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pyplot scatter plot marker size

In the pyplot document for scatter plot:

matplotlib.pyplot.scatter(x, y, s=20, c='b', marker='o', cmap=None, norm=None,
                              vmin=None, vmax=None, alpha=None, linewidths=None,
                              faceted=True, verts=None, hold=None, **kwargs)

The marker size

s: size in points^2. It is a scalar or an array of the same length as x and y.

What kind of unit is points^2? What does it mean? Does s=100 mean 10 pixel x 10 pixel?

Basically I'm trying to make scatter plots with different marker sizes, and I want to figure out what does the s number mean.

Answer*

*Because other answers here claim that `s` denotes the area of the marker, I'm adding this answer to clearify that this is not necessarily the case.*

###Size in points^2
The argument `s` in `plt.scatter` denotes the `markersize**2`. As the documentation says

> `s` : scalar or array_like, shape (n, ), optional  
size in points^2. Default is rcParams['lines.markersize'] ** 2.

This can be taken literally. In order to obtain a marker which is x points large, you need to square that number and give it to the `s` argument.

So the relationship between the markersize of a line plot and the scatter size argument is the square. In order to produce a scatter marker of the same size as a plot marker of size 10 points you would hence call `scatter( .., s=100)`.

[![enter image description here][1]][1]

import matplotlib.pyplot as plt
    
    fig,ax = plt.subplots()
    
    ax.plot([0],[0], marker="o",  markersize=10)
    ax.plot([0.07,0.93],[0,0],    linewidth=10)
    ax.scatter([1],[0],           s=100)
    
    ax.plot([0],[1], marker="o",  markersize=22)
    ax.plot([0.14,0.86],[1,1],    linewidth=22)
    ax.scatter([1],[1],           s=22**2)
    
    plt.show()

###Connection to "area"

So why do other answers and even the documentation speak about "area" when it comes to the `s` parameter?

Of course the units of points**2 are area units.
 
* For the special case of a square marker, `marker="s"`, the area of the marker is indeed directly the value of the `s` parameter. 
* For a circle, the area of the circle is `area = pi/4*s`. 
* For other markers there may not even be any obvious relation to the area of the marker.

[![enter image description here][2]][2]

**In all cases however the area of the marker is proportional to the `s` parameter**. This is the motivation to call it "area" even though in most cases it isn't really.

Specifying the size of the scatter markers in terms of some quantity which is proportional to the area of the marker makes in thus far sense as it is the area of the marker that is perceived when comparing different patches rather than its side length or diameter. I.e. doubling the underlying quantity should double the area of the marker.

[![enter image description here][3]][3]

###What are points?

So far the answer to what the size of a scatter marker means is given in units of points. Points are often used in typography, where fonts are specified in points. Also linewidths is often specified in points. The standard size of points in matplotlib is 72 points per inch (ppi) - 1 point is hence 1/72 inches.

It might be useful to be able to specify sizes in pixels instead of points. If the figure dpi is 72 as well, one point is one pixel. If the figure dpi is different (matplotlib default is `fig.dpi=100`),

1 point == fig.dpi/72. pixels

While the scatter marker's size in points would hence look different for different figure dpi, one could produce a 10 by 10 pixels^2 marker, which would always have the same number of pixels covered:

[![enter image description here][4]][4]
[![enter image description here][5]][5]
[![enter image description here][6]][6]

import matplotlib.pyplot as plt
    
    for dpi in [72,100,144]:
    
        fig,ax = plt.subplots(figsize=(1.5,2), dpi=dpi)
        ax.set_title("fig.dpi={}".format(dpi))
        
        ax.set_ylim(-3,3)
        ax.set_xlim(-2,2)
        
        ax.scatter([0],[1], s=10**2, 
                   marker="s", linewidth=0, label="100 points^2")
        ax.scatter([1],[1], s=(10*72./fig.dpi)**2, 
                   marker="s", linewidth=0, label="100 pixels^2")
    
        ax.legend(loc=8,framealpha=1, fontsize=8)
        
        fig.savefig("fig{}.png".format(dpi), bbox_inches="tight")
        
    plt.show()

<hr>

If you are interested in a scatter in data units, check [this answer](https://stackoverflow.com/a/48174228/4124317).

[1]: https://i.sstatic.net/vxlWd.png
  [2]: https://i.sstatic.net/RcDoA.png
  [3]: https://i.sstatic.net/HanbD.png
  [4]: https://i.sstatic.net/SHlDG.png
  [5]: https://i.sstatic.net/EfEmQ.png
  [6]: https://i.sstatic.net/tO2zx.png

Edit Summary*

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1

Wondering how would one calculate what s parameter to give to scatter to get a circle which covers diameter of, let's say, 0.1 in real coordinates of the plot (so as to fill the gap between let's say 0.4 and 0.5 on a plot from (0,0) to (1,1)?
– Anatoly Alekseev
Commented Dec 26, 2018 at 19:56
@AnatolyAlekseev That should be answered by this question.
– ImportanceOfBeingErnest
Commented Feb 17, 2019 at 4:28
@ImportanceOfBeingErnest could you pls explain how to get the radius of a scatter based on the s param passed? I thought it is np.sqrt(s)/2. stackoverflow.com/q/64399664/9900084
– steven
Commented Oct 17, 2020 at 15:46

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pyplot scatter plot marker size

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