Isometric Graph Paper
Isometric graph paper is a grid of equilateral triangles: vertical lines, and lines sloping up and down at 30 degrees. Set the distance between the lines in millimetres or inches, the line weight and color, and the paper size, and the sheet is drawn for you.
Your sheet
Printing: choose Actual size or 100%, not “Fit to page”, so 1 cm prints as 1 cm. How to check.
How is the isometric grid built?
Three sets of parallel lines: vertical, at +30° and at −30°, each set spaced by the chosen distance. Triangle side = spacing ÷ cos 30° = spacing × 1.1547.
Worked example. With 8 mm between lines, each triangle has sides of 8 ÷ 0.866 = 9.24 mm. All three families of lines, the verticals included, are 8 mm apart, and the verticals pass through the points where the sloping lines cross, so every triangle has a vertex on a vertical. The sloping lines are drawn only inside the margin, so nothing runs off the printable area.
Drawing a cube on isometric paper
Draw a vertical edge, then from its top and bottom follow the 30° lines left and right for the same number of triangles. Join the ends with verticals and close the top with two more 30° lines. Every edge of the cube is the same length on paper, which is what makes isometric drawing quick: no vanishing points, no measuring angles.
Isometric paper in maths and design
Schools use it for 3D shapes, nets, plans and elevations, and for counting cubes in a solid. Designers use it for furniture, room layouts, pipework and game maps. Engineers sketch parts on it before moving to CAD.
Isometric or oblique?
Oblique drawing keeps the front face true and slopes only the depth, usually at 45°, on ordinary graph paper. Isometric slopes two faces at 30°, so no face is true but the drawing looks more natural. Choose isometric for anything you want to look solid.
Questions about isometric paper
What is isometric graph paper?
A grid of equilateral triangles made by vertical lines and lines at 30 degrees above and below horizontal. Drawing along the lines gives a view of a solid where all three axes are equally foreshortened, which is what “isometric” means.
What triangle size should I use?
For school geometry and simple 3D sketches, 8 mm or 1/4 inch between parallel lines (the default). For detailed technical sketches, 5 mm. For large block drawings with young children, 10 to 12 mm.
Is the spacing the triangle side or its height?
The height: the distance between two parallel lines. The side is a little longer, height ÷ cos 30°, so 8 mm lines make triangles with 9.24 mm sides.
Portrait or landscape?
Landscape gives more width for long objects such as buildings and furniture; portrait suits tall shapes. The grid is symmetrical, so turning the page does not change the angles.
Can I get isometric dot paper instead of lines?
Not yet. Use faint lines (0.1 mm, light grey) for a similar effect: the lines fade on a copy and the drawing stands out.