CoordinateBounds[coords]
gives a list {{xmin,xmax},{ymin,ymax},…} of the bounds in each dimension of the region defined by coords.
CoordinateBounds[coords,δ]
pads the ranges of coordinates by ±δ in each dimension.
CoordinateBounds[coords,Scaled[s]]
pads by the scaled amount s in each dimension.
CoordinateBounds[coords,{p1,p2,…}]
pads by p1, p2, … in successive dimensions.
CoordinateBounds[coords,{{p1min,p1max},{p2min,p2max},…}]
gives {{xmin-p1min,xmax+p1max},{ymin-p2min,ymax+p2max},…}.
CoordinateBounds
CoordinateBounds[coords]
gives a list {{xmin,xmax},{ymin,ymax},…} of the bounds in each dimension of the region defined by coords.
CoordinateBounds[coords,δ]
pads the ranges of coordinates by ±δ in each dimension.
CoordinateBounds[coords,Scaled[s]]
pads by the scaled amount s in each dimension.
CoordinateBounds[coords,{p1,p2,…}]
pads by p1, p2, … in successive dimensions.
CoordinateBounds[coords,{{p1min,p1max},{p2min,p2max},…}]
gives {{xmin-p1min,xmax+p1max},{ymin-p2min,ymax+p2max},…}.
Details
- CoordinateBounds yields a definite result if all of the coordinates are real numbers.
- In other cases, CoordinateBounds carries out some simplifications.
Examples
open all close allBasic Examples (1)
Find bounds for coordinates in 2 dimensions:
CoordinateBounds[{{0, 1}, {1, 2}, {2, 1}, {3, 2}, {4, 0}}]CoordinateBounds[{{0, 1}, {1, 2}, {2, 1}, {3, 2}, {4, 0}}, 1]Pad by 1/4 of the span in each dimension:
CoordinateBounds[{{0, 1}, {1, 2}, {2, 1}, {3, 2}, {4, 0}}, Scaled[1 / 4]]Scope (4)
Find the coordinate bounds of the vertices of a pentagon:
CirclePoints[5]CoordinateBounds[%]Find the coordinate bounds of pairs of numbers in a ragged array:
CoordinateBounds[{{1, 2}, {{{{{5, 6}}}}, {9, 10}}}]Find the bounds of a collection of 2D points, padding out one unit in all directions:
pts = {{3, -3}, {3, 3}, {-3, 3}, {-3, -3}};CoordinateBounds[pts, 1]Pad differently in the horizontal and vertical directions:
CoordinateBounds[pts, {1, 2}]Specify different paddings in each of the four directions:
CoordinateBounds[pts, {{1, 2}, {3, 4}}]Take 3D coordinates of different types:
coords = {{{0.0736388, 2.2431, -0.34123}, {-1.1412, 0.75341, 5.34125}}, {π, E, Sqrt[2]}, {Exp[2], Log[10000], Csc[(1/10)]}, {{{2, 1, 7}, {-9, -5, 7}}, {{-2, 9, 5}, {8, -9, 9}}}};CoordinateBounds[coords]CoordinateBounds[coords, 1]Pad by a fraction of the difference in each dimension:
CoordinateBounds[coords, Scaled[.1]]Pad by different amounts for different dimensions:
CoordinateBounds[coords, {.1, Scaled[.2], .3}]Pad the minima and maxima differently:
CoordinateBounds[coords, {0, 1}]Pad differently in each direction:
CoordinateBounds[coords, {{0, 1}, {1.5, 0.5}, {1 / 2, 1 / 3}}]Generalizations & Extensions (1)
Applications (1)
Properties & Relations (4)
Generally, CoordinateBounds[coords] is the transpose of CoordinateBoundingBox[coords]:
coords = RandomReal[1, {12, 4}];CoordinateBounds[coords]Transpose[CoordinateBoundingBox[coords]]For coordinates given in a matrix, CoordinateBounds[coords] is equivalent to Map[MinMax, Transpose[coords]]:
coords = RandomInteger[{-9, 9}, {47, 6}];CoordinateBounds[coords]Map[MinMax, Transpose[coords]]pol = RandomPolygon[10]Find the coordinate bounds of its coordinates:
CoordinateBounds[PolygonCoordinates[pol]]The same result can be obtained using RegionBounds on the polygon:
RegionBounds[pol]Graphics[{Opacity[0.5], pol, EdgeForm[Magenta], FaceForm[], Rectangle@@Transpose[%]}, Frame -> True]Take a collection of 500 random geo positions in France:
gps = RandomGeoPosition[Entity["Country", "France"], 500]Find the coordinate bounds of the latitude and longitude quantities:
CoordinateBounds[LatitudeLongitude[gps]]The same result can be obtained with GeoBounds, expressed as numbers in degrees:
GeoBounds[gps]Draw the 500 points and the geo bounds region on a map:
GeoGraphics[{GeoBoundsRegion[%], Orange, Point[gps]}]Related Guides
History
Text
Wolfram Research (2015), CoordinateBounds, Wolfram Language function, https://reference.wolfram.com/language/ref/CoordinateBounds.html.
CMS
Wolfram Language. 2015. "CoordinateBounds." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoordinateBounds.html.
APA
Wolfram Language. (2015). CoordinateBounds. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoordinateBounds.html
BibTeX
@misc{reference.wolfram_2026_coordinatebounds, author="Wolfram Research", title="{CoordinateBounds}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/CoordinateBounds.html}", note=[Accessed: 12-June-2026]}
BibLaTeX
@online{reference.wolfram_2026_coordinatebounds, organization={Wolfram Research}, title={CoordinateBounds}, year={2015}, url={https://reference.wolfram.com/language/ref/CoordinateBounds.html}, note=[Accessed: 12-June-2026]}