Free Triangular Grid Generator

The tessellation itself is simple to state. Take an equilateral triangle. Lay a row of them side by side, all pointing up. Start the next row half a triangle to the right and lay another row. The gaps between the upward triangles in each row are themselves triangles, pointing down, and the plane is covered with no overlaps and no gaps.

This overlay draws only the upward-pointing ones. The downward-pointing half of the tessellation appears as the space between them, identical in size and shape. That is not a shortcut — it is what makes the drawing correct at low opacity, because every interior edge belongs to exactly one drawn triangle and is therefore stroked exactly once. Draw both sets and every shared edge doubles up, and the lattice picks up an uneven weight that is very hard to see and impossible to unsee.

The row height is where the arithmetic gets awkward, and it is worth knowing rather than discovering. The height of an equilateral triangle with side s is s√3⁄2, which is 0.86603 of the side. Rows are therefore about 13.4% shorter than the triangles are wide.

The consequence is that a triangular grid never gives you a matching count in both directions. Set the density to eight and you get eight triangles across the short side and about nine and a quarter rows down a square canvas. That mismatch is inherent to the geometry, not a rendering artefact, and any triangular graph paper you have ever used has it too.

Six triangles meet at every interior vertex, and 6 × 60° = 360°, which is the condition for a regular tessellation. The square grid meets that condition with four 90° corners, and the hexagonal grid with three 120° ones. Those three are the only regular polygons for which it works — the pentagon's 108° does not divide 360, and everything above six has angles too large.

The triangular and hexagonal lattices are the same lattice seen two ways — the hexagonal grid generator draws the other view — which is worth internalising because it saves a lot of confusion. Join the centres of a hexagonal tiling and you get triangles. Join the centres of a triangular tiling and you get hexagons. They are duals, and choosing between them is a question of whether you want to work with the cells or with their corners.

That lattice is everywhere in the physical world, for one reason: it is the densest way to pack circles in a plane. Each circle touches six others, and the arrangement wastes about 9.3% of the area — the theoretical minimum, proved by Thue in 1910 and Fejes Tóth later. Anything that packs — bubbles, cells, seeds, atoms in a metal sheet — arrives at it without being told.

Honeycomb is the famous example, and the reason is the dual relationship. Bees build hexagonal cells, and the centres of those cells form a triangular lattice. The hexagon minimises the wall material needed to enclose a given area with a repeating tile — a claim conjectured for two thousand years and finally proved by Thomas Hales in 1999.

In art the lattice shows up wherever three-way symmetry is wanted. Islamic geometric pattern uses it constantly, generally as the underlying framework for six- and twelve-fold star figures. Celtic knotwork is often built on it. So are quilt blocks based on triangles — half-square and quarter-square units are square-grid constructions, but the equilateral families, the sixty-degree diamonds and the tumbling-block patterns, all sit on this lattice.

The isometric grid generator draws a triangular grid seen from a specific angle. Isometric paper is exactly this lattice with one of the three directions vertical, and the reason isometric works so easily by hand is that the paper already provides all three axes at the right angles.

For pattern design, the practical advantage over a square grid is repeat flexibility. A square repeat can be offset by a half-drop or not at all. A triangular repeat has three directions and a natural half-offset built into the row structure, so patterns that would need careful planning on a square grid fall out of the lattice.

For transfer work, the three-way registration helps with subjects that have strong diagonal structure. A square grid keeps cutting across a diagonal at an unhelpful angle; a triangular one is very likely to have a lattice direction that runs more or less along it, which gives you edges to measure against rather than through.

Choosing a density means choosing what a triangle represents. Three across the short side is a compositional armature — a way of dividing a picture into large three-way regions. Twenty-four is a transfer grid, and each triangle is a small enough area to copy by eye.

One thing that surprises people is how much a triangular grid changes the perceived movement of a composition. Square grids are static — the two directions oppose each other and cancel. Three directions cannot cancel, so a triangular lattice always has a slight rotational feel, and compositions built on it tend to read as more dynamic even when nothing is moving.

That is also its limitation. If your subject wants stillness — an architectural elevation, a formal portrait, a product shot — the triangular grid works against you, and a square or rectangular one is the right choice.

For crafts, the lattice maps onto specific techniques. English paper piecing with sixty-degree diamonds is a triangular-lattice construction. So is much of what happens in beadwork with peyote and brick stitch, where the offset rows are the same offset rows drawn here.

Tabletop gaming uses it too, though usually in its hexagonal dual, because a hex grid solves the diagonal-movement problem that plagues square grids: on a square grid a diagonal step is √2 times a straight one and every rule set has to fudge it, while on a hex grid all six neighbours are equidistant.

The overlay draws over your own image rather than exporting a fixed template because placement matters. Shifting the lattice by half a triangle changes which of the subject's features land on vertices, and vertices are what you register against.

Export sizes itself from the paper format and the DPI you choose rather than from your screen, so a grid exported at A3 and 600 DPI is a printable sheet with genuinely fine lines rather than merely small ones. SVG keeps every triangle as an editable path, which is what you want for pattern work where cells will be filled selectively.

A note on printing: a triangular grid at high density prints heavier than a square grid at the same density, because there are half again as many lines per unit area — three directions rather than two. Drop the opacity a step below what you would use for a square grid and the printed result will match. The triangular grid overlay page works through its uses, beside the rest of the specialty grid category.

Everything runs in your browser. Images you load are never uploaded, because there is no server for them to reach. The drawing, the transform and the export all happen on your own machine.