Calculating the longest distance within polygon in QGIS

I want to calculate the "diameter" of polygons in QGIS.

The "diameter" defined as the distance between the two most distant points of the polygon.

I couldn't find a fitting solution in the field calculator. Maybe you have some ideas?

• Conceptually thinking: get the smallest possible bounding box (tool), then you should be able to calculate the length of the diagonal using area & perimeter.
– Erik
May 13 '20 at 13:36

You can use PyQGIS to measure the distances between all vertices of each polygon and find max:

import itertools

layer = iface.activeLayer() #Click layer in tree

for feat in layer.getFeatures():
verts = [v for v in feat.geometry().vertices()] #List all vertices
maxdistance = max([p1.distance(p2) for p1,p2 in itertools.combinations(verts, 2)]) #Find max distance for all combinations of vertices (https://stackoverflow.com/questions/464864/how-to-get-all-possible-combinations-of-a-list-s-elements)
print('Polygon: {0}, max distance: {1}'.format(feat.id(), round(maxdistance,0))) #Print results To save max distances in a field:

import itertools

layer = iface.activeLayer() #Click layer in tree
field_to_save_maxdistance_in = 'maxdist' #Change maxdist to the name of your field

fields = layer.fields()
fx = fields.indexFromName(field_to_save_maxdistance_in)

with edit(layer):
for feat in layer.getFeatures():
verts = [v for v in feat.geometry().convexHull().vertices()] #List all vertices
maxdistance = max([p1.distance(p2) for p1,p2 in itertools.combinations(verts, 2)]) #Find max distance for all combinations of vertices
layer.changeAttributeValue(feat.id(), fx, maxdistance) You can also create a line layer:

import itertools

layer = iface.activeLayer() #Click layer in tree

#Create line layer
vl = QgsVectorLayer("LineString?crs={}&index=yes".format(layer.crs().authid()), "myLayer", "memory")
provider = vl.dataProvider()

#For each polygon find the two points most far apart
for feat in layer.getFeatures():
all_points = []
verts = [v for v in feat.geometry().vertices()] #List all vertices
for p1,p2 in itertools.combinations(verts, 2):
all_points.append([p1,p2])

#Create a line feature
pointpair_most_far_apart = max(all_points, key=lambda x: x.distance(x))
gLine = QgsGeometry.fromPolyline(pointpair_most_far_apart)
f = QgsFeature()
f.setGeometry(gLine) • This seems like exactly what I want to do! Since I am not familiar with Python and pyqgis: is there a way to save the maximum distance that the console is showing me as a column in my layer? So I can continue using it for my following calculations. May 13 '20 at 13:55
• Somehow the newest code doesn't work. I get a "SyntaxError: invalid syntax" error or QGIS just shuts down while trying to run it. The first one you posted without saving it to my layer worked perfectly. May 13 '20 at 14:23
• Added it as a real type. But now it somehow worked. QGIS shut down again and when I restarted it, the column was there and the results seem correct. Weird indeed! But anyways, thank you! This has helped me a lot already! May 13 '20 at 14:34

Bear in mind that someone correctly pointed out very soon in comments that I had misread the question. My answer gives the diameter of the minimal circle but this does not always correspond to the longest distance between vertices in a polygon. As soon as more than 2 vertices touch the circle or if the vertices defining the circle are adjacent, the values can differ. I left it there as it provides an answer for a similar problem but even I agree it should not be the accepted answer.

It is possible to do with simple expressions in the field calculator (at least in QGIS 3.12.x). Take for example these two polygons. The symbology shows four things (using the geometry generator, for explanation purposes):

• Red outline of the true polygon
• Semi-transparent orange circle resulting from the minimal_circle() function
• Blue point resulting from the centroid() function of the minimal circle
• White point resulting from the point_n() function of the minimal circle's first vertex So to get the diameter of the minimal circle containing the polygon, go to the field calculator and use this expression in a new decimal field:

distance(centroid(minimal_circle(\$geometry)),point_n(minimal_circle(\$geometry),1)) * 2

This will calculate the distance between the centroid and the first vertex along the circle (the radius), then multiply it by two.

• @Jan-PieterVanParys There we go. Expressions have received a LOT of love since then. May 13 '20 at 15:37
• @Jan-PieterVanParys You can go with the current LTR, 3.10.5. It should be quite stable although you will probably need a little bit of adjusting to the new UI and ways of doing things. May 13 '20 at 15:41
• What about an Equilateral triangle? I think the diameter of the circle is bigger than the longest edge of the triangle... Your solution works only for polygons for which the smallest circle touches only two vertices. May 25 '20 at 11:54
• @Legisey Yes, triangles don't work well. That's something to keep in mind, but I've observed that they aren't very common in the datasets I've had to use. It could be possible to aggregate the distances from the centroid to each vertex then build a minimal circle from the two largest value points. I'll try that out. edit Also I think it was maybe a problem with the question as asked as the diameter (minimal circle) can often be different from the distance between the two most distant vertices. May 25 '20 at 12:58
• @GabrielC. so you're not looking for the "the distance between the two most distant points of the polygon" as stated in the question? Are you looking for the diameter of the smallest circle that fully contains the shape? It's not the same thing, even though in some cases (like the ones of this answer) it will be the same. It's not only in triangles that there is a difference, it is also the case with most shapes that have more than two vertices that touches the circle. I think this is not a correct answer to the question. So either you asked the wrong question, or accepted the wrong answer. May 26 '20 at 8:34

Let's assume there is a polygon layer "Layer_A" (blue) with its corresponding attribute table accordingly, see image below. Step 1. Proceed with 'Polygons to lines' Step 2. Proceed with 'Points along geometry'. Mind that the distance affects the quality of the final result and the efficiency of the Virtual Layer in Step 3. Step 3. By means of a "Virtual Layer" through Layer > Add Layer > Add/Edit Virtual Layer... apply this query

SELECT p1.id,
setsrid(make_line(p1.geometry, p2.geometry), 'put your srid here'),
max(st_length(make_line(p1.geometry, p2.geometry))) AS length
FROM "Points" AS p1
JOIN "Points" AS p2 ON p1.id = p2.id
WHERE NOT st_equals(p1.geometry, p2.geometry)
GROUP BY p1.id P.S. if you are interested in the longest distances between vertices, than extract vertices from polygon via 'Extract vertices' and go directly to Step 3. • I just tried this and unfortunately QGIS can't finish the third step. It runs for a long time already, but never ends. May 13 '20 at 15:10
• How many points did you generate ? How many polygons do you have ? May 13 '20 at 18:01
• I have more than 400 polygons and I've got 371939 points. Maybe those are too many? May 23 '20 at 11:51
• yes, you are right Jun 26 '20 at 9:35

If you have your data in PostGIS you can use these functions:

https://postgis.net/docs/ST_MinimumBoundingCircle.html

Returns the smallest circle polygon that can fully contain a geometry.