<p>As others have said, a single set of coordinates gives a point rather than an area.</p>

<p>However, I assume that the intent of the question is an understanding of the precision of these coordinates - i.e. what's the area covered by the 1"x1" shape comprising all of the lat and lon values that would round to a whole number of seconds. The answer to that is "it depends". </p>

<p>The distance covered by one arc minute of latitude, by definition, is one nautical mile. One nautical mile is 1852 metres, therefore one arc second (1/60 minutes) of latitude represents just under 31m.</p>

<p>So far, so straightfoward. But longitude isn't so simple, because the distance represented by an arc second of longitude is not the same everywhere on the planet - it depends on the latitude. This makes sense if you look at a map and see how the lines of longitude converge - i.e. have less distance between them - towards the poles. </p>

<p>As Barry Carter said in a comment, the distance represented by an arc second of longitude is approximately equal to <span class="math-container">$31 \cos(lat)$</span> metres[1]. Hence, the area of a 1" ~square around any given point is equal to <span class="math-container">$31^2 \cos(lat)$</span> m<sup>2</sup>. That will vary from zero[2], at the poles, to 961 m<sup>2</sup> on the equator. At the particular coordinates that you gave as an example, it'd be <span class="math-container">$31 \times 31\cos(51.434^{\circ}) \approx 599$</span> m<sup>2</sup>.</p>

<p>[1] Before anybody corrects me, all of the above does assume a spherical earth. In reality It's A Bit More Complicated.</p>

<p>[2] Very nearly zero.</p>

CC BY-SA 4.0
2019-12-11T15:13:16.687Z
2019-12-11T15:13:16.687Z
Semidiurnal Simon
<p>A point do not have an area. </p>

<blockquote>
  <p><a href="http://mathworld.wolfram.com/Point.html" rel="nofollow noreferrer">A point is a 0-dimensional mathematical object which can be specified in <em>n</em>-dimensional space using an <em>n</em>-tuple (x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>) consisting of <em>n</em> coordinates.</a></p>
</blockquote>

<p>The area of a point cannot be calculated. So the area must be null.</p>

CC BY-SA 4.0
2019-12-09T19:06:52.570Z
2019-12-09T19:06:52.570Z
marsisalie
<p>tldr; ~10,000 ft² (100 ft x 100 ft)</p>
<p>The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km or 1.153 miles, while the length of 1 second of it is 0.016 geographical mile or 30.916 m or 101.43 feet.</p>
<p>Degrees of latitude are divided into 60 minutes. To be even more precise, those minutes are divided into 60 seconds. One minute of latitude covers about 1.8 kilometers (1.1 miles) and one second of latitude covers about 32 meters (105 feet).</p>
<p>At the equator 101.43 ft x 105 ft = 10,650.15 ft²</p>

CC BY-SA 4.0
2024-05-06T04:30:41.793Z
2024-05-06T04:30:41.793Z
Kevin Hendricks
<p>As stated in the title, I wonder how large the area covered by certain coordinates actually is, when they have the accuracy XX°YY'ZZ", for example:</p>

<pre><code>51°26'02"N, 07°20'04"E
</code></pre>

<p>How can this be calculated?</p>

<coordinate-system>
How large is the area covered by coordinates XX°YY'ZZ"N/XX°YY'ZZ"E?
cheesus
# How large is the area covered by coordinates XX°YY'ZZ"N/XX°YY'ZZ"E?

(Asked by: username_0 on 2019-12-09)

As stated in the title, I wonder how large the area covered by certain coordinates actually is, when they have the accuracy XX°YY'ZZ", for example:

```
51°26'02"N, 07°20'04"E

```

How can this be calculated?

**Tags:** coordinate-system


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## 3 answers

### Answer by username_1 on 2019-12-11. Score: 5

As others have said, a single set of coordinates gives a point rather than an area.

However, I assume that the intent of the question is an understanding of the precision of these coordinates - i.e. what's the area covered by the 1"x1" shape comprising all of the lat and lon values that would round to a whole number of seconds. The answer to that is "it depends".

The distance covered by one arc minute of latitude, by definition, is one nautical mile. One nautical mile is 1852 metres, therefore one arc second (1/60 minutes) of latitude represents just under 31m.

So far, so straightfoward. But longitude isn't so simple, because the distance represented by an arc second of longitude is not the same everywhere on the planet - it depends on the latitude. This makes sense if you look at a map and see how the lines of longitude converge - i.e. have less distance between them - towards the poles.

As Barry Carter said in a comment, the distance represented by an arc second of longitude is approximately equal to $31 \cos(lat)$ metres[1]. Hence, the area of a 1" ~square around any given point is equal to $31^2 \cos(lat)$ m2. That will vary from zero[2], at the poles, to 961 m2 on the equator. At the particular coordinates that you gave as an example, it'd be $31 \times 31\cos(51.434^{\circ}) \approx 599$ m2.

[1] Before anybody corrects me, all of the above does assume a spherical earth. In reality It's A Bit More Complicated.

[2] Very nearly zero.


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### Answer by username_2 on 2019-12-09. Score: 1

A point do not have an area.

> [A point is a 0-dimensional mathematical object which can be specified in *n*-dimensional space using an *n*-tuple (x1, x2, ..., xn) consisting of *n* coordinates.](http://mathworld.wolfram.com/Point.html)

The area of a point cannot be calculated. So the area must be null.


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### Answer by username_3 on 2024-05-06. Score: 1

tldr; ~10,000 ft² (100 ft x 100 ft)

The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km or 1.153 miles, while the length of 1 second of it is 0.016 geographical mile or 30.916 m or 101.43 feet.

Degrees of latitude are divided into 60 minutes. To be even more precise, those minutes are divided into 60 seconds. One minute of latitude covers about 1.8 kilometers (1.1 miles) and one second of latitude covers about 32 meters (105 feet).

At the equator 101.43 ft x 105 ft = 10,650.15 ft²


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