This may seem like a strange question but when I am running pen and paper campaigns and the party enters a new area from somewhere high up (like a mountain overlooking a city) I am always unsure about how to describe what they see because I have no sense of how much distance one can see given the curvature of the world and a given height. Knowing this information would help me design my maps as well as give an appropriate description to the players.

So, leaving out things such as atmospheric conditions and other high objects in the way (assume the vantage point looking out is by far the highest object), how could I calculate the field of view and distance for an average human? Other simplifications may be necessary; I'm just looking for a quick and dirty estimate (an equation) that is realistic enough for an RPG where everything is in the player's heads. However, I have seen very complicated answers on this SE so if you want to add more detail please feel free. For the purpose of this answer, assume that we are dealing with Earth.

  • $\begingroup$ This is a question for google or physics.stackexchange.com Unless of course it has to do with the conditions of a different world than our own. $\endgroup$ – Martine Votvik Jun 30 '16 at 14:32
  • $\begingroup$ What Martine said; this is not a question about building a world, so it's off topic for us. It'd be a better fit for Physics or maybe even Mathematics because it's really just trigonometry. $\endgroup$ – a CVn Jun 30 '16 at 14:40
  • $\begingroup$ This is a question for roleplaying, and it has been answered there already though it was closed as off-topic there since it did not ask in terms of rpg. $\endgroup$ – Gary Walker Jun 30 '16 at 14:56
  • $\begingroup$ Fair enough. I just figured that this would factor into building a world - it certainly does for my own worldbuilding and seems more like a worldbuilding question than an RPG one. If the world was for a novel or movie this question could still be relevant for the characters. I asked the question in terms of Earth because it's curvature has a known value. Then anyone could change the formula to the curvature of their world as necessary. I don't know the curvature of my world offhand. Regardless, the roleplaying topic linked above seems to have enough information for me to figure it out. $\endgroup$ – syntonicC Jun 30 '16 at 15:47
  • $\begingroup$ Do you want travelling distance or miles? $\endgroup$ – Bookeater Jun 30 '16 at 17:52

The quick and dirty estimate is in imperial units for an Earth size world.

Distance to horizon in miles is half your height in feet.

If you're 6ft tall it's about 3 miles, if you're 100ft up and 6ft tall it's 53 miles.

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  • $\begingroup$ That estimate is only good for fairly small heights. If you're 100ft up and 6ft tall, the horizon is about 12 miles away, not 53 miles. A better approximation is that (on the earth) if your eyes are $h$ feet above sea level, the horizon distance in miles is about the square root of 1.5 times $h$. $\endgroup$ – Rick Decker Jun 30 '16 at 17:29
  • $\begingroup$ @RickDecker you're correct, but the important thing to remember is that it doesn't actually matter $\endgroup$ – Separatrix Jun 30 '16 at 17:33

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