The dozen formulas behind most sewing answers, each stated plainly with a worked number, and a quick calculator for the three asked most: gathering, elastic, and bias yield.
Cut the strip
49in long
gathers to 24 in at 2× fullness
- Strip length49.0 in (seams included)
- Gather withtwo rows of basting, ¼ and ½ in
- Hem to sew first48 in
The Working Formulas
| Question | Formula | Worked once |
|---|---|---|
| Gathering strip | finished × fullness + 2 sa | 24″ at 2× → cut 49″ |
| Waist elastic | body − 2 + 1 overlap | 30″ waist → cut 29″ |
| Continuous bias from a square | (side − ½)² ÷ tape width | 18″ square, 2″ tape → 153″ |
| Circle skirt radius | waist ÷ 2π − sa | 30″ → 4¼″ |
| Boxed corner square | depth ÷ 2 + sa | 4″ deep → 2½″ |
| Shirring rows | panel cut 1.5–2× finished; rows ½″ apart | 6″ of shirring → 12 rows |
| Ruffle hem allowance | hem × fullness | 2× ruffle doubles the hem to sew |
| Pattern piece yardage | strip math | · |
| French seam | sew ⅜ wrong-out, trim, sew ¼ | uses ⅝″ total |
| Thread per seam | ≈ 3 × seam length | 4 yd of seams → 12 yd |
The Three Quick Calculators
Gathering, elastic, and bias yield answer the most repeated questions, so they live in the card above. The rest of the table states its math plainly enough to run in your head at the cutting table, and the linked tools go deeper where depth helps.
Rules the Formulas Lean On
- Seam allowances: garment patterns carry ⅝ in, quilting ¼, bag-making usually ½: know which world your pattern comes from before adding.
- Gathering fullness by fabric: lawn and voile earn 2½–3×, quilting cotton 2, home-dec weight 1½: stiffness fights fullness.
- Elastic snugness varies by job: waists −2, wrists −1, necklines barely negative. Stretch the cut loop over the body part before sewing it shut.
Assumptions and Defaults
- Formulas state finished-size math; cut sizes add the seam allowances named beside them.
- The bias-square formula subtracts the ½ in the joining seams consume.
- Shirring spacing of ½ in suits elastic thread in the bobbin; closer rows gather harder.
Formula Questions, Answered
How much fabric do gathers take?
Gathers take the finished length times the fullness, so a 24 in gathered edge at the standard 2× cuts a 48 in strip plus seams. Drapey fabrics look best at 2½ to 3×, stiff ones at 1½×, because the fabric decides the ratio more than the style does.
How long do I cut waist elastic?
Waist elastic is cut at the body measurement minus 2 in, plus an inch to overlap and join, so a 30 in waist cuts 29 in. Try the loop on before closing the casing, because elastic brands grip differently even at the same width.
How much bias tape can I cut from a square?
A square yields (side − ½)² ÷ cut width inches of bias tape, so an 18 in square gives about 153 in of 2 in tape. The binding calculator works the other way around, finding the square a needed length requires.