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VectorPlot3D
✖
VectorPlot3D

✖
VectorPlot3D[{vx,vy,vz},{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

generates a 3D vector plot of the vector field {vx,vy,vz} as a function of x, y, and z.

✖
VectorPlot3D[{field1,field2,…},{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

plots several vector fields.

✖
VectorPlot3D[…,{x,y,z}∈reg]

takes the variables {x,y,z} to be in the geometric region reg.

Details and Options

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

Plot a vector field:

In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-e8vvkn
Out[3]=3

Include a legend for the vector magnitudes:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-sgxlon
Out[1]=1

Use tube segments as markers to represent the vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-62np7l
Out[1]=1

Plot a vector field inside the unit ball:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-x3jzdi
Out[1]=1

Scope  (14)Survey of the scope of standard use cases

Sampling  (5)

Use Evaluate to evaluate the vector field symbolically before numeric assignment:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-wsetn
Out[1]=1

Plot vectors over specified regions:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-2z4i7
Out[1]=1

Plot a vector field with vectors placed with specified densities:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-e44lkt
Out[1]=1

Plot a field with arrows placed at random locations:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-bliq74
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-illqfm
Out[2]=2

Plot multiple vector fields with different colors for each field:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-jsekl8
Out[1]=1

Presentation  (9)

Plot a vector field with arrows scaled according to their magnitudes:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-cvj26o
Out[1]=1

Use a single color for the arrows:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-oyavbn
Out[1]=1

Plot with 3D arrows:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-nrzzgh
Out[1]=1

Color and scale the vectors based on the norm of the field:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-d540zk
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-b9b4ip
Out[2]=2

Plot a vector field with arrows of specified size:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-eejww2
Out[1]=1

Vary the arrow length and arrowhead size:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-eirmoa
Out[1]=1

Include a legend:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-znxf0
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-osm2fc
Out[2]=2

Use a highly stylized theme:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-j0oo7n
Out[1]=1

Use a log scale for the x axis:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-nvp776
Out[1]=1

Reverse the y scale so it increases toward the bottom:

In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-nq43yb
Out[2]=2

Options  (65)Common values & functionality for each option

BoxRatios  (2)

By default, BoxRatios is set to Automatic:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-c3rytn
Out[1]=1

Make the height appear twice the width and length:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-gp9a3b
Out[1]=1

EvaluationMonitor  (2)

Show where the function is sampled:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ej
Out[1]=1

Count how many times the vector field function is evaluated:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-c1heav
Out[1]=1

PerformanceGoal  (2)

Generate a higher-quality plot:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-tpxw7r
Out[1]=1

Emphasize performance, possibly at the cost of quality:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-b9mdd8
Out[1]=1

PlotLegends  (5)

No legends are included by default:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-hsg59b
Out[1]=1

Add a legend that indicates vector norms:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-b7g2oh
Out[1]=1

Include a legend for two fields:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ksjv6o
Out[1]=1

Include the vector fields in the legend:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-bejvz
Out[1]=1

Control the placement of the legend:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-h6oib
Out[1]=1

PlotRange  (9)

The full plot range is used by default:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-e5htpa
Out[1]=1

Use all points to compute the range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-blj3hi
Out[1]=1

Specify an explicit limit for , , and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-iujowz
Out[1]=1

Specify an explicit range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-nvj2f1
Out[1]=1

Specify an explicit minimum range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-6mhl8
Out[1]=1

Specify an explicit range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-f1b74a
Out[1]=1

Specify an explicit maximum range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-dv35v5
Out[1]=1

Specify an explicit range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-tns6h
Out[1]=1

Specify different , , and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-eji1ea
Out[1]=1

PlotRangePadding  (8)

Padding is computed automatically by default:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-d2h2aw
Out[1]=1

Specify no padding for all , , and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-0h4yz
Out[1]=1

Specify an explicit padding for all , , and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-cl0fye
Out[1]=1

Add 10% padding to all , , and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-djbx3
Out[1]=1

Specify padding for and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-eirhh1
Out[1]=1

Specify different padding for , , and ranges:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-em1fr
Out[1]=1

Specify padding for the range:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-n1k40
Out[1]=1

Use different padding forms for each dimension:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-iz9ibd
Out[1]=1

PlotTheme  (2)

Use a theme with dense vector points and legends:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ssqbcb
Out[1]=1

Reduce the number of vector points:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-1pnjif
Out[1]=1

RegionBoundaryStyle  (5)

Show the region defined by a region function:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-yrk32
Out[1]=1

Use None to not show the boundary:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-mzy3v
Out[1]=1

Specify a style for the boundary:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-3hu16t
Out[1]=1

The boundaries of full rectangular regions are not shown:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-7wf5ba
Out[1]=1

Specify a style for full rectangular regions:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-bkobwf
Out[1]=1

RegionFunction  (3)

Plot vectors only over certain quadrants:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-juf837
Out[1]=1

Plot vectors only over regions where the field magnitude is above a given threshold:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-q5srw6
Out[1]=1

Use any logical combination of conditions:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-gbou4u
Out[1]=1

ScalingFunctions  (1)

Use a log scale for the x axis:

In[4]:=4
✖
https://wolfram.com/xid/0b8ens9p0o-370rn4
Out[4]=4

Reverse the y scale so it increases toward the bottom:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-7rdsjm
Out[1]=1

VectorAspectRatio  (2)

The default aspect ratio for a vector marker is 1/4:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-cj1gt3
Out[1]=1

Increase the relative width of a vector marker:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-flh1i1
Out[1]=1

VectorColorFunction  (4)

Color the vectors according to their norm:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-l4o9lw
Out[1]=1

Use any named color gradient from ColorData:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-jk16xa
Out[1]=1

Color the vectors according to their value:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-f41zkj
Out[1]=1

Use VectorColorFunctionScaling->False to get unscaled values:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-l4us3
Out[1]=1

VectorColorFunctionScaling  (4)

By default, scaled values are used:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ehenrc
Out[1]=1

Use VectorColorFunctionScaling->False to get unscaled values:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-qk8lj6
Out[1]=1

Use unscaled coordinates in the direction and scaled coordinates in the direction:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-vnou8
Out[1]=1

Explicitly specify the scaling for each color function argument:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-f14zf7
Out[1]=1

VectorMarkers  (3)

By default, 3D arrows are used:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-bjkrd9
Out[1]=1

Use other named markers:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-kx459h
Out[1]=1

Use Placed to control the arrow placement relative to the vector points:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-8ybcqb
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-h3294t
Out[2]=2

VectorPoints  (7)

Use automatically determined vector points:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-likp
Out[1]=1

Use symbolic names to specify the set of field vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-i2b0f2
Out[1]=1

Create a regular grid of field vectors with the same number of arrows for , , and :

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ekb8ya
Out[1]=1

Create a regular grid of field vectors with a different number of arrows for , , and :

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-74eh0
Out[1]=1

Specify a list of points for showing field vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-koe9z
Out[1]=1

Use a different number of field vectors on a packed grid:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-b59v42
Out[1]=1

The location for vectors is given in the middle of the drawn vector:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-l3pdr
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-4f45g
Out[2]=2

Start the vectors at the points:

In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-sjkpfe
Out[3]=3

VectorRange  (4)

The clipping of vectors with very small or very large magnitudes is done automatically:

In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-bvc580
Out[2]=2

Specify the range of vector norms:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ycbb09
Out[1]=1

Suppress the clipped vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-m0tgf
Out[1]=1

Show all the vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-qe76s
Out[1]=1

VectorStyle  (2)

VectorColorFunction takes precedence over colors in VectorStyle:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-cwffmy
Out[1]=1

Use VectorColorFunction→None to specify colors with VectorStyle:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-c3z248
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

An electrostatic potential built from a collection of point charges at positions :

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-dcbhq9
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-cg2qge

An electric field between two charges and :

In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-d0m638

The electrostatic potential between two charges and :

In[4]:=4
✖
https://wolfram.com/xid/0b8ens9p0o-d4tz6d
Out[4]=4

The electric field between two charges and :

In[5]:=5
✖
https://wolfram.com/xid/0b8ens9p0o-clmggh
Out[5]=5

Combine both visualizations:

In[6]:=6
✖
https://wolfram.com/xid/0b8ens9p0o-bqt1os
Out[6]=6

Properties & Relations  (14)Properties of the function, and connections to other functions

Use ListVectorPlot3D to visualize data:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-cbq7px
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-ii6evm
Out[2]=2

Plot vectors along surfaces with SliceVectorPlot3D:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ckcmzh
Out[1]=1

Plot data vectors on surfaces with ListSliceVectorPlot3D:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-dgaz9l
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-exn4uf
Out[2]=2

Use StreamPlot3D to plot streamlines for a 3D vector field:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-tfo4y9
Out[1]=1

Use ListStreamPlot3D to plot with data:

In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-hsvgak
In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-bviuq7
Out[3]=3

Use VectorDisplacementPlot to visualize the effect of a displacement vector field on a specified region:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-czkc2f
Out[1]=1

Use ListVectorDisplacementPlot to visualize the effect of displacement field data on a region:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-c4etvu
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-g31h2t
Out[2]=2

Use VectorDisplacementPlot3D to visualize the effect of a displacement vector field on a specified 3D region:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-mhw7bs
Out[1]=1

Use ListVectorDisplacementPlot3D to visualize the effect of 3D displacement vector field data on a specified region:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-e9pqu
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-kk9hv3
Out[2]=2

Use VectorPlot for plotting 2D vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-bzenb8
Out[1]=1

Use ListVectorPlot to plot with data:

In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-exrywf
In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-dv90zq
Out[3]=3

Use StreamPlot to plot with streamlines instead of vectors:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-ey0nl
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-f8x037
In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-eqnaj8
Out[3]=3

Use VectorDensityPlot to add a density plot of the scalar field:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-gljrl7
Out[1]=1

Use StreamDensityPlot to plot streamlines instead of vectors:

In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-f4yecd
Out[2]=2

Use ListVectorDensityPlot or ListStreamDensityPlot for plotting data:

In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-i1hwev
In[4]:=4
✖
https://wolfram.com/xid/0b8ens9p0o-fktigc
Out[4]=4

Use LineIntegralConvolutionPlot to plot the line integral convolution of a vector field:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-biddpp
Out[1]=1

Plot a complex function as a vector field:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-rjlzpk
Out[1]=1

Plot streams instead of vectors with ComplexStreamPlot:

In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-h5phyg
Out[2]=2

Use GeoVectorPlot to generate a vector plot over the Earth:

In[1]:=1
✖
https://wolfram.com/xid/0b8ens9p0o-jyfddy
In[2]:=2
✖
https://wolfram.com/xid/0b8ens9p0o-jpldfa
In[3]:=3
✖
https://wolfram.com/xid/0b8ens9p0o-bm7stf
Out[3]=3

Use GeoStreamPlot to use streams instead of vectors:

In[4]:=4
✖
https://wolfram.com/xid/0b8ens9p0o-fspawf
Out[4]=4
Wolfram Research (2008), VectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorPlot3D.html (updated 2022).
✖
Wolfram Research (2008), VectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorPlot3D.html (updated 2022).

Text

Wolfram Research (2008), VectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorPlot3D.html (updated 2022).

✖
Wolfram Research (2008), VectorPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorPlot3D.html (updated 2022).

CMS

Wolfram Language. 2008. "VectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/VectorPlot3D.html.

✖
Wolfram Language. 2008. "VectorPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/VectorPlot3D.html.

APA

Wolfram Language. (2008). VectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorPlot3D.html

✖
Wolfram Language. (2008). VectorPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorPlot3D.html

BibTeX

@misc{reference.wolfram_2025_vectorplot3d, author="Wolfram Research", title="{VectorPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/VectorPlot3D.html}", note=[Accessed: 26-April-2025 ]}

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@misc{reference.wolfram_2025_vectorplot3d, author="Wolfram Research", title="{VectorPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/VectorPlot3D.html}", note=[Accessed: 26-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_vectorplot3d, organization={Wolfram Research}, title={VectorPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/VectorPlot3D.html}, note=[Accessed: 26-April-2025 ]}

✖
@online{reference.wolfram_2025_vectorplot3d, organization={Wolfram Research}, title={VectorPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/VectorPlot3D.html}, note=[Accessed: 26-April-2025 ]}