Distance to horizon:
R is Earth's radius (6370km), h1 is the altitude of the observer, h2 is the altitude of the object being observed, d1 is the distance netween observer and horizon, d2 is the distance between object and horizon.
Using Pythagoras' theorem:
d1^2 = (R+h1)^2 - R^2 = 2*h1*R*( 1+h1/(2*R) )
Hence, if h1 much smaller than R, then d1 = sqrt(2*h1*R) is about 113 km at 1 km altitude, or 58.3 nm at 3000 feet, going as sqrt(h1)!
(33.6 nm at 1000 feet; 3 statute miles (or 1 league) at 1.8m; 2.6nm at 1.8m)