Earth Curvature Calculator

by NyttNorge.com

Accurately calculate the curvature you are supposed to see on the ball Earth. Distance: 0.02476 miles = 130.71 feet

DistanceCurvature
1 mile0.00013 miles = 0.67 feet
2 miles0.00051 miles = 2.67 feet
5 miles0.00316 miles = 16.67 feet
10 miles0.01263 miles = 66.69 feet
20 miles0.05052 miles = 266.75 feet
50 miles0.31575 miles = 1667.17 feet
100 miles1.26296 miles = 6668.41 feet
200 miles5.05102 miles = 26669.37 feet
500 miles31.5336 miles = 166497.53 feet
1000 miles125.632 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)

curvature

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.