Isometric paper for drawing in 3D

What is isometric paper used for?

Isometric paper helps you draw three dimensional objects on a flat page. In an isometric drawing, the height of an object runs straight up the page and its width and depth run along lines 30 degrees from horizontal. Because the paper already has those three directions printed, you only have to follow the grid.

Every edge drawn along a grid line keeps its true length, so a cube with sides of three triangles looks right from any corner. That makes isometric paper useful in maths, design and technology, engineering sketches and games.

• Students: drawing cube buildings in maths and working out volume and views from the front, side and top.
• Teachers: nets of solids, spatial reasoning tasks and building challenges with interlocking cubes.
• Engineers and designers: quick 3D sketches of parts, packaging and furniture before going to CAD.
• Gamers and artists: isometric maps, pixel art rooms and tessellating patterns.

How do I draw a cube on isometric paper?

Once one cube works, stack and join cubes to build steps, letters, buildings and impossible shapes.

1. Use the upright direction, so the grid has vertical lines.
2. Pick a point for the nearest bottom corner of the cube.
3. Draw a vertical edge up from it, the height you want, along a vertical line.
4. From the bottom corner, draw one edge up and to the left and one up and to the right, following the 30 degree lines, the same number of triangles each way.
5. Add vertical edges at the ends of those two lines, then join their tops to close the top face.
6. Shade the three visible faces with three different tones so the cube reads as solid.

What triangle size should I pick?

The triangle side is the length of each edge of each small triangle. Smaller triangles, at 5 mm or 1/4 inch, suit detailed drawings and older students. 10 mm is a comfortable everyday size for classroom cube drawings. Large triangles, at 15 mm or 20 mm, are easier for younger children and for activities where students count edges.

If a task gives measurements, such as a cuboid 4 by 3 by 2 units, choose a size where the whole shape fits with room around it. On an upright grid, the distance between vertical lines is a little less than the triangle side, about 0.87 times it, so a page fits more columns than you might expect.

How is isometric paper used in maths lessons?

A common task is to build a shape from cubes, then draw it on isometric paper. Students practise seeing a solid from one corner, then count cubes to find the volume, including the hidden ones at the back. The reverse works too: give students a drawing and ask them to build it, or to draw its front, side and top views on square graph paper.

Isometric paper also supports work on nets, surface area and enlargement. Draw a cuboid, then draw it again with every edge doubled and compare the volumes. Because each edge along a grid line is the same length in every direction, students can count units straight off the page instead of measuring.

Should I use isometric lines or isometric dots?

• Lines are best for learning, because every direction is visible and it is hard to go wrong.
• Dots are cleaner for finished drawings, since only your lines show once the drawing is done.
• Lines with dots at the corners help when students count units along an edge.
• Fine soft blue lines stay in the background. Dark grey suits work that will be scanned or photocopied.

Which way round should the grid go?

Upright, with vertical lines, is the standard direction for isometric drawing, because the height of objects follows the vertical lines. Turned, with horizontal lines, gives rows of triangles that point up and down, which is better for tessellations, quilt patterns, hexagon designs and triangle number puzzles. Both use the same equilateral triangles, just rotated by 90 degrees.

How do I print isometric paper accurately?

Choose A4 or US Letter and print at 100% or Actual size. Fit to page shrinks the grid, which matters if students measure their drawings. The grid is centred on whole triangle columns so the left and right edges match. Choose a number of pages to print a class set, or save as PDF to keep a copy for later lessons.