Semicircle Perimeter Calculator

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 — useful 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: people compute just the curved part (πr) and forget the diameter. The semicircle is a closed shape with two boundaries — the half-arc on top AND the diameter line on the bottom. Both contribute to the perimeter unless you’re explicitly only asking about the curved part (called the “arc length” in that case).

For just the arc length (the curved part alone, no diameter): Arc = π × r — half of the full circumference 2πr.

Quick mental check: for a semicircle with r = 1, the perimeter is π + 2 ≈ 5.14. Half a unit-circle ≈ 3.14 of arc, plus 2 across — yes, 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.