The inscribed-square rule for round frames
A round hoop or ornament has no corners, but most designs do. A rectangle fits inside a circle only when its diagonal is no longer than the circle's usable diameter. For a square design, that means its side can be at most the diameter divided by √2, which is about 71% of the diameter. This is called the inscribed square, and it is the honest limit for any square design that has to show completely inside a round frame.
usable diameter d = hoop diameter − 2 × margin
longest line across = d × stitches per inch
largest square = (d ÷ √2) × stitches per inch
a W × H design fits if √(W² + H²) ÷ stitches per inch ≤ d
Both numbers matter. The "longest line across" is what a round or oval design such as a wreath or a circular mandala can use. The "largest square" is what a square or rectangular design can use without losing its corners under the ring. For a 6-inch hoop with a 1-inch margin on 14-count fabric, the usable circle is 4 inches: a round design can be 56 stitches across, but a square design must be no more than 39 × 39.
Hoop capacity table
Largest square design (and longest line across) for standard round hoops with a 1-inch margin on each side.
| Hoop | 14-count | 16-count | 18-count |
|---|---|---|---|
| 3 in | 9² (14) | 11² (16) | 12² (18) |
| 4 in | 19² (28) | 22² (32) | 25² (36) |
| 5 in | 29² (42) | 33² (48) | 38² (54) |
| 6 in | 39² (56) | 45² (64) | 50² (72) |
| 7 in | 49² (70) | 56² (80) | 63² (90) |
| 8 in | 59² (84) | 67² (96) | 76² (108) |
| 9 in | 69² (98) | 79² (112) | 89² (126) |
| 10 in | 79² (112) | 90² (128) | 101² (144) |
| 12 in | 98² (140) | 113² (160) | 127² (180) |
| 14 in | 118² (168) | 135² (192) | 152² (216) |
Read "39² (56)" as "a 39 × 39 square fits; 56 stitches across the middle". Evenweave over two gives the same numbers as Aida of half the count, so 28-count over two matches the 14-count column.
Ornament frames: 3, 4 and 5 inch
Small ornament frames are popular for gifts and holiday decorations. Because they are small, the margin makes a big difference: a 3-inch round ornament with a 1-inch margin would leave only 1 inch to stitch in. Ornaments usually need only a quarter to half an inch around the design, so set the margin to 0.25 or 0.5 when you choose an ornament. Square ornament frames do not have the corner problem, so the design can use the full opening minus the margin in both directions.
On 18-count fabric, a 3-inch round ornament with a quarter-inch margin holds a square design of up to 31 × 31 stitches, which is plenty for an initial, a small motif or a short name. Make names and initials in the pattern maker under the Text tab.
From hoop size to a finished pattern
In "Hoop → max stitches" mode, the "Generate at this size" button opens the pattern maker with your fabric and frame already selected. The maker then sizes your photo or text so that the whole design, corners included, fits inside the frame with your margin. If you are using a different margin from the default, the maker uses the largest square size as the width instead.
Going the other way, if you already have a chart, enter its width and height in "Design → hoop". The cross stitch hoop size calculator finds the finished size on your fabric, measures the diagonal, adds the margin and recommends the smallest standard hoop that holds it. It also tells you which ornament frames are big enough. To work out fabric to cut around a design that will be framed rather than hooped, use the size calculator.
Example results
6 in hoop, 14-count
1 in margin: usable 4 in circle, 56 stitches across, largest square 39 × 39.
70 × 50 design
On 14-count: 5.0 × 3.6 in, diagonal 6.1 in. With a 1 in margin it needs 8.1 in, so a 9 in hoop to show it all; if you move the hoop as you stitch, 3.6 + 2 = 5.6 in, so a 6 in hoop is enough.
3 in ornament
Round, 18-count, 0.25 in margin: 45 stitches across, largest square 31 × 31.