The exact values depend, or course, on the local topography, but we usually get close enough simply by assuming the Earth is a sphere. We need to know the size of the Earth to do the sums.
Interestingly, the distance to the horizon calculation is effectively identical to the calculation of orbital velocity.
Find a formula for the distance to the horizon from a height h on a spherical planet of radius R.
Formulate an experiment to find the minimum height from which people would perceive the horizon to be curved rather than a straight line