--- title: "GeoLength" language: "en" type: "Symbol" summary: "GeoLength[g] gives the length of the geo path g." keywords: - geo length - geographic length - geo path length - geo curve length - geo distance - geodesic length - loxodrome length - rhumb line length - departure canonical_url: "https://reference.wolfram.com/language/ref/GeoLength.html" source: "Wolfram Language Documentation" related_guides: - title: "Geodesy" link: "https://reference.wolfram.com/language/guide/Geodesy.en.md" - title: "Maps & Cartography" link: "https://reference.wolfram.com/language/guide/MapsAndCartography.en.md" related_functions: - title: "GeoDistance" link: "https://reference.wolfram.com/language/ref/GeoDistance.en.md" - title: "GeoDistanceList" link: "https://reference.wolfram.com/language/ref/GeoDistanceList.en.md" - title: "ArcLength" link: "https://reference.wolfram.com/language/ref/ArcLength.en.md" - title: "GeoArea" link: "https://reference.wolfram.com/language/ref/GeoArea.en.md" - title: "Quantity" link: "https://reference.wolfram.com/language/ref/Quantity.en.md" - title: "GeoPath" link: "https://reference.wolfram.com/language/ref/GeoPath.en.md" - title: "GeoBoundary" link: "https://reference.wolfram.com/language/ref/GeoBoundary.en.md" - title: "GeoCircle" link: "https://reference.wolfram.com/language/ref/GeoCircle.en.md" - title: "GeoBoundsRegionBoundary" link: "https://reference.wolfram.com/language/ref/GeoBoundsRegionBoundary.en.md" - title: "GeoHemisphereBoundary" link: "https://reference.wolfram.com/language/ref/GeoHemisphereBoundary.en.md" - title: "GeoVisibleRegionBoundary" link: "https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.en.md" related_tutorials: - title: "GeoGraphics" link: "https://reference.wolfram.com/language/tutorial/GeoGraphics.en.md" --- # GeoLength GeoLength[g] gives the length of the geo path g. ## Details and Options * The path ``g`` in ``GeoLength[g]`` can be any one-dimensional geo primitive, such as ``GeoPath``, ``GeoCircle``, or ``GeoVisibleRegionBoundary``. * ``GeoLength[GeoPath[{p1, p2, …}]]`` computes the length of the path formed by geodesic segments joining the locations ``pi``. * ``JoinedCurve`` and ``GeoGroup`` can be used to combine multiple paths. * ``GeoLength[g]`` returns a ``Quantity`` object with units of length. * ``GeoLength[{g1, g2, …}]`` gives ``{GeoLength[g1], GeoLength[g2], …}``. * Possible options of ``GeoLength`` include: | | | | | ----------- | ------------ | ------------------------------------ | | GeoModel | Automatic | model of the Earth or celestial body | | UnitSystem | \$UnitSystem | unit system to use in the result | --- ## Examples (13) ### Basic Examples (4) Compute the total length of a geo path on the Earth: ```wl In[1]:= GeoLength[GeoPath[{Entity["City", {"NewYork", "NewYork", "UnitedStates"}], Entity["City", {"Chicago", "Illinois", "UnitedStates"}], Entity["City", {"Toronto", "Ontario", "Canada"}]}]] Out[1]= Quantity[1159.8294630322225, "Miles"] ``` --- Compute the total length of a path formed by geodesic segments: ```wl In[1]:= GeoLength[GeoPath[{{0, 0}, {0, 40}, {40, 70}}]] Out[1]= Quantity[6105.97585791728, "Miles"] ``` Compute the total length of the rhumb lines joining the same points: ```wl In[2]:= GeoLength[GeoPath[{{0, 0}, {0, 40}, {40, 70}}, "RhumbLine"]] Out[2]= Quantity[6111.167059303452, "Miles"] ``` --- Length of the Earth's equator: ```wl In[1]:= GeoLength[GeoPath["Equator"]] Out[1]= Quantity[24901.460896848952, "Miles"] ``` Length of a full meridian: ```wl In[2]:= 2GeoLength[GeoPath["PrimeMeridian"]] Out[2]= Quantity[24859.733479555565, "Miles"] ``` --- Compute the perimeter of a geo disk: ```wl In[1]:= GeoLength[GeoCircle[Entity["City", {"London", "GreaterLondon", "UnitedKingdom"}], Quantity[500, "Miles"]]] Out[1]= Quantity[3133.2776040763447, "Miles"] ``` ### Scope (3) Compute the length of different one-dimensional geo elements: ```wl In[1]:= GeoLength[GeoPath[{{0, 0}, {40, 30}, {20, -10}}]] Out[1]= Quantity[6072.339433495231, "Miles"] In[2]:= GeoLength[GeoCircle[{0, 0}, Quantity[500, "Miles"]]] Out[2]= Quantity[3133.2095489363473, "Miles"] In[3]:= GeoLength[DayNightTerminator[DateObject[{2015, 12, 21}]]] Out[3]= Quantity[24866.37592283172, "Miles"] In[4]:= GeoLength[GeoHemisphereBoundary[Here]] Out[4]= Quantity[24876.997896811146, "Miles"] ``` --- Length of the perimeter of a region with holes, as a single joined object: ```wl In[1]:= outer = GeoPath[{{0, 0}, {40, 0}, {40, 100}, {0, 100}, {0, 0}}]; inner1 = GeoPath[{{10, 10}, {30, 10}, {30, 40}, {10, 40}, {10, 10}}]; inner2 = GeoPath[{{10, 60}, {30, 60}, {30, 90}, {10, 90}, {10, 60}}]; In[2]:= g = JoinedCurve[{{outer}, {inner1}, {inner2}}]; In[3]:= GeoGraphics[{Red, g}] Out[3]= [image] In[4]:= GeoLength[g] Out[4]= Quantity[30575.81362380393, "Miles"] ``` It can also be obtained by adding the lengths of the outer and inner curves: ```wl In[5]:= GeoLength[outer] + GeoLength[inner1] + GeoLength[inner2] Out[5]= Quantity[30575.81362380393, "Miles"] ``` --- Paths of different types can be combined with ``GeoGroup`` : ```wl In[1]:= g1 = GeoCircle[Entity["City", {"NewYork", "NewYork", "UnitedStates"}], Quantity[600, "Miles"]]; g2 = GeoPath[{Entity["City", {"NewYork", "NewYork", "UnitedStates"}], Entity["City", {"Chicago", "Illinois", "UnitedStates"}], Entity["City", {"Toronto", "Ontario", "Canada"}]}]; In[2]:= GeoLength[GeoGroup[{g1, g2}]] Out[2]= Quantity[4915.341221747185, "Miles"] In[3]:= % == Total[GeoLength[{g1, g2}]] Out[3]= True ``` ### Generalizations & Extensions (1) ``GeoLength[Line[{p1, p2, …}]]`` is equivalent to ``GeoLength[GeoPath[{p1, p2, …}]]`` for geo locations ``pi`` : ```wl In[1]:= GeoLength[Line[GeoPosition[{{0, 0}, {0, 40}, {40, 70}}]]] Out[1]= Quantity[6105.97585791728, "Miles"] In[2]:= % == GeoLength[GeoPath[{{0, 0}, {0, 40}, {40, 70}}]] Out[2]= True ``` ### Options (2) #### UnitSystem (1) Use the units determined by the value of ``\$UnitSystem`` : ```wl In[1]:= $UnitSystem Out[1]= "Imperial" In[2]:= GeoLength[GeoPath["NorthernTropic"]] Out[2]= Quantity[22859.219868472403, "Miles"] ``` Specify the unit system to use: ```wl In[3]:= GeoLength[GeoPath["NorthernTropic"], UnitSystem -> "Metric"] Out[3]= Quantity[36788.34834000685, "Kilometers"] ``` #### GeoModel (1) Length of a geo path on the Earth: ```wl In[1]:= g = GeoPath[{{10, 40}, {20, 50}, {-40, 120}}]; GeoLength[g] Out[1]= Quantity[7064.395810227721, "Miles"] ``` Length of the corresponding path on Mars: ```wl In[2]:= GeoLength[g, GeoModel -> "Mars"] Out[2]= Quantity[3754.6175205296854, "Miles"] ``` ### Applications (2) Compute the length of the boundary of a country from its polygon: ```wl In[1]:= GeoLength[GeoBoundary[Entity["Country", "Spain"]["Polygon"]]] Out[1]= Quantity[4014.753603939431, "Miles"] ``` That value is shorter than the actual length of the boundary, due to approximations in the polygon: ```wl In[2]:= Entity["Country", "Spain"]["BoundaryLength"] Out[2]= Quantity[4276.214407858109, "Miles"] ``` --- The length of a segment of parallel, or the projection on a parallel of any geo path, is called departure: ```wl In[1]:= GeoLength[GeoPath[{"Parallel", 38, {0, 5}}]] Out[1]= Quantity[272.88280515268525, "Miles"] ``` Express it in nautical miles: ```wl In[2]:= UnitConvert[%, "NauticalMiles"] Out[2]= Quantity[237.12867450088723, "NauticalMiles"] ``` ### Properties & Relations (1) For a geo path defined by a list of points, ``GeoLength[GeoPath[list]]`` is equivalent to ``GeoDistance[list]`` : ```wl In[1]:= list = RandomReal[{-90, 90}, {10, 2}] Out[1]= {{8.85956, 24.5283}, {54.3463, 53.9451}, {-58.1838, 52.5296}, {-50.818, -14.0151}, {-57.5593, -63.6563}, {61.8156, -20.4106}, {31.6636, 13.6522}, {82.1434, 53.2884}, {-72.0694, -53.4474}, {67.9236, 33.2725}} In[2]:= GeoLength[GeoPath[list]] Out[2]= Quantity[52319.51545870635, "Miles"] In[3]:= % == GeoDistance[list] Out[3]= True ``` ## See Also * [`GeoDistance`](https://reference.wolfram.com/language/ref/GeoDistance.en.md) * [`GeoDistanceList`](https://reference.wolfram.com/language/ref/GeoDistanceList.en.md) * [`ArcLength`](https://reference.wolfram.com/language/ref/ArcLength.en.md) * [`GeoArea`](https://reference.wolfram.com/language/ref/GeoArea.en.md) * [`Quantity`](https://reference.wolfram.com/language/ref/Quantity.en.md) * [`GeoPath`](https://reference.wolfram.com/language/ref/GeoPath.en.md) * [`GeoBoundary`](https://reference.wolfram.com/language/ref/GeoBoundary.en.md) * [`GeoCircle`](https://reference.wolfram.com/language/ref/GeoCircle.en.md) * [`GeoBoundsRegionBoundary`](https://reference.wolfram.com/language/ref/GeoBoundsRegionBoundary.en.md) * [`GeoHemisphereBoundary`](https://reference.wolfram.com/language/ref/GeoHemisphereBoundary.en.md) * [`GeoVisibleRegionBoundary`](https://reference.wolfram.com/language/ref/GeoVisibleRegionBoundary.en.md) ## Tech Notes * [GeoGraphics](https://reference.wolfram.com/language/tutorial/GeoGraphics.en.md) ## Related Guides * [`Geodesy`](https://reference.wolfram.com/language/guide/Geodesy.en.md) * [Maps & Cartography](https://reference.wolfram.com/language/guide/MapsAndCartography.en.md) ## Related Links * [An Elementary Introduction to the Wolfram Language: Geocomputation](https://www.wolfram.com/language/elementary-introduction/18-geocomputation.html) ## History * [Introduced in 2016 (10.4)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn104.en.md)