Piper Diagrams



Piper Diagram

A Piper diagram is a form of the trilinear diagram. The Piper diagram has two simple triangular plots on the right and left side of a 4-sided center field as shown in the sample plot below.

Click here to view a training video on creating Piper Diagrams in EnviroInsite.

For each sample, there are three variables to determine the plotting position  in each triangular plot, for example the axes may be the three major cations (left) and anions (right) and the variables are the cation/anion composition of the sample. Each of the three cation/anion variables, in milliequivalents, is divided by the sum of the three values, to produce a percent of total cations.  For example, if Ca= 0.80 meq, Mg =0.26 meq, and Na+K = 0.89 meq, then %Ca = 41, %Mg = 13, and %[Na+K] = 46.

The data points in the center field are located by extending the points in the lower triangles to the point of intersection in the center field.  The axis values at the top and bottom of the center field are 100; the axis values on the left and right side of the center field are 0. 

To create a Piper diagram, select Window - New - Piper Diagram.  Then select the ions to be plotted and other plotting options and hit the OK button.  Most commonly, the selected anions are (1) Cl, (2) HCO3 + CO3 and (3) SO4 and the selected cations are (1) Na + K, (2) Ca and (3) Mg as shown in the dialog box image below. 

One of the unique features of Piper diagrams generated in EnviroInsite is the ability to post the well and screen label.  Individual well labels may be turned on or off by deselecting the check box associated with each label from the tree control menu.


The Piper diagram plots results based on parameter concentrations expressed in equivalents per volume.  The value in the Equivalent Weight field in the constituents table is used to convert between the measured mass concentration and the concentration in equivalents or milliequivalents per volume.  The Equivalent Weight field should be entered as positive for cations and negative for anions.  If the concentration values are entered as milligrams per liter or parts per million then the following values in the Equivalent Weight field will convert the concentrations to meq per liter.

Cation / Anion

Equivalent Weight









Fe (II)


Fe (III)



















(Description of Piper diagram adapted from a note by Virginia McGuire, Water Resources Division, US Geological Survey posted at www.biostat.wustl.edu. )