (d)



Source code

Note: Using the formula 8 times the distance in miles squared is not accurate
for long distances but is fine for practical use.

Made by Eldøy Projects, Oslo, Norway