Quarter-inch triangle graph paper
Equilateral triangles with quarter-inch sides, fine enough for detailed tessellation and small piecing.
Opens with these settings already loaded. Change anything you like, then download as PDF, PNG or SVG.
A fine triangle grid is a design grid, not a drawing one
At one-inch sides you draw individual shapes. At a quarter inch you design pattern: tessellations, half-square triangle layouts, and the repeating geometry behind quilt blocks and tile work. There are roughly 30 triangles across a Letter sheet at this size, which is enough to lay out a whole repeat and see how it behaves at the edges.
The measurement is the side, not the height
The quarter inch is the length of each triangle edge, which is also the distance between adjacent grid points along any of the three directions. The perpendicular height of each triangle is smaller, about 0.217 inches, because height is the side times the square root of three over two. Measuring a printed sheet vertically and concluding the scale is wrong is the usual confusion here. Measure along an edge.
Triangles and hexagons are the same lattice
Join the centers of a hexagon grid and you get triangles; join the triangle centers and you get hexagons. Which you print depends on what the unit of your design is. Use triangles when the triangle is the piece you are cutting or drawing, and hexagons when the hexagon is. For quilting specifically, remember the drawn line is the finished size and seam allowance goes outside it.
Printing it accurately
This only measures correctly if your printer doesn't rescale the page. In the print dialog set Scale: 100%, not "Fit to page" or "Shrink oversized pages". If you're not sure it worked, print the calibration page, measure the ruler on it with a real ruler, and it will tell you exactly what your printer is doing to the page.