Semicircle Area Calculator

Enter a semicircle's radius to get its area (A = ½πr²), arc length (πr), and total perimeter (r(π + 2)), plus an optional material cost estimate.

Quick Facts

Area formula
A = ½πr²
Half the area of a full circle of the same radius.
Perimeter formula
P = r(π + 2)
Curved arc (πr) plus the straight diameter edge (2r).
Centroid
4r / (3π) ≈ 0.4244r
Distance from the flat edge's center along the axis of symmetry.

Your Results

Calculated
Area
-
A = ½πr², in square units
Arc Length
-
Curved edge only, πr
Total Perimeter
-
Arc + diameter, r(π + 2)
Estimated Material Cost
-
Area × cost per square unit

Ready

Enter a radius and unit, then press Calculate.

Formula and Method for Semicircle Area

A semicircle is exactly half of a circle, formed by cutting a full circle along a diameter. Because it is half a circle, its area is simply half the area of a full circle of the same radius: A = (π × r²) / 2, where r is the radius. This calculator also derives the arc length (the curved edge only), the total perimeter (the curved edge plus the straight diameter edge), and an optional material cost estimate from the area.

How the calculation works

Enter the radius and choose the unit it is measured in. The calculator squares the radius, multiplies by π, and divides by 2 to get the area (in square units, such as ft² or m²). The curved arc length is half the circumference of a full circle, πr. The total perimeter — the full boundary you would walk around, including the straight edge — adds the diameter (2r) to the arc length, giving P = πr + 2r = r(π + 2). If you enter a cost per square unit, the tool multiplies it by the area to estimate total material cost.

Common mistakes

  • Confusing arc length with perimeter: the arc length (πr) is only the curved edge. The full perimeter of the shape also includes the straight diameter edge: P = πr + 2r, not just πr.
  • Diameter vs. radius: this calculator expects the radius (half the diameter). Entering the diameter where the radius is expected roughly quadruples the computed area, since area scales with r².
  • Mixing units: keep the radius in one consistent unit — convert inches to feet, or centimeters to meters, before entering the value.

Real-world applications

  • Window and doorway design uses semicircle area for arched (Palladian) window glass and trim quantities.
  • Landscaping uses semicircle area and perimeter to plan half-round garden beds, patios, or driveway turnarounds.
  • Structural engineering uses the semicircle's centroid (4r/(3π) from the flat edge) to compute the centroid of composite cross-sections that include a semicircular portion.
  • Fabrication and construction use the arc length separately from the total perimeter when ordering curved trim, edging, or flashing versus straight baseboard.

Frequently Asked Questions

What is the formula for the area of a semicircle?
The area of a semicircle is half the area of a full circle: A = (π × r²) / 2, where r is the radius. For example, a semicircle with a 6 ft radius has an area of (π × 6²) / 2 ≈ 56.55 ft².
How do I find the perimeter of a semicircle?
Add the curved arc length to the straight diameter: P = πr + 2r = r(π + 2). A semicircle with a 6 ft radius has a perimeter of 6 × (π + 2) ≈ 30.85 ft.
What is the difference between arc length and perimeter for a semicircle?
The arc length is only the curved edge, πr. The perimeter (total boundary) also includes the straight diameter edge, so perimeter = arc length + diameter = πr + 2r.
Where is the centroid of a semicircle located?
The centroid lies on the axis of symmetry at a distance of 4r / (3π) ≈ 0.4244r from the center of the flat (diameter) edge, which is closer to the flat edge than to the curved arc.

Related calculators