One of the funniest things about the ocean is the fact that its surface is curved. We tend to think about water forming large flat sheets, but the surface of a large body of water is not actually flat at all -- it follows the curvature of the Earth. Show Because of the curvature of our planet, the distance between you and the horizon when you look out over the ocean depends on your height above the surface of the water. The following diagram shows you how the distance to the horizon can change depending on the height of the observer: So the distance to the horizon depends on the height of your eyes above the water. If your eyes are 8 inches (20 cm) above the water, the distance of the horizon is about 1 mile (1.6 km) away. A rough formula for calculating the distance to the horizon is: SquareRoot(height above surface / 0.5736) = distance to horizon where "height above surface" is in feet and "distance to horizon" is in miles. If you are 6 feet tall and standing right at the water's edge, then your eyes are about 5.5 feet above the surface. The distance to the horizon is: SquareRoot(5.5 / 0.5736) = 3 miles In metric, the equivalent is: SquareRoot(height above surface / 6.752) = distance to horizon where "height above surface" is in centimeters and "distance to horizon" is in kilometers. These links will help you learn more:
Originally Published: Apr 1, 2000 How Far Is The Horizon FAQWhat is the horizon?The horizon is the mid-way point between the Earth and the sky. It's where these two parts seem to meet. How far can you see on the horizon?
If you are looking at the horizon from the ground, the horizon is approximately 5 kilometers from you. How far is the horizon in miles?The furthest distance to the horizon that the human eye can see varies slightly depending on a person’s height. In miles, the horizon is approximately 3.1 miles away. How far can you see clouds on the horizon?If you’re standing on level ground, in clear weather and with ample light, you can see clouds on the horizon from about 66 kilometers away. How do you calculate the distance to the horizon?The formula to calculate the distance from you to the horizon is 1.17 times the square root of the height from the ground to your eyes. Boat Safe is a community supported site. We may earn commission from links on this page, but we have confidence in all recommended products. Calculating the distance to the horizon takes a bit of clever math. Not necessarily complicated, but not intuitive either. Consider what you’re trying to figure out, after all. You’re looking out from your boat across the water to the horizon line. And though it looks like a flat run from you to the edge of the planet, you know that’s not true. The water you’re looking at is actually curving into the distance with the shape of the Earth. It’s a little mind bending when you think about it. So, how do we determine the distance from where we’re standing to the horizon? If you have an app on your phone or even an old almanac it may not be so hard. But let’s say you don’t have it. Well, the first thing you need to know is where you’re standing. Not all of us stand the same, right? And you’ll be using the height of your eyes as a guide, since that’s the point you’re measuring from. The calculation will therefore be different for a person standing on the deck of a fishing trawler compared to someone sitting in a kayak. The one piece of information you need going into this is the radius of the Earth itself. For our calculation we’re going to use 3,958.8 miles. The Formula The full method of achieving this formula is needlessly complicated but know that, when using the proper radius of the Earth, you can get a simple formula for determining distance to horizon. That formula is: 1.22459√hThat means 1.22459 (a number we derive from knowing the radius of the earth and using the Pythagorean Theorem) times the square root (√) of your eye height (h). This calculation uses a fairly precise measurement for the earth’s radius and will give you very accurate numbers. If you’re curious about how the entire equation is developed, you can check it out on this site here. Many sites that offer up similar calculations tend to round their numbers up. This is fine, of course, the difference between 2.8 miles and 3 miles when you’re eyeballing the horizon isn’t all that significant. But for the purposes of accuracy we’re giving you some solid, if longer, numbers. So let’s say you’re sitting in your boat and your eyes are 3 feet above the surface of the water. The formula becomes: 1.22459√3The square root of three is 1.73205080757. So now the formula becomes: 1.22459 x 1.73205080757So the distance to horizon, based on this, is 2.12105209844 miles. If you’re standing up and you’re about 6 feet tall, let’s say your eyes are sitting at about 5.5 feet. That means; 1.22459√5.5 or 1.22459 X 2.34520787991That equals 2.87191811766 or nearly 3 miles off. Things to RememberCalculating square roots in your head isn’t always the easiest thing to do. That’s why having your phone handy for the calculations is ideal. And, as you can see, the distance increases the greater the height. That means standing on the deck of a massive cruise liner will offer you a distance to horizon far greater than what you’ll get sitting in a canoe. One thing you’ll want to remember here is converting to decimals. This is important for height. In our second example we used 5.5 feet. That works out to 5’6”. But if your eye line is higher, say 5’9” you’ll need to convert to decimal. So it’s not 5.9 feet, it’s 5.75 feet. Calculation ErrorsOur previous distance to horizon calculation involved a similar equation however the number used was 1.17 rather than 1.22459. Some folks asked where that number came from. We looked into it and, because this is such a prevalent issue, we’ll pass it on to you. 1.17 miles comes from the USCG Light List. This list, published annually by the Coast Guard, details all lighthouses, sound signals, beacons, buoys and other aids to navigation in a Coast Guard area. At the beginning of these lists you will find general information. In that general information you’ll find a calculation to determine the distance a person is able to see an object on the horizon. Their calculation is 1.17 X the square root of your eye height. So there are two issues with this equation. 1 – What does 1.17 refer to? There is no indication from what source that number was derived. In our new calculation we show you how that number is determined by way of the radius of the Earth itself. The 1.17 is unknown. 2 – Is this actually a calculation to the horizon? The equation, as written, seems to indicate that it will determine how far you can see something, not necessarily where the horizon is. Those two may be and likely often are the same, but not always. However, without knowing how anyone came up with that 1.17 number, it’s a moot point. So, if you see a calculation anywhere that offers up that number, take it with a grain of salt. The calculation will not offer a mathematically correct way to determine the distance to the horizon from your current point of view. What About Maximum Visibility?If you watch the weather report on TV, you may hear the local weather person mention maximum visibility. On a foggy day it may be very minimal, less than a quarter of a mile. On a clear day they may say upwards of 10 miles. But how can that be if the distance to horizon when you’re standing on shore may be less than 3 miles? The thing you need to remember here is that maximum visibility is not about calculating where the horizon is. Instead, it refers to the ability to see and identify a prominent dark object against the sky at the horizon during the day. This is all related to the opacity of the atmosphere. So if it’s a hazy day, a smoggy day, or a rainy day, the visibility will decrease. The horizon is irrelevant in this case. A Note of ThanksSpecial thank you to Boatsafe visitor Robert Gillies who, among a couple of others, noticed our previous calculations were not entirely correct and pointed us in the direction of some superior math. Math is not always everyone’s strong suit but it’s nice to know how to use it when and where you need it! Once we were on the right track we discovered many sites were using that same calculation. And since it was derived from the United States Coast Guard it seemed perfectly legit. But now we know better! How far can your eyes see out to sea?At sea level the curvature of the earth limits the range of vision to 2.9 miles. The formula for determining how many miles an individual can see at higher levels is the square root of his altitude times 1.225.
How far can you see horizon on the ocean?How far is the horizon in miles? The furthest distance to the horizon that the human eye can see varies slightly depending on a person's height. In miles, the horizon is approximately 3.1 miles away.
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