Checked reference
Circle, Pleat, and Gather Formula Sheet
These formulas expose every variable so a result can be reconciled by hand. They describe geometry and a user-selected fullness ratio; they do not select fit, style, fold depth, or construction for a project.
Reviewed on 2026-07-13.
| Item | Formula | Meaning | Note |
|---|---|---|---|
| Circle waist radius | r = (waist + ease) ÷ (2π × fraction) | Lengths share one unit; fraction is unitless. | |
| Outer radius | R = r + waist seam allowance + skirt length + hem allowance | R uses the selected length unit. | |
| Fullness source width | S = finished width × ratio | Ratio is unitless and selected by the user. | |
| Pleat repeats | count = floor(finished width ÷ repeat width) | Remainder stays separate. |
Variables and units
r and R = radii in a length unitfraction = 0.25, 0.5, 0.75, or 1S = source width; ratio = source width ÷ finished width
Worked example
A 100-centimeter finished span at 3× fullness needs 300 centimeters of source width. With a 12-centimeter repeat it has eight whole repeats and 4 centimeters remaining.
Cautions
- Fullness ratio is a design input, not a universal rule.
- Commercial pattern instructions take precedence over general equations.
Specific commercial pattern instructions take precedence whenever they differ from this general reference.