You might need to take advantage of some really clever math calculations to get the distance from you to the horizon. It isn’t necessarily all that complicated, but it won’t be intuitive either. Don’t forget that you’re actually trying to find out the distance from your boat to the visible horizon line. And it is a little harder because although it looks like a flat line from you to the farthest visible point, I`m sure you know this is not actually the case. Although it’s not the first thing people think of, the water you’re seeing isn’t actually straight, but curving to the shape of the Earth. It’s actually pretty interesting if you’re thinking about it, right?
S, how will we know what is the real distance to the horizon from our current place? It will be a lot easier to do this if you have an old almanac or even an app on your phone, of course. But what if you don’t have any of these things at hand? Well, although more difficult, it is still doable. The first thing you will need to figure out is your exact location. And most importantly, you’ll need to know the height of your eyes, because that’s the exact point you’ll be measuring from. As This means, of course, that this calculation will differ for a person sitting in a kayak than for someone standing as high as on a deck of a fishing trawler.
You can use the radius of the Earth as a guide. So, for a correct calculation, you will have to use 3,958.8 miles.
The Actual Formula
Although the complete roadmap to getting to the formula is very complicated if you’re using Earth’s proper radius, you can get a really easy formula to get the distance from you to the horizon. This is the formula to use:
1.22459√h
What this translates to is 1.22459, which is the number that we derive from using the radius of the earth in the Pythagorean Theorem, times the square root, or √ of your eye height (h). This formula will actually give a fairly accurate result because it will use a very precise measurement of the Earth’s real radius. You can get a lot more information on how this equation was developed in this PDF file from Washington.edu.
You might also like my article on the Nautical mile to Statute Mile formula.
Although there are websites that try to give you this answer on the spot, most of them will round the numbers to some degree. This isn’t a big deal most of the time, because there isn’t a big difference between 3.2 and 3 miles when you’re looking at the horizon. But if you want to be really accurate, then my calculation will give you a longer, and also more accurate, number.
So let’s get down to real-life examples. What if you’re sitting on a boat with your eyes about 3 feet above the surface of the water? Then you should have a formula like this:
1.22459√3
The square root of three is 1.73205080757. This means that your formula will actually turn into:
1.22459 x 1.73205080757
So based on this, the actual distance from you to the horizon is 2.12105209844 miles.
Things to Keep in Mind
Of course, if you’ve ever tried to, you surely know that it won’t always be easy to calculate the square root of a number in your head. This is why it would be great if you had your phone at hand for these calculations. Another interesting thing is that the distanec will actually extend the higher you are so you will get a far bigger distance to the horizon when standing on the deck of a massive ship than the one you’d get when sitting in a small canoe.
One thing you should keep in mind is that there are decimals that will have to be converted. For example, when dealing with 5.5 feet in your equation, for a 5’6″ height, things won’t be very hard. But when your eye line will be at 5’9″, you will have to convert to decimal, which means you won’t have to calculate using 5.9, but 5.75.
What About Maximum Visibility?
If you get your weather-related information from TV, you’ve surely already heard some local weather forecasters talk about maximum visibility. When there’s a lot of fog outside, the visibility might be very limited, up to a quarter of a mile on some occasions. But there are also sunny days when you would have a maximum visibility of 10 miles or more. But this seems impossible if the distance from you to the horizon is only around 3 miles when you’re standing on the shore, right?
What you should remember when talking about maximum visibility, is that this number has nothing to do with the horizon line and calculating the distance to it. It instead refers to your ability to see an object against the sky during the day. It is basically related to the opacity of the atmosphere on a given day, and not about the distance itself. This means that the actual visibility will decrease on rainy, smoggy, or hazy days. For these particular cases, the horizon and the horizon line is actually irrelevant.