Inputs
Values are converted when changing unit systems. Earth radius defaults to 6371 km.
About this app
Calculate how Earth curvature and atmospheric refraction affect a distant target. Set the surface distance, observer and target heights, Earth radius and refraction model to see eye height, horizon distance, drop below eye level at the target, sagitta, direct distance, and the visible and hidden portions of the target.
Compare refraction models in the table, then explore the same geometry in the interactive 3D viewer using globe or flat reference surfaces, five object scenes, atmospheric clarity, zoom, field of view and movable observer controls.
Eye height12.00 ft
Height of the observer’s eye above the modeled surface.Eye level
Horizontal line at the observer’s eye height.Horizon4.58 mi
The farthest visible point on the surface.Drop below eye level9675.36 ft
Apparent vertical displacement from the observer’s horizontal eye-level line to the target surface, including the selected refraction model.Sagitta2415.00 ft
Vertical gap between the straight chord and Earth’s curved surface at the marked point.Distance130.00 mi
Straight chord between the observer and the target base.Visible11316.02 ft
Part of the target remaining above the modeled horizon.Hidden8993.98 ft
Part of the target concealed below the modeled horizon.Refraction Comparison
| Title | No refraction | Weak 1.13 | Standard 7/6 | Intense 1.33 | Strong 1.5 | Polar* 7/2 |
|---|---|---|---|---|---|---|
| Visible horizon | 4.24 mi | 4.51 mi | 4.58 mi | 4.90 mi | 5.20 mi | 7.94 mi |
| Maximum visible distance | 178.69 mi | 189.95 mi | 193.01 mi | 206.35 mi | 218.87 mi | 334.39 mi |
| Hidden below horizon | 10551.13 ft | 9296.77 ft | 8993.98 ft | 7829.51 ft | 6926.20 ft | 2839.00 ft |
| Visible over horizon | 9758.87 ft | 11013.23 ft | 11316.02 ft | 12480.49 ft | 13383.80 ft | 17471.00 ft |
| Visibility | Partly visible | Partly visible | Partly visible | Partly visible | Partly visible | Partly visible |
| Refraction angle | 0.00° | 0.22° | 0.27° | 0.47° | 0.63° | 1.34° |