Graph Paper

Grid paper measured by the area of a cell.

Square, rectangular, triangular, hexagonal, kagome and polar grids, drawn for the paper you print on. The size of a cell is given as its area, so 50 mm² squares and 50 mm² hexagons divide the page into cells of the same size: changing the grid does not change the scale.

Every few cells are joined into a larger cell with a darker line, for counting and measuring without a ruler, and the grid fills the page with whole larger cells. The lines come in four shades or a colour of your own. The sheet is drawn in your browser; the link keeps the settings, so it opens the same sheet again.

The grids

Grid	Cell	Larger cell
Square	a square	k × k squares
Rectangular	a rectangle with sides 1 : √2, like an A sheet	k × k rectangles
Triangular	an equilateral triangle	a triangle with side k, made of k² cells
Hexagonal	a regular hexagon	a hexagon with k² times the area, centred on a small one
Kagome	a regular hexagon, with a triangle of a sixth of its area at each corner	every k-th line (k odd, up to 9): the same pattern k times larger
Polar	a piece of a ring, the same area everywhere	a piece of a ring of k × k cells, close to a square; a whole field in the centre
Polar, ½, ⅓ or ¼ of a circle	the same, on a part of the circle	the same

In every grid but kagome k goes from 1 to 10. There is no separate direction for the grid: turning the paper turns it, so a landscape sheet of tall rectangles is a portrait sheet of wide ones. Larger triangles held to the rest by one side only would stick out as sharp teeth, so the triangular grid and kagome leave them off and keep blunt corners at the edge.

Hexagons do not tile into hexagons, so the outline of a larger hexagon crosses small cells: it shows the scale rather than a group of whole cells.

Kagome is the triangular grid with one of its three families of lines moved by half the spacing: no three lines meet any more, so every crossing opens into a small triangle, with hexagons between them. Every line runs straight through — good for ornaments and star patterns, weaving and embroidery, and boards where the hexagons are spaces and the triangles junctions. The area is that of the hexagon, the same as in the hexagonal grid. The sheet holds whole larger cells — large hexagons and the large triangles beside them — so its edge has the notches of their outline.

The polar grid is experimental: its drawing and the links to it may still change. It has a field in the centre, left whole, and rings of larger cells around it. Every larger cell has the area of the centre field, and each ring takes as many of them as makes them closest to squares — 6, 12, 20, 25, 32, 40… around the circle, at every size; the size only decides how many rings fit. The counts come from Human Scale Numbers rounded to whole ones (2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32…), whose steps of about a quarter keep every ring close to square. A larger cell holds k × k small ones, and the rings inside it divide it into equal areas, so every small cell has the chosen area. Past the last whole ring, the larger cells that fit on the page are drawn as well.

The polar grid can also be drawn on half, a third or a quarter of the circle — a half and a third with a straight edge along the long side of the page, a quarter in a corner. The field in the centre is then that part of the circle's, so a part starts as a slice of the whole circle. Such a part suits diagrams that widen from one point, such as a fan chart of ancestors, and a single sheet rolls into a cone.

The area is chosen from Human Scale Numbers — 1, 1.25, 1.6, 2, 2.5, 3.2, 4, 5, 6.4, 8, 10… — from 1 mm² (millimetre paper) to 10 cm². Every third step doubles the area and every tenth multiplies it by ten: 25 mm² is the usual 5 mm square, 1 cm² the 1 cm square. The name at the bottom of the sheet, such as square_grid_24x36x50mm2, gives the grid, the number of larger cells, the cells in each of them and the area of one cell.