ing angle


MIXTRI 2.0 - an MS Excel 97 VBA macro to draw
LCA results in a mixing triangle (aka ternary plot)

Sample Graph | Download Excel workbook | Related 3rd party freeware | References

The new damage-oriented method for Life Cycle Impact Assessment 'Eco-indicator'99' allows to aggregate environmental effects in three damage categories: damages to human health, ecosystem quality and resources. To arrive at a single score environmental measure the relative weighting of these three types of damages is required. Besides a - necessarily subjective - default weighting scheme for these three damages one can also use a graphic representation of all possible weighting schemes: the mixing triangle.

Within the triangle, preferred weighting points can be selected. Different cultural archetypes, as described by Cultural Theory, opt for typical weighting schemes within the triangle according to their cultural value setting. Thus, this method is able to combine "hard" findings from life cycle inventories with "soft" results from sociology, philosophy and psychology.

The triangle shows which product is environmentally less burdening depending on the weighting scheme for that point in the triangle. Lines of indifference can be drawn where two products cause equal - or to be more precise: equally perceived - damages.

I wrote an Excel VBA macro scanning the whole weighting triangle for the best (or dominating) product option out of an unlimited number of product options. Areas of dominance are faded to white when an other product scores close to the best product. ('closeness' is defined by the parameter delta , this 'level of significance' is set to 35%, user definable.).

MIXTRI 2.0 saves plots as space saving GIF files approx 28kB (but retains an editable 300kB PICT copy in the clipboard).

Mixing Triangle Sample Graph

Above you see a sample graph to compare the environmental impacts of a number of product options and the various results when giving different weights for damages to human health (HH), ecosystem quality (EQ), and resources (R). Sum of the weights is always 100% for every point. The triangle shows which product has the lowest burden. Only two products (#2 and #3) have areas where they alone are significantly best (lowest burden and no hatching).
Product No. 4 has an unsignificant area of dominance (hatched), i.e. No. 4 is not significantly the best, but other products score comparably there.
Product No. 1 is not shown at all since it is never the best product.


This is a workbook written on a German MS Excel 97 for Macintosh. Import to Windows machines, higher or other language versions of Excel should not be a problem. If so; tell me.

Download uncompressed excel workbook MIXTRI 2.0

NO manual available yet! coming soon...

The thing is checked and virus free. I can't take any responsibility for this product, you use it on your own account. If you'd like to give me some credit though, I won't mind. Have fun.

older Version 1.0, for 3 Products, with explicit lines of indifference

Other freeware for ternary plots
Some other freeware tools to draw ternary plots are listed below. Ternary plots are mainly used in geology and chemistry and hence, none of these are fit to show dominance areas, as my tool does.




Gabor Doka, Zürich, Switzerland, 3rd July 2000