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)
Sauce: http://earthcurvature.com/