Ternary Plot
A triangular coordinate system that plots three variables summing to a constant — revealing compositional relationships at a glance. Widely used in geology, chemistry, and materials science.
// 01 — The chart
What it looks like
A ternary plot showing soil samples classified by their sand, silt, and clay composition. Each point represents a soil sample whose three components sum to 100%.
// 02 — Definition
What is a ternary plot?
A ternary plot (also called a ternary diagram, triangle plot, or simplex plot) is a specialized chart drawn on an equilateral triangle. Each vertex represents 100% of one component, and any point within the triangle represents a unique mixture of all three components. The key constraint is that the three proportions must always sum to a fixed total — usually 100% or 1.0.
This constraint is what makes the triangle work: because any two proportions determine the third, a point in two-dimensional space can encode three variables without ambiguity. Moving toward a vertex increases that component’s proportion while reducing the other two. Moving along an edge means one component is zero.
Ternary plots are indispensable in geology (soil and rock classification), chemistry (phase diagrams and alloy composition), and materials science (polymer blends, ceramic formulations). They compress three-dimensional compositional data into a flat, readable format that reveals clusters, trends, and boundaries between compositional regions.
Origin: The ternary diagram was first used systematically in the early 19th century by mineralogists classifying rock compositions. The modern form was popularized by geologist J. F. W. von Wolff in 1908 and became standard in petrology for classifying igneous rocks by their mineral content.
// 03 — Anatomy
Parts of a ternary plot
// 04 — Usage
When to use it — and when not to
- You have exactly three components that sum to a fixed total (100% or 1.0)
- Classifying samples into compositional regions (soil texture, rock type, alloy grade)
- Visualizing phase diagrams where three substances interact in a closed system
- Comparing mixtures or blends across a large number of samples
- Showing how samples cluster by composition in geology, chemistry, or ecology
- Identifying trends in compositional change over time or across conditions
- Your variables do not sum to a constant — use a scatter plot or radar chart instead
- You have more or fewer than three components (use parallel coordinates for 4+)
- Your audience is unfamiliar with triangular coordinates — the learning curve is steep
- You need to show absolute quantities rather than proportions
- One component dominates so heavily that all points cluster near a single vertex
- You want to show time-series changes — consider a connected scatter plot instead
// 05 — Reading guide
How to read a ternary plot
Ternary plots can seem confusing at first. Follow these steps to decode any triangular diagram.
Identify the three components
Each vertex of the triangle represents 100% of one component. Read the labels at each corner to understand what is being measured — for example, Sand, Silt, and Clay in a soil texture diagram.
Learn the direction of each axis
For each component, the axis runs from the opposite side (0%) toward the labeled vertex (100%). Lines parallel to each side represent constant values of the component associated with the opposite vertex. Trace these gridlines to gauge proportions.
Read a point’s composition
For any data point, draw (or imagine) a line parallel to each side of the triangle through the point. Where that line intersects the axis tick marks tells you the percentage of each component. The three values will always sum to 100%.
Look for clusters and regions
Ternary plots often have labeled regions (like “loam” or “clay loam” in soil science). Notice where your data points fall relative to these boundaries. Clusters indicate samples with similar compositions.
Spot trends and mixing lines
If samples lie along a straight line, it suggests they are mixtures of two end-member compositions. If points trend toward a vertex over time, one component is becoming dominant. These linear patterns often reveal underlying geochemical or industrial processes.
// 06 — Common mistakes
Mistakes to watch out for
Components don’t sum to 100%
The fundamental requirement of a ternary plot is that the three values sum to a constant. If your data doesn’t satisfy this constraint, normalize it first or reconsider whether a ternary plot is the right choice. Plotting non-compositional data on a triangle produces misleading positions.
Misreading the axis directions
Each axis runs from a side toward the opposite vertex, which is counterintuitive for people used to Cartesian coordinates. The most common error is reading the wrong gridlines for a component. Always verify by checking that your three readings sum to 100%.
Ignoring the constant-sum constraint in statistics
Standard correlation and regression analyses can produce spurious results on compositional data because the components are not independent — increasing one necessarily decreases the others. Use specialized methods like log-ratio transforms (Aitchison, 1986) for statistical analysis.
Overcrowding with too many points
When hundreds of data points overlap inside the triangle, patterns become impossible to see. Use density contours, hexbin aggregation, or transparency to manage overplotting. Color-coding by group can also help, but only with a limited number of groups.
Using inconsistent axis scales
Some software allows zooming into a portion of the triangle (e.g. showing only the 0–50% range for each component). While useful, this can mislead readers who assume they’re seeing the full triangle. Always label the axis range clearly if you zoom in.
// 07 — Real-world examples
Where you’ll see ternary plots used
Geology: USDA soil texture classification
The USDA soil texture triangle classifies soil into 12 categories (sand, loam, clay, silt loam, etc.) based on the proportions of sand, silt, and clay. Every soil science textbook includes this diagram, and it remains the standard tool for field geologists worldwide.
Earth ScienceMaterials Science: Alloy phase diagrams
Metallurgists use ternary phase diagrams to map the equilibrium phases of three-component alloy systems. Each region of the triangle corresponds to a different crystal structure or phase, guiding alloy design for aerospace, automotive, and electronics applications.
EngineeringEcology: Diet composition analysis
Ecologists plot the proportions of protein, carbohydrate, and fat in animal diets on a ternary diagram. This reveals dietary strategies across species and how diet shifts under different environmental conditions.
Biology// 08 — At a glance
Quick reference
// 09 — Variations
Types of ternary plots
The basic ternary plot has several important adaptations used across scientific disciplines.
Ternary contour plot
Overlays density contours or response surface values onto the triangle, showing how a fourth variable (like yield or hardness) changes across the compositional space.
Ternary heat map
Colors the interior of the triangle by a continuous variable, creating a gradient map. Used extensively in experimental design to visualize optimal mixture ratios.
Piper diagram
Combines two ternary triangles and a central diamond to classify water chemistry. A specialized extension used in hydrogeology for groundwater analysis.
QFL diagram
A ternary plot used in sedimentary geology to classify sandstone provenance by quartz, feldspar, and lithic fragment proportions. The Dickinson diagram is a well-known example.
// 10 — FAQs
Frequently asked questions
What is a ternary plot?+
A ternary plot (also called a ternary diagram, triangle plot, or simplex plot) is a specialized chart drawn on an equilateral triangle. Each vertex represents 100% of one component, and any point within the triangle represents a unique mixture of all three components. The key constraint is that the three proportions must always sum to a fixed total — usually 100% or 1.0.
When should you use a ternary plot?+
Use a ternary plot when you have exactly three components that sum to a fixed total (100% or 1.0). It also works well when classifying samples into compositional regions (soil texture, rock type, alloy grade), and when visualizing phase diagrams where three substances interact in a closed system.
When should you avoid a ternary plot?+
Avoid a ternary plot when your variables do not sum to a constant — use a scatter plot or radar chart instead. It is also a poor fit when you have more or fewer than three components (use parallel coordinates for 4+), or when your audience is unfamiliar with triangular coordinates — the learning curve is steep.
How is a ternary plot different from a piper diagram?+
Both a ternary plot and a Piper diagram can look similar at first glance, but they answer different questions. Reach for a ternary plot when the comparisons and patterns it was designed to reveal match what you need to communicate, and choose a Piper diagram when its particular strengths better fit your data and audience.
Is a ternary plot suitable for dashboards?+
Yes — a ternary plot can work well in dashboards as long as the panel is large enough for readers to perceive the encoded values, has a clear title, and includes the legend or axis labels needed to interpret it.
What category of chart is a ternary plot?+
Ternary Plot belongs to the Scientific family of charts. Charts in that family are designed to answer the same kind of question, so they often work as alternatives when one doesn't quite fit your data.