Isometric Graph Paper

How to make isometric paper

1. Lines or dots. Under Paper type, "Isometric paper" rules the full triangle grid and "Isometric dot paper" marks only the points.
2. Triangle side. The distance between neighbouring points along a line. 1/4 in or 5 mm for detailed drawings, 1/2 in or 1 cm for classroom cube drawings.
3. Which way the lines run. "Lines run" vertical gives the usual drafting grid, with vertical lines for heights; horizontal turns the triangles a quarter turn, which suits tessellations and borders.
4. Weights and page. A heavier line, or bigger dot, every few steps helps with counting long edges. Then choose the page, margins and number of pages, and print at 100%.

How the grid works

The lattice is made of equilateral triangles. In an isometric drawing the object's three main directions, height, width and depth, run along the three line directions: height up the verticals, width and depth along the two 30° lines. Every edge parallel to one of those directions is drawn at its true length, counted in triangle sides, so a 3 × 4 × 2 box is 3 sides tall, 4 along one slope and 2 along the other.

Columns are the strips between vertical lines; rows count triangle sides down each vertical line. Counts are for portrait sheets with the starting margins (1/2 in on Letter, 10 mm on A4), worked out by the generator.

Drawing a box, step by step

1. Pick a point near the bottom of the page for the box's nearest bottom corner.
2. Draw its front edge straight up the vertical line, 3 sides long.
3. From the same bottom corner, draw 4 sides up the line sloping to the right and 2 sides up the line sloping to the left.
4. Draw vertical edges, 3 sides tall, up from the ends of those two lines.
5. Close the top with lines parallel to the bottom edges: you have a box with its top and two sides showing.

Cut shapes out of boxes the same way: draw the enclosing box first, then mark the cuts along grid lines. Slanted edges that don't follow a grid direction are drawn point to point and aren't true length, and circles become ellipses. Hidden edges are left out, or dashed if you need to show them.

What it's used for

• Technical drawing and design classes. Isometric sketches of parts, alongside the plan and elevations drawn on graph paper. Isometric projection is one of the axonometric representations defined in ISO 5456-3 for technical drawings.
• Woodworking and making. Furniture, boxes and shelving sketched to scale before cutting, with each triangle side standing for an inch or a centimetre.
• Maths. Drawing solids built from cubes, counting volume, and matching 3D drawings with their plans and elevations. Isometric dot paper at 1 cm or 1/2 in is a common classroom sheet.
• Game maps and level design. Dungeons, cities and board-game art with depth, drawn on the triangle grid so walls and floors stay consistent.
• Patterns and quilting. The grid is made of 60° angles, so it holds equilateral-triangle and 60° diamond patterns, including the tumbling-blocks design in which three diamonds make a cube.

Printing it

True scale matters when each triangle side stands for a real length. Print the PDF at Actual size and measure the ruler at the foot of the sheet, which checks the width. To check the height, measure down a vertical line: on 1/4 in paper 4 triangle sides (5 points) span exactly 1 in, and on 5 mm paper 20 sides (21 points) span 10 cm. Settings for each browser and PDF reader are in the guide to printing at actual size.