Semicircle Perimeter Calculator
Compute the perimeter of a semicircle: half a circle plus the diameter.
For arch trim, half-moon window molding, and curved patios.
A semicircle’s perimeter is the curved part (half the full circumference) plus the diameter straight across the bottom:
P = π × r + 2r = r × (π + 2)
That works out to roughly 5.1416 × r, which is worth carrying as a mental shortcut.
Worked example: half-moon window trim A half-round transom over a 48-inch wide doorway. Radius r = 24 in. Curved part: π × 24 ≈ 75.40 in. Straight bottom (diameter): 48 in. Total perimeter = 123.40 in ≈ 10.28 ft of trim.
If you’re buying decorative molding, order 12 ft (10-15% buffer covers the mitre cuts at the corners where the curve meets the verticals).
Where semicircle perimeter matters in practice:
- Half-round window and doorway trim. Crown molding curves around the top, then runs straight along the bottom sill.
- Arched doorway openings. Sound or weatherstripping seal around the inside perimeter.
- Curved garden beds. Landscape edging for a half-circle planting bed against a fence.
- Half-pipe and tunnel linings. Lining sheet metal in a culvert cross-section.
- Half-round bay-window seats. The cushion-edge trim for a curved bench seat.
Why “πr + 2r” not “πr”:
A common mistake is to compute the curved part alone and forget the flat bottom. A semicircle is a closed shape with two boundaries: the half-arc on top AND the diameter across the bottom. Both count, unless what you actually want is the arc length by itself.
For just the arc length (the curved part alone, no diameter): Arc = π × r, exactly half the full circumference of 2πr.
Quick mental check. For r = 1 the perimeter is π + 2 = 5.14. Half a unit circle gives 3.14 of arc, plus 2 straight across the bottom, and the two add to 5.14.
Relationships:
- Semicircle perimeter / full-circle circumference = (πr + 2r) / (2πr) = 1/2 + 1/π ≈ 0.818. So a semicircle has about 82% the perimeter of the full circle, not 50%.
- Semicircle area / full-circle area = 0.5 exactly. The area splits cleanly; the perimeter does not.
That asymmetry is the reason a half-moon window with a diameter base often needs more trim material than you’d expect from just glancing at it.
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