# Thread: How do you calculate what percentage of the Earth's surface a land or water area is?

1. Member
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## How do you calculate what percentage of the Earth's surface a land or water area is?

For example, Australia. What percentage of the Earth's surface does Australia occupy? Or the Atlantic Ocean. How much of Earth's surface does the Atlantic take up?

How do you calculate a land or water body's percentage of the Earth's surface?

2. Order of Kilopi
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I suspect that what you want to know isn't how to calculate the
percentage, but how to measure the area. Once you have a measure
of the area you are interested in, and a measure of the area of Earth's
entire surface, finding the percentage is basic sixth-grade arithmetic.

Area of Australia = 7,617.930 km^2
Area of the Earth = 510,072,000 km^2

7,617,930 / 510,072,000 = 0.014935
0.014935 x 100 = 1.4935

So Australia is about 1.5% of Earth's surface area.

Now, what are you really asking? How the figures for the areas
were generated? Or what?

-- Jeff, in Minneapolis

3. Given that it's easy to calculate the area of a sphere, and easy to calculate a percentage, presumably you want to know how to calculate the area of Australia (for example)? I'm guessing this is done by covering the map with suitably big and small rectangles so that the area around the coastline can be measured accurately.

If this is not what you are asking, then what is your question?

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The methodological problems of measuring the area of dry land and the area of permanent water. Different people trying to measure, for example, the area of China (before we even get into the argument over disputed borders) come up with quite significantly different areas. How to decide exactly where the coastline runs - and vegetated saltmarshes don't make that easy - at what detail of gradation to measure it. How to decide what the borderline of permanently inundated land is, this is difficult too.

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The shape of land is often compared to mathematical structures called fractals, e.g. the Mandelbrot set. To measure the area exactly is a problem because there is always a level of detail as you zoom in, so I suppose it is always only approximate, depending on how accurate you want to measure.

A surface element in spherical coordinates can be used to integrate an area on a sphere. Larger analytically calculable surface elements can be used for the inland area and small surface elements around the coast. The same idea as Paul Beardley's, except it's not rectangular elements. All the elements must then be added on a computer to get the total area. The more accurate the measurements, the more data, and thus a numerical approach is better.

6. Originally Posted by Ivan Viehoff
Different people trying to measure, for example, the area of China (before we even get into the argument over disputed borders) come up with quite significantly different areas.
Usually, using modern definitions of the borders, it's not that hard to compute the value to a given accuracy.

Area doesn't have the same problem that coastline length does. If a coastline is a fractal, its length is infinite (an example: take a triangle, then augment each side by adding another triangle with sides a third the length, then do it again and again. Each time, the boundary increases by a factor of 4/3.) Clearly, the area of Australia is limited. There is no way to measure it so that it gets beyond certain limits.

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In a nutshell I just want to know how much land x or water y takes up of the Earth's surface. That's all. The actual calculating is easy. But I want to be sure I'm doing it right.

For example, North America is alot of land. But before anything, we know North America's fraction of the Earth's surface, whatever that number is, will be <29%.

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In a nutshell I just want to know how much land x or water y takes up of the Earth's surface. That's all. The actual calculating is easy. But I want to be sure I'm doing it right.

For example, North America is alot of land. But before anything, we know North America's fraction of the Earth's surface, whatever that number is, will be <29%.
Various sources put percentage of Earth's surface covered by water at 71% and land 29%, but it appears that you already know this. You also say the calculating is easy. We've shown some possible methods of measuring. So it is not clear what it is that you want to know. I think you're playing with us here.

9. Order of Kilopi
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In a nutshell I just want to know how much land x or water y
takes up of the Earth's surface. That's all. The actual calculating
is easy. But I want to be sure I'm doing it right.
I take it that you simply did not know how to calculate
percentages. Is that correct? Or is there more?

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
I take it that you simply did not know how to calculate
percentages.
Is that correct? Or is there more?

-- Jeff, in Minneapolis
As you correctly stated upthread, the actual calculating is just simple arithmetic. My interest here is to apply these things when speculating about what Earthlike exomoons & exoplanets surface configurations might be like, Earth in the past when the continental arrangements were different, & also, even, to Titan's surface.

11. Order of Kilopi
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In that case, we still have absolutely no idea what you were
asking for. If you know where to find area measurements of
the regions you are interested in, and of the Earth, and accept
those figures as suitable for your purposes, and know how to
calculate a percentage, then there does not appear to be any
actual question that you are asking.

-- Jeff, in Minneapolis

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Originally Posted by grapes
Usually, using modern definitions of the borders, it's not that hard to compute the value to a given accuracy.
Borders are a problem in specific cases, but they aren't the problem I was alluding to. In the Wikipedia article http://en.wikipedia.org/wiki/List_of..._by_total_area we find this footnote on the area of China vs the area of the US:

"There are two reasons for the dispute in rankings between the United States and China. The first reason is China's inclusion of several disputed territories. ... The second reason relates to how "total area" is calculated. The figure given for the United States additionally includes coastal waters, while the figure for China does not. The inclusion of coastal waters is the calculation method used by the CIA World Factbook, whereas the latter is the method employed by Encyclopędia Britannica, reaching differing conclusions. "

In other words, are coastal lagoons and tidal reaches of rivers to be treated as inland waters therefore part of the area of the country, or part of the sea and therefore not part of the area of the country. This is significant for the areas of the USA and China, since both these countries have large quantities of coastal lagoons and tidal waterways. In other words, it is not clear where sea stops and inland waters start, and this can make a substantial difference to what is treated as the area of a country. On some definitions, it ceases to be sufficient to examine a satellite photograph to make the distinction.

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Bump: As some the other posts infered, there are few problems if plus or minus 3% is close enough. If you want 3 parts per million, good luck. We can start with existing maps and other measurement sourses including aireal photos and satelite photos and compare. Where opinions very, we try to figure out why. Often some original assumptions are the problem such as mean low tide or mean high tide. For lakes, ponds and rivers, we need to sellect some area between largest ever recorded and smallest area ever recorded. Salt marshes and swamps are definately a problem. To get to one part per million we have to decide what we will ignore and what scale is relevant = one meter or one millimeter. Is the water under a bridge or peir count as land or water? In my home town a several meter wide river ran under dozens of buildings. South of where I live now, about a thousand lakes shrunk to to less than half their previous area. After we decide on the standard assumptions, we probably need to resurvey all of Earth to get an error bar of plus or minus one part per million, and that will be wrong for most other sets of assumptions. Neil
Last edited by neilzero; 2013-May-03 at 05:28 PM.