Is there a particular name for bar plots, in which bars are rectangular, with unequal bases?

That is:

  • width represents size (e.g. population),
  • height represents intensive variable (e.g. CO$_2$ emission per capita),
  • area represents extensive variable (e.g. total CO$_2$ emission).

Example (from David JC MacKay, "Sustainable Energy - without the hot air", page 14):

CO2 emission rate by country

In the same vein: this and that. Another one: "Real GDP Per Capita and Shares of Global Population" (found here):

enter image description here

I find these plots immensely useful, as they show both the local effect (is a country particularly rich, polluting, militaristic...) and the global share (of economy/pollution/military power).

I have even made one: Research publications per capita? - Academia.SE. I care for its name both to search for examples, plotting libraries/functions etc, and to propagate this way of presenting data.

  • 1
    $\begingroup$ All bars are rectangular (quadrilateral with four right angles)! What's a little unusual here are the varying (unequal) bar widths. Plotting cumulative shares like this is perhaps more commonly done using a Lorenz curve, which in turn is a kind of P-P (probability-probability) plot. You have here discrete versions with several bars identified. I don't know that this has, or really needs, a distinctive name. Your second graph is closer to a Lorenz curve; the first has extra structure given by grouping. $\endgroup$
    – Nick Cox
    Commented Jun 29, 2015 at 13:17
  • $\begingroup$ @NickCox I missed "uneven base" (fixed). Thanks for brining Lorenz curve (I know it, but I was not thinking about it as bar plots from this question can, but don't have to be, ordered). $\endgroup$ Commented Jun 29, 2015 at 13:21
  • $\begingroup$ Small corrections: In English we would not say "uneven"; that's for surfaces not quite flat or smooth. It's Lorenz: Lorentz was a different person altogether. Key point: You are correct: bar charts with touching unequal width bars do not have to be ordered. But they are not of much use or interest without an ordering of some kind. $\endgroup$
    – Nick Cox
    Commented Jun 29, 2015 at 13:24
  • $\begingroup$ @NickCox Lorenz - fixed (I can never remember, same Schwar(t)z). Well, there are other orderings, which make sense (e.g. as in the example 1); or there may be no ordering if there are only a few values. Is "variable bases" OK? $\endgroup$ Commented Jun 29, 2015 at 13:31
  • 1
    $\begingroup$ Kaiser Fung points out the shortcomings of that GDP chart in his junkcharts blog and a follow-up post. $\endgroup$
    – xan
    Commented Jun 30, 2015 at 12:55

1 Answer 1


Apparently they are called cascade charts, see:

As a bonus, ggplot2: Variable Width Column Chart.

However, sometimes cascade chart is used as a synonymous of waterfall chart (which is a different thing from the discussed above), see e.g.:

In any case, judging for length I needed to get this answer, this name may be not that popular even among people creating similar bar plots (and perhaps a descriptive way may be better).

As was pointed out by @NickCox, if bars are sorted by their height, it is a discrete variant of the Lorenz curve.

  • 2
    $\begingroup$ I found three quite different meanings for waterfall plot or chart in a search a while back. Picturesque name, inconstant interpretation. $\endgroup$
    – Nick Cox
    Commented Jun 29, 2015 at 18:42

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