Semicircle Area Calculator — Area & Perimeter
Enter the radius of a semicircle to instantly get its area (πr²/2), perimeter (πr + 2r), arc length, and diameter — with a full step-by-step solution.
Half the area of a full circle with the same radius
Area formula
Substitute r = 5
Area
Perimeter formula
Perimeter
- 1
Square the radius
r² = 5² = 25 - 2
Area = π × r² ÷ 2
π × 25 ÷ 2 = 39.2699A semicircle is exactly half a full circle, so area is halved.
How does this calculator work?
Semicircle area = πr²/2 (half a full circle). Perimeter = r(π + 2) — arc plus diameter. Arc length alone = πr. Enter the radius to get all four values with a step-by-step breakdown. Units of the result match the radius units you enter.
Formula
How this is calculated
A semicircle is exactly half of a full circle, created by cutting along a diameter. Its area is therefore half the area of the full circle with the same radius: A = πr² ÷ 2. For a radius of 5, the area is π × 25 ÷ 2 ≈ 39.27 square units.
The perimeter (total boundary length) has two components: the curved arc and the straight diameter. The arc length equals half the circumference of the full circle — πr — and the straight edge is the diameter 2r. The total perimeter is therefore πr + 2r = r(π + 2). The arc length alone (just the curved portion, without the straight edge) is πr.
These formulas apply to a perfect semicircle where the flat edge is an exact diameter. The units of the result match the units of the input radius (e.g., enter cm → area in cm², perimeter in cm). For elliptic half-shapes the formulas differ and require numerical integration.
Frequently asked questions
The arc length (πr) is only the curved edge. The perimeter is the complete boundary — it adds the straight diameter (2r) to the arc, giving r(π + 2). Use arc length for fencing the curved part only; use perimeter when enclosing the entire region.
Rearrange A = πr² ÷ 2 to r = √(2A ÷ π). For example, an area of 50 gives r = √(100 ÷ π) ≈ 5.64.
Geometrically, a semicircle is the closed region bounded by the arc AND the diameter, so both edges are part of the shape. The perimeter formula πr + 2r counts both. Some problems ask only for the arc — use πr in those cases.
Also known as
TG we-Calculate Editorial Team. (2026). Semicircle Area Calculator — Area & Perimeter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/semicircle-area-calculator
TG we-Calculate Editorial Team. "Semicircle Area Calculator — Area & Perimeter." TG we-Calculate. 2026. https://we-calculate.com/calculator/semicircle-area-calculator.
TG we-Calculate Editorial Team, "Semicircle Area Calculator — Area & Perimeter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/semicircle-area-calculator
@misc{wecalculate_semicircle_area_calculator, title = {Semicircle Area Calculator — Area & Perimeter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/semicircle-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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