Ternary diagrams are triangular plots of three variables that sum to a constant, typically 100%. First introduced by August Mobius in 1827, they are sometimes called simplex plots, Gibbs triangles, or de Finetti diagrams. Ternary diagrams are commonly used within the geosciences as classification/discrimination diagrams.

Below are examples of common ternary diagrams used in the earth sciences: the USDA soils classification diagram and the Sheperd’s Sediment classification diagram.

Other notable ternary diagrams in the earth sciences include the QFL diagram, QAPF diagram, and a large variety of ternary phase diagrams.

Plotting Onto a Ternary Diagram

Ternary diagrams make the assumption that the three variables plotted make up 100% of the sample. Before you can plot a data point (say, A = 700, B = 200, and C = 100) you must first normalize that data to 100%. This is done by dividing each value for a point (A, B, and C) by the sum of those values. The generalized equation for this is below:

For value A in our example above this becomes:

Thus, after normalization the above data point becomes (A = 70, B = 20, C = 10).

Adding a point to a ternary diagram is relatively simple once you get your head around how points move along the axes. Because we plot normalized data onto a ternary plot, all axes are in units of percent (%) and the values range from 0 to 100 (sometimes 0 to 1). The maximum for each ternary axis is located at the triangle node with the axis label. Zero for the any ternary axis is located along the line opposite the axis label. So, to move along a ternary axis you start at the line opposite the axis label and then move perpendicularly away from the line toward the axis label.

Thus, our example point from above (A = 70, B = 20, C = 10) will plot on a ternary diagram like so.

In practice, you will generally only need two coordinates to find a point location on a ternary plot. This is because ternary points always sum to 100, so after plotting a point on axis A and B, axis C will be solved.