How this calculation works
A half-circle skirt must fit the same waist around half as much circle. Its radius is therefore twice the full-circle radius for the same opening. That change also affects the bounding fabric size, even though the requested garment length is unchanged.
Waist seam radius = (waist + ease) / (2π × fullness fraction); inner cut = radius − seam allowanceA worked example
A 72 cm waist opening in a full circle has radius about 11.46 cm. A 1 cm waist seam allowance makes the inner cut radius about 10.46 cm.
Good to know
The cut edge sits inside the waist seam line, so the waist seam allowance is subtracted from the seam-line radius. The hem is added outward. Radial panel seams, closures and waistband construction are separate. The square shown is a conservative bounding footprint, not a promise of an optimized folded fabric layout.
Reference: OpenStax — volume and surface area (opens in a new tab) ↗
Fullness changes the waist radius
A half-circle skirt must fit the same waist around half as much circle.
Its radius is therefore twice the full-circle radius for the same opening. That change also affects the bounding fabric size, even though the requested garment length is unchanged.
The Bias strip fabric square area calculator can budget material for a separate edge-finishing strip. Its unfolded cut width is a different measurement from the skirt’s radial hem allowance.
The waist cut goes inward
The cut edge sits inside the waist seam line, so the waist seam allowance is subtracted from the seam-line radius.
The hem is added outward. Radial panel seams, closures and waistband construction are separate. The square shown is a conservative bounding footprint, not a promise of an optimized folded fabric layout.
Distinguish the waist opening from the body measurement
The body waist and entered ease form the seam-line circumference. Any closure or waistband treatment must still produce that intended opening. Do not add ease again when transferring the radius to a pattern, or the finished waist will become larger than the modelled one.
The outer radius includes finished skirt length and the radial hem allowance. The conservative square uses the full diameter of that outer circle. A half or quarter sector may fit a smaller or differently folded piece, but fabric width, panel seams and print direction must be checked in an actual cutting layout.
Work through the entered example
A 72 cm waist opening in a full circle has radius about 11.46 cm. A 1 cm waist seam allowance makes the inner cut radius about 10.46 cm.
Start with this case, then change one input and calculate again. Keep the other assumptions fixed so the result has an interpretable cause. The result table exposes intermediate quantities and units rather than hiding them behind a single headline number.
Use the output in a real plan
The cut edge sits inside the waist seam line, so the waist seam allowance is subtracted from the seam-line radius. The hem is added outward. Radial panel seams, closures and waistband construction are separate. The square shown is a conservative bounding footprint, not a promise of an optimized folded fabric layout.
Before purchasing material or comparing alternatives, check the measurements at the point where they enter the calculation. A mathematically precise answer can still be a poor plan when the measured size, loss allowance or price basis is wrong. Save the input assumptions with any result you intend to reuse.
A few questions, answered
What is the calculation method?
Waist seam radius = (waist + ease) / (2π × fullness fraction); inner cut = radius − seam allowance
Does this use live prices or automatic measurements?
No. All measurements, prices and allowances come from your entries. The example values are illustrative and are not a recommendation for your situation.
Can I reuse the result for a different case?
Change the inputs and calculate again. Read the stated units and limits; the assumptions must still apply to the new case.