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Scaled[{x,y,…}]

gives the position of a graphical object in terms of coordinates scaled to run from 0 to 1 across the whole plot range in each direction.

Scaled[{dx,dy,…},{x0,y0,…}]

gives a position obtained by starting at ordinary coordinates {x0,y0,…}, then moving by a scaled offset {dx,dy,…}.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Scaled Positions  
Scaled Sizes  
Scaled Offsets  
Scaled radii  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
Related Workflows
History
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Scaled

Scaled[{x,y,…}]

gives the position of a graphical object in terms of coordinates scaled to run from 0 to 1 across the whole plot range in each direction.

Scaled[{dx,dy,…},{x0,y0,…}]

gives a position obtained by starting at ordinary coordinates {x0,y0,…}, then moving by a scaled offset {dx,dy,…}.

Details

  • Scaled can be used to specify scaled coordinates in any two‐ or three‐dimensional graphics primitive.
  • You can use Scaled to represent objects that occupy a fixed region in a plot, independent of the specific range of coordinates in the plot.
  • Scaled refers only to the region of a plot defined by its PlotRange and PlotRangePadding. It does not take account of elements such as tick labels, or of margins introduced by ImageMargins.
  • Scaled can be used not only for coordinates, but also for scalar length measures such as radii.
  • In 2D graphics, Scaled[r] is taken to be relative to the width of the whole graphic. In 3D graphics, it is taken to be relative to the diagonal of the 3D bounding box.

Examples

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Basic Examples  (3)

Positions of objects by fractions of the plot range:

Plot range padding by fractions of the plot range:

Cell sizes by a fraction of the document width:

Scope  (10)

Scaled Positions  (3)

Specify coordinates by fractions of the plot range:

Specify radii by fractions of the plot range:

Specify the positions of light sources by scales of the plot range:

Scaled Sizes  (4)

Specify ImageSize by a fraction of the enclosing region:

Specify ItemSize by a fraction of the document width:

Specify PlotRangePadding by fractions of the plot range:

Specify the font size according to the width of the plot range:

Scaled Offsets  (1)

Specify scaled offsets from the ordinary coordinates:

Scaled radii  (2)

In 2D graphics, Scaled radius is taken to be relative to the width of the whole graphic:

In 3D graphics, it is taken to be relative to the diagonal of the 3D bounding box:

Applications  (1)

Place text at the top right-hand corners:

Properties & Relations  (6)

Scaled is proportional to PlotRange. ImageScaled is proportional to ImageSize:

Scaled operates relative to the plot range:

ImageScaled operates relative to the whole image:

Scaled coordinates do not have to be between 0 and 1:

In 2D the transformation from world coordinates to Scaled coordinates is given by:

From Scaled to world coordinates:

In 3D the transformation from world coordinates to Scaled coordinates is given by:

From Scaled to world coordinates:

Possible Issues  (3)

Objects with Scaled coordinates outside 0 and 1 may not be displayed in 3D:

Using Scaled sizes will depend on the PlotRange:

Using automatic plot range with Scaled may cause an ambiguity:

Having objects in the graphic with nonscaled coordinates will disambiguate the scale:

Using a fixed plot range will also disambiguate the scale:

Wolfram Research (1988), Scaled, Wolfram Language function, https://reference.wolfram.com/language/ref/Scaled.html (updated 2008).

Text

Wolfram Research (1988), Scaled, Wolfram Language function, https://reference.wolfram.com/language/ref/Scaled.html (updated 2008).

CMS

Wolfram Language. 1988. "Scaled." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/Scaled.html.

APA

Wolfram Language. (1988). Scaled. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Scaled.html

BibTeX

@misc{reference.wolfram_2025_scaled, author="Wolfram Research", title="{Scaled}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Scaled.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_scaled, organization={Wolfram Research}, title={Scaled}, year={2008}, url={https://reference.wolfram.com/language/ref/Scaled.html}, note=[Accessed: 08-August-2025]}