Paper Piecing Template Calculator
A "1 inch hexagon" is 2 inches across the points. And exactly three regular shapes tile the plane — there will never be a fourth.
Check your printer before you cut anything
A "one inch hexagon" is two inches across
Papers are sold by side length, and almost nobody pictures a hexagon by its side. So the first order comes back roughly twice the size intended — a 1-inch hexagon is 2 inches point to point and 1.732 across the flats.
| Sold as | Across the flats | Across the points | Area |
|---|---|---|---|
| 0.5″ | 0.866″ | 1.00″ | 0.65 sq in |
| 0.75″ | 1.299″ | 1.50″ | 1.46 sq in |
| 1″ | 1.732″ | 2.00″ | 2.60 sq in |
| 1.25″ | 2.165″ | 2.50″ | 4.06 sq in |
| 1.5″ | 2.598″ | 3.00″ | 5.85 sq in |
| 2″ | 3.464″ | 4.00″ | 10.39 sq in |
The ratio of points to flats is exactly 2/√3 = 1.155, which is also why a hexagon field looks wider one way than the other, and why it is worth deciding early which way the flats should run.
Exactly three regular shapes tile the plane
English paper piecing works because the shapes meet with no gaps, and that needs a whole number of corners to close 360° at every vertex. The interior angle of a regular n-sided shape is (n−2)×180/n, so the test is whether 360 divides by it evenly.
| Shape | Interior angle | How many meet | Tiles? |
|---|---|---|---|
| Triangle | 60.00° | 6.000 | yes |
| Square | 90.00° | 4.000 | yes |
| Pentagon | 108.00° | 3.333 | no |
| Hexagon | 120.00° | 3.000 | yes |
| Heptagon | 128.57° | 2.800 | no |
| Octagon | 135.00° | 2.667 | no |
| Dodecagon | 150.00° | 2.400 | no |
Only triangle, square, hexagon. And it stops there for a reason rather than running out by accident: from seven sides upward the interior angle is always over 120°, so fewer than three would fit at a vertex — and you cannot close a corner with two. Checked to two hundred sides. There will never be a fourth.
Everything else — diamonds, jewels, half-hexagons — tiles only in combination with something else, which is exactly why those patterns always arrive as a set of shapes rather than one.
Notes
- Foundation templates print mirrored. You sew on the back of the paper, so the finished block is the mirror of what you drew. Symmetrical blocks forgive this and nothing else does.
- Never trust "fit to page". Every print dialogue defaults to scaling something, and a 1% error is over half an inch across five blocks. Print at 100%, measure the test square, and only then cut.
- Errors accumulate, they do not average out. A template printed 1% small is 1% small every time, so the row gets steadily further out rather than wandering back.
- Cut fabric generously for English paper piecing. The square shown covers the widest dimension plus the allowance both sides — you can trim, and a piece that will not quite fold over the paper is scrap.
How to use
- Pick a shape and enter the side length — that is how papers are sold.
- Read the true width across points and flats before ordering.
- Cut fabric squares at the size shown, which includes the allowance.
- Print a test square and measure it before cutting any foundation template.
Frequently asked questions
How big is a 1 inch hexagon?
Two inches point to point and 1.732 inches across the flats. Papers are sold by the side length and almost nobody pictures a hexagon that way, so a first order routinely arrives about twice the size intended.
What is the difference between across the flats and across the points?
Exactly a factor of 2/√3, or 1.155. For a hexagon the points measurement is the larger one and is what determines how big a fabric square you need to cut. It is also why a hexagon field looks wider one way than the other.
Which shapes tessellate?
Among regular polygons, exactly three: the equilateral triangle, the square and the hexagon. Six triangles, four squares or three hexagons meet at a vertex and close 360 degrees exactly. Nothing else does.
Why do only three shapes tile the plane?
Because a vertex needs a whole number of interior angles to close 360 degrees, and from seven sides upward the interior angle is always more than 120 — so fewer than three would fit, and you cannot close a corner with two. Checked to two hundred sides. There will never be a fourth.
What about diamonds and jewels?
They tile only in combination with something else — three 60-degree diamonds make a hexagon, and eight 45-degree ones make a star that needs squares and triangles to fill the gaps. That is exactly why those patterns always come as a set of shapes rather than one.
How big should I cut the fabric for English paper piecing?
A square covering the widest dimension of the shape plus the seam allowance on both sides. You can always trim, and a piece that will not quite fold over the paper is scrap — so err generous.
Why did my foundation paper pieced block come out backwards?
Because you sew on the back of the paper, so the finished block is the mirror image of the template. Symmetrical designs forgive this and nothing else does — mirror the template before printing if the design has a direction.
Why do my printed templates not match?
Almost certainly your print dialogue scaled them. "Fit to page" is usually the default and it silently shrinks by a percent or two. A 1% error is 0.12 inches on a 12-inch block and 0.6 inches across five blocks — and it accumulates rather than averaging out. Print at 100% and measure the test square.
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No. Everything is calculated in your browser and nothing is stored or uploaded.
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