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}]

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 $r=\dfrac{y \,\, \text{axis unit}}{x \,\, \text{axis unit}}$.

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])]

Comments

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I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

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