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plotting - How to Set the Ratio of Units of the Axes in a 2D Plot?


Consider the following plot


Plot[{Sin[x]}, {x, 0, 2*Pi}, PlotRange -> {{0, 2*Pi}, {-1.05, 1.05}}, 
 AxesLabel -> {x, y}, AxesOrigin -> {0, 0}]

enter image description here


It is evident that 1 unit on the y axis is not as the same length of 1 unit on the x axis. I want the ratio of these units to be one or any other desired value r=yaxis unitxaxis unit.



I searched for how to determine the scaling of these units of the axes. I encountered this post and this one. But I could not find a nice answer explaining a simple way to do the job. Also, I couldn't find a nice example in the documentation. I just learned from documentation that



AspectRatio determines the ratio of PlotRange, not ImageSize.



So here is my question


What is a simple way to manually edit the ratio of the units of the axes?.



Answer



To get 1:1 unit ratio you can use


Plot[{Sin[x]}, {x, 0, 2*Pi},
 PlotRange -> {{0, 2*Pi}, {-1.05, 1.05}},

 AxesLabel -> {x, y}, AxesOrigin -> {0, 0},
 AspectRatio -> Automatic
 ]

To get for example 1:2 unit ratio you can use:


Plot[{Sin[x]}, {x, 0, 2*Pi},
 PlotRange -> {{0, 2*Pi}, {-1.05, 1.05}},
 AxesLabel -> {x, y}, AxesOrigin -> {0, 0},
 AspectRatio -> 2*(1.05 + 1.05)/(2 Pi - 0)
 ]


Mathematica graphics


As stated by @Sjoerd to define AspectRatio properly you should take into account the PlotRange as I did.


If you don't know in advance the PlotRange of your plot you can also use the following to get it after making an "hidden" plot:


g = Plot[{Sin[x]}, {x, 0, 2*Pi},
   AxesLabel -> {x, y}, AxesOrigin -> {0, 0}
   ];
Show[g, AspectRatio -> 2 / Divide @@ (Subtract @@@ PlotRange[g])]

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