I have obtained a height map that represents a 64 square kilometer area.
Its resolution is 1081 x 1081 pixels.
How do I calculate and set the necessary landscape settings so that it is to 1:1 scale in engine?
That is to say, what is the mathematical process for taking a real world height map and importing it to proper scale?
Generally the conversion landscape does for images is 1 pixel = 1 meter. In unreal engine 1 unit is 1 cm. So for your case you should do this conversion:
1081 pixels = 1081 mts (108100 cms or 1.081 kms) in normal conversion, for it to represent 64 square kilometers you need to make 108100 cms to be 800000 cms (to be 8kms x 8kms).
So 800000/108100 = 7.40055.
So, for an image of 1081*1081 pixels to represent a 64km2 you need to multiply the scale of your terrain by 7.40055.
BE AWARE that doing this will greatly reduce the quality of your terrain. I would recomend you to use a software like world machine to enlarge your heightmap and divide it 16 sections of 2*2kms (16 2k textures). Also 64km2 is a huge size for a map, at that point you should start thinking on using level streaming and world composition:
Hope this helped you. Have a nice day!