Editing Incubator escapee wiki:WikiProject Geographical coordinates (section)

==={{anchor|Precision}}Precision guidelines===
{{shortcut|WP:OPCOORD}}
Regardless of how coordinates are obtained, consider the precision specified in a Wikipedia article. Reliable secondary sources exist for some locations. ''Without a reliable source, the larger the object being mapped, the less precise the coordinates need to be.'' Cities must be specified with a precision of degrees, minutes and seconds to respect historical norms. When the [[#Which coordinates to use]] guideline is used, degrees, minutes and seconds or d.dddd are the default. To specify a particular point in the city, such as a building, generally requires precision down to degrees-minutes-seconds or d.dddd° if decimal degrees are used. In the case of objects such as fountains or statues, it may be necessary to use d°m's.s" or d.ddddd°. Higher precisions should be avoided, as they greatly exceed the accuracy of civilian GPS and online mapping services. (Using 4 m accuracy as an estimate for civilian GPS: Depending on the coordinates format and the latitude, the next-higher precisions exceed the accuracy by a factor of somewhere between 13 and 72.)

A general rule is to give precisions approximately one-tenth the size of the object, unless there is a clear reason for additional precision. Overly precise coordinates can be misleading by implying that the object is smaller than it truly is.

There is no set way to determine object size, and the boundaries of many geographical objects are not clearly defined or not readily available. The difference rarely affects the suggested coordinates precision, so a rough size estimate is usually adequate. However, it should be noted that object size is always linear (one-dimensional), not an area measurement.

In the two most-used coordinate representations, degrees-minutes-seconds and decimal degrees, precision is, as a useful approximation,

{|
|- style="vertical-align:top;"
|
{| class="wikitable" style="text-align:right;"
|+ Degrees-minutes-seconds format
!Precision
!Diff. at equator
!Diff. at 30°
!Diff. at 45°
!Diff. at 60°
|-
|1°||111 km||96.4 km||78.7 km||55.7 km
|-
|1′||1.85 km||1.61 km||1.31 km||0.93 km
|-
|0.1′||185 m||161 m||131 m||93 m
|-
|0.01′||18.5 m||16.1 m||13.1 m||9.3 m
|-
|1′′||31 m||27 m||22 m||15 m
|-
|0.1′′||3.1 m||2.7 m||2.2 m ||1.5 m
|}
||
{| class="wikitable" style="text-align:right; margin-left:20px;"
|+ Decimal degrees format
!Precision
!Diff. at equator
!Diff. at 30°
!Diff. at 45°
!Diff. at 60°
|-
|1°||111 km||96.4 km||78.7 km||55.7 km
|-
|0.1°||11 km||9.64 km||7.87 km||5.57 km
|-
|0.01°||1.1 km||964 m||787 m||557 m
|-
|0.001°||110 m||96.4 m ||78.7 m||55.7 m
|-
|0.0001°||11 m||9.64 m||7.87 m||5.57 m
|-
|0.00001°||1.1 m||96.4 cm || 78.7 cm || 55.7 cm
|}

|}

Conversions: {{convert|1|km|mi|3}}, {{convert|1|m|ft|2}}, {{convert|1|cm|in|3}};
{{convert|1|mi|km|2}}, {{convert|1|ft|m|3}}, {{convert|1|in|cm|2}}

The values in the table give distances in the east-west direction corresponding to a small change in longitude, at different latitudes. You can take the equator columns of the table as a rough guide to distances in the north-south direction that correspond to a small change in latitude, since they vary only a little bit at different latitudes. For simplicity, however, the latitude precision is commonly copied from that of the longitude. 

====Precision tables====
{{shortcut|WP:COORDPREC}}
The following tables show suggested coordinates precisions for various object sizes and latitudes. Refer to the preceding section for more information about coordinates precision. To use these tables:
* Choose one of the tables depending on whether you want '''degrees-minutes-seconds''' format or '''decimal degrees''' format
* Find the column that is closest to the latitude of your object
* Find the row that is closest to the size of your object
* Note the coordinates precision at the intersection of your row and column
{{Collapse top|title=Usage example|bg=#daf0da}}
Example: You want coordinates, in decimal degrees format, for Yosemite National Park, California, U.S.
* The size of the object is roughly 70 km
* [https://geonames.usgs.gov/apex/f?p=138:1:0::::: GNIS query] gives the Park's location, in decimal degrees, as: 37.8483188 (north latitude), −119.5571434 (west longitude)
To solve:
* Choose the '''Decimal degrees format''' table
* Find the '''45°''' column; 37.8483188 is (slightly) closer to 45° than to 30°
* Find the '''50 km''' row; 70 km is closer to 50 km than to 100 km
* Note the precision at the intersection of row and column: d.d°
* [[Rounding|Round]] to the selected precision: 37.8, −119.6
(This is a good example of a ''borderline case'', as the latitude is quite close to 37.5°, the midpoint between 30° and 45°. If the Park were a mere 25 miles to the south, you would use the '''30°''' column instead, yielding a different precision: d.dd°. You could opt for that precision instead, giving 37.85, −119.56. That's your call. But the table shows that ''more than'' two decimal positions would definitely be too precise for this case.)
{{Collapse bottom}}
<!-- 
     BACKGROUND COLORS: 
     #f2f2f2 - gray for the object size header columns (latitude header rows have this color by default)
     #ffe7e7 - pink for data cells
     #daf0da - blue-green for data cells
-->
{|
|- style="vertical-align:middle;"
|
{| class="wikitable" style="text-align:left;"
|+ Degrees-minutes-seconds format
!
!0°
!30°
!45°
!60°
|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''10 m'''
|colspan="3" style="background:#f2f2f2; text-align:center;"|d° m' s.s" or d.ddddd° <sup>[note 3]</sup>
|style="background:#ffe7e7;"|d° m' s.s"

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''50 m'''
||d° m' s.s"  ||d° m' s.s"  ||d° m' s.s"  ||d° m' s.s"

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''100 m'''
||d° m' s.s"  ||d° m' s.s"  ||d° m' s.s"  ||style="background:#daf0da;"|d° m' s"

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''500 m'''
||d° m' s"  ||d° m' s"  ||d° m' s"  ||d° m' s"

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''1000 m<br>1 km'''
||d° m' s"  ||d° m' s"  ||d° m' s"  ||d° m' s"

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''5 km'''
||d° m' s"  ||d° m' s"  ||d° m' s"  ||style="background:#ffe7e7;"|d° m'

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''10 km'''
||d° m'  ||d° m'  ||d° m'  ||d° m'

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''50 km'''
||d° m'  ||d° m'  ||d° m'  ||d° m'

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''100 km'''
||d° m'  ||d° m'  ||d° m'  ||d° m'

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''500 km''' ||style="background:#ffe7e7;"|d° m' ||d° ||d° ||d°

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''1000 km'''
||d°  ||d°  ||d°  ||d°
|}
||
{| class="wikitable" style="text-align:left; margin-left:20px;"
|+ Decimal degrees format
!
!0°
!30°
!45°
!60°
|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''10 m'''
||d.ddddd°  ||d.ddddd°  ||d.ddddd°  ||d.ddddd°

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''50 m'''
||d.ddddd°  ||d.ddddd°  ||style="background:#ffe7e7;"|d.dddd°  ||style="background:#ffe7e7;"|d.dddd°

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''100 m'''
||d.dddd°  ||d.dddd°  ||d.dddd°  ||d.dddd°

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''500 m'''
||d.dddd°  ||d.dddd°  ||style="background:#daf0da;"|d.ddd°  ||style="background:#daf0da;"|d.ddd°

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''1000 m<br>1 km'''
||d.ddd°  ||d.ddd°  ||d.ddd°  ||d.ddd°

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''5 km'''
||d.ddd°  ||d.ddd°  ||style="background:#ffe7e7;"|d.dd°  ||style="background:#ffe7e7;"|d.dd°

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''10 km'''
||d.dd°  ||d.dd°  ||d.dd°  ||d.dd°

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''50 km'''
||d.dd°  ||d.dd°  ||style="background:#daf0da;"|d.d°  ||style="background:#daf0da;"|d.d°

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''100 km'''
||d.d°  ||d.d°  ||d.d°  ||d.d°

|- style="background:#daf0da;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''500 km'''
||d.d°  ||d.d°  ||style="background:#ffe7e7;"|d°  ||style="background:#ffe7e7;"|d°

|- style="background:#ffe7e7;"
|style="background:#f2f2f2; text-align:right; padding-right:10px;"|'''1000 km'''
||d°  ||d°  ||d°  ||d°
|}
|}
#{{smaller|The tables are derived from the precision data at {{section link||Precision guidelines}}, above. As suggested there, they use a target resolution of one-tenth of the object size.}}
#{{smaller|The tables are not perfect. Some cases will yield a precision that is different from what you would get by doing the math (including trigonometry) for that specific case. This is because it is impossible to represent all cases correctly in a usable tabular format. The tables provide the correct precision for a majority of cases. Any error should be limited to one level of precision (e.g., '''d° m'''' vs. '''d° m' s"''', or '''d.ddd°''' vs. '''d.dddd°'''), which is acceptable for the purposes of Wikipedia coordinates.}}
#{{smaller|'''d.ddddd°''' is roughly three times more precise than '''d° m' s.s"'''.}}

====Mathematical formulas====
You can also calculate the kilometers per degree of longitude, ''k,'' using one of the following formulas (θ is the latitude, 6378.14&nbsp;km is the [[Earth radius|equatorial radius]], and 6356.8&nbsp;km is the polar radius):

Accurate, assuming a [[spheroid]]: 
* <math>k = \frac{\pi}{180}\cos(\theta)\sqrt{\frac{(6378.14^2\cos\theta)^2+(6356.8^2\sin\theta)^2}{(6378.14\cos\theta)^2+(6356.8\sin\theta)^2}}</math>

Approximate: 
* <math>k = 111.3\cos\theta\,</math>  Equator to latitude 25° (north or south)
* <math>k = 111.2\cos\theta\,</math>  Latitude 30° to 40°
* <math>k = 111.1\cos\theta\,</math>  Latitude 45° to pole