# Ternary Plot Paper > Equilateral triangle with three sets of grid lines: the standard format for plotting three-component compositions in chemistry, metallurgy and soil science. Free printable ternary plot paper from Printable Graph Paper. Page: https://printablegraphpaper.org/graph-paper/ternary-plot-paper A ternary plot, also called a triangular plot or simplex chart, displays the relative proportions of three components that sum to 100%. The equilateral triangle has gridlines parallel to each side at 10% intervals, so any composition (a, b, c) where a + b + c = 100% maps to a single point inside the triangle. ## At a glance - Category: [Scientific](https://printablegraphpaper.org/category/scientific) - Paper sizes: Letter (8.5" × 11"), A4 (210 × 297 mm), 11" × 17", Legal (8.5" × 14"), A3 (297 × 420 mm), A2 (420 × 594 mm), Poster (18" × 24"), Movie Poster (27" × 40") - Line colors: Faint, Light, Gray, Dark, Black, Blue, Green (default: Gray) - Format: vector PDF download at exact physical scale, or direct browser print - Price: free, no signup, no watermark; printed sheets may be used for personal, classroom and commercial work ## Good for - Phase diagrams in metallurgy and chemistry (three-component alloys, solutions) - Soil classification (sand / silt / clay percentages) - Color theory (additive RGB or subtractive CMY blends) - Voting and demographic data (three-party shares, three-group surveys) ## About ternary plot paper The ternary plot solves a specific visualisation problem: how do you show three quantities that sum to a fixed total on a 2D page? A bar chart shows three values but loses the constraint that they add to 100%. A pie chart shows the constraint but only for one row of data — a hundred rows give you a hundred pies. The ternary plot collapses three constrained values into a single point in an equilateral triangle, and the resulting plot can show hundreds of compositions at once on a single page. Each vertex represents 100% of one component; the opposite side represents 0% of that component. As you move from a vertex toward the opposite side, that component's percentage decreases linearly. The format is the standard in any field where three-component compositions matter: phase diagrams in materials science, soil-texture classification, three-party political vote shares, color-blend theory. The convention dates from at least Willard Gibbs' work in chemical thermodynamics in the 1870s, where ternary diagrams became the standard tool for representing phase equilibria; soil scientists picked up the format in the early 20th century for the USDA soil triangle, which is still the international classification standard. ## What's on the page An equilateral triangle filling the printable area, with gridlines parallel to each side at 10% intervals (heavier accent lines at every 50% mark) and finer subdivisions at every 10%. Vertices are labelled A, B and C; you assign component names when you use the paper. The grid is centred horizontally and the triangle sits within the page's usable area without crowding the edges. ## How to use it well - **Read percentages along the parallel gridlines.** To read the percentage of component A at a point, find the gridline that runs parallel to the side opposite vertex A and passes through your point. The percentage of A is given by where that gridline meets the A-axis edge. The same trick works for B and C. The three percentages always sum to 100%. - **Choose vertex order to match convention in your field.** Soil scientists put clay at the top vertex, sand at the bottom-right, silt at the bottom-left. Metallurgists vary by alloy system. Pick the convention used in your discipline's textbooks; consistency matters more than which assignment is 'right'. - **Mark compositions before plotting curves.** For phase diagrams, plot the key compositions (eutectics, peritectics, pure-phase boundaries) as labelled dots before drawing any curves through them. Curves drawn through dots look intentional; curves drawn freehand sometimes drift through compositions that don't exist in the real system. - **Two ternary plots can show a four-component system.** If you fix one component and vary the others, you get a ternary plot in three remaining components. Stacking several such plots (each at a different fixed value of the fourth) is a common way to visualise four-component systems where a 3D representation would be illegible. ## Common mistakes to avoid - Misreading the gridlines. The lines parallel to the bottom side give percentages of the top-vertex component (not the bottom-vertex). Beginners often read the wrong axis; check by verifying that all three percentages sum to 100% before trusting a reading. - Forgetting that values must sum to 100%. A ternary plot only works when the three components add to a fixed total. If you have absolute values (not percentages), normalise them before plotting. Two compositions with the same ratios but different totals plot to the same point. - Using a ternary plot for unconstrained three-variable data. If your three variables don't sum to a fixed total, a ternary plot is misleading. Use 3D plots, parallel coordinates, or multiple bivariate plots instead. ## FAQ ### What's the difference between a ternary plot and a [triangular graph paper](/graph-paper/triangular-graph-paper)? Triangular graph paper is a general-purpose grid of equilateral triangles tiling the page — useful for isometric drawing, certain design layouts and triangular pixel art. A ternary plot is a single large equilateral triangle with axes labelled in percentages — used specifically for plotting three-component compositions. Different formats, different purposes. ### Why are the vertices at 100% and the opposite sides at 0%? It's the geometric consequence of the constraint A + B + C = 100%. Each vertex is the point where one component is 100% and the others are 0%; the opposite side is the locus of points where that component is 0% and the other two share the full 100% between them. The linear gridlines between are the loci of constant percentage for each component. ### What does a curve on a ternary plot represent? Depends on context. In phase diagrams, a curve typically represents a boundary between phases (where two phases coexist). In soil classification, the bounded regions are named soil types (sandy loam, clay loam, silty clay). The curves themselves are domain-specific; the ternary plot is the canvas, not the content. ### Can I use this for two-component or four-component systems? No. Two components fit on a single line (binary phase diagram); four or more components require higher-dimensional projections (tetrahedron for four; you'd need stacked or rotated representations). The ternary plot is specifically for three-component compositions. ### What's a 'eutectic point' on a ternary plot? The composition at which three phases coexist at the lowest melting temperature in the system. On a ternary phase diagram, it's a single point — usually a key feature of any alloy or solution system being studied. Find the eutectic, label it, and the rest of the phase diagram organises around it. ## How to print at the correct size Set the browser print scale to 100% (never "Fit to page") and margins to None or Minimum, or use the Download button for a PDF dimensioned in millimetres. To check, measure 5 cells with a ruler: a 5 mm grid should read 25 mm.