Delaunay Triangulation

Triangulate a set of points (dual of Voronoi)

V = 6, E = 10, T = 5 (V − E + T = 1)

Points

Triangles

Edges

5 on hull · 5 interior

Total area

Smallest angle

16.59°

Of every possible triangulation of these points, the Delaunay one makes this smallest angle as large as possible.

Empty-circle property: no point lies inside the circumscribed circle of any triangle.

About this calculator

The Delaunay Triangulation Calculator triangulates a set of 2D points with the Bowyer–Watson algorithm, producing the mesh whose triangles satisfy the empty-circumcircle property and maximize the smallest angle. It reports each triangle's area, circumradius, and minimum angle, counts hull versus interior edges, and gives the total triangulated area — with duplicates removed automatically and collinear input detected as untriangulable.

How to use the Delaunay Triangulation calculator

Enter the measurements you know into the input fields.
Read the computed properties — they update instantly as you type.
Compare the diagram with your figure to confirm the setup is right.
Copy the page URL to share the exact calculation.

Common examples

Square (0,0), (4,0), (4,4), (0,4) plus center (2,2) → 4 triangles, 8 edges, total area 16, smallest angle 45°
Triangle (0,0), (4,0), (0,3) → 1 triangle, area 6, smallest angle ≈ 36.87°
Six scattered points → 5 triangles, 10 edges (5 on the hull), total area 21.5
Collinear points (0,0), (1,1), (2,2) → no triangulation possible: all points lie on one line

Frequently asked questions

How does the Delaunay Triangulation calculator work?

Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.

When would I use the Delaunay Triangulation calculator?

It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.

How accurate are the results?

Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.