Earth curvature calculation spreadsheet
Labels Values formula
R, radius of Earth (miles) 3963
D, distance from observer (miles) 18.7
α, angle to observer (radians) 0.004718647 D / R
A 3962.955881 R ∙ cos(α)
B 18.69993061 R ∙ sin(α)
C 0.044119272 R - A
E 18.69998265 sqrt(B+C)
F 9.349991326 E / 2
G 3962.98897 sqrt(R-F)
H 0.011029833 R - G
H in feet 58.2375203 H x 5280 ft/mi
Calculate the height of the effective barrier between observer and object under observation,
created by the curvature of the Earth, as a function of the distance between observer and
object under observation. I.e., calculate the maximum height difference between a straight
line and a curve which follows the curvature of the Earth.
The fundamental deficiency in this approach is the assumption that Earth has no atmosphere.
In the real world, the Earth's atmosphere acts as a lens, which refracts light. Depending
on atmospheric conditions, it is often possible for things beneath the horizon to appear at the
horizon, or even above the horizon. Here are a couple of very good web pages on this topic:
Note: the previous version of this spreadsheet (using 60 miles as the distance) is here:
This is an exported Excel spreadsheet. You can load it directly into
Microsoft Excel 2003 or later, or another compatible spreadsheet
program, such as Kingsoft WPS Office "Spreadsheets" (but not
OpenOffice), to view (or change) the formulae & values.

Dave Burton

30 April, 2016
(minor updates 3 November, 2017)