Semicircle Area
Calculate the area, radius, and perimeter of a semicircle. Free half-circle geometry tool using the formula A = pir^2/2 for students, engineers, and designers.
About This Calculator
The semicircle area calculator computes the area of a half-circle using the formula A = pir^2/2, where r is the radius. A semicircle is exactly half of a full circle, formed by cutting a circle along its diameter. This tool is essential for students learning geometry, architects designing arched structures, and professionals in engineering and construction who need quick and accurate half-circle measurements.
The derivation is straightforward: the area of a full circle is pir^2, so a semicircle -- being exactly half -- has half that area: pir^2/2. The calculator also shows the radius and can be used to compute the perimeter: P = pir + 2r = r(pi + 2).
For best results, enter the radius in any consistent unit (inches, feet, cm, or m). The output area is in the corresponding square unit. Always use positive numbers -- the calculator validates that the radius is greater than zero.
Frequently Asked Questions
What is the formula for the area of a semicircle?
The area of a semicircle is exactly half the area of a full circle: A = pir^2/2, where r is the radius. For example, a semicircle with radius 5 units has an area of pi x 25 / 2 ≈ 39.27 square units.
How is semicircle area different from circle area?
A semicircle is exactly half of a circle, so its area is half the area of the full circle. If a full circle of radius r has area pir^2, the corresponding semicircle has area pir^2/2.
What units should I use for the radius?
You can use any consistent unit of length -- inches, feet, centimeters, meters, etc. The area will be expressed in the corresponding square unit (sq in, sq ft, cm^2, m^2).
Can I calculate the perimeter of a semicircle with this tool?
Yes. The semicircle perimeter formula is P = pir + 2r = r(pi + 2). This includes both the curved arc length (pir) and the straight diameter edge (2r).
How do I find the radius if I only know the diameter?
Simply divide the diameter by 2. For example, if the semicircle has a diameter of 10 units, the radius is 5 units. Then apply the formula A = pir^2/2.
Where is semicircle area calculation used in real life?
Semicircle area calculations are commonly used in architecture (archways, windows, domes), engineering (pipe cross-sections, structural components), landscaping (garden beds, fountains), and manufacturing (cutting half-circle shapes from materials).
What is the difference between arc length and perimeter of a semicircle?
The arc length is just the curved part of the semicircle boundary: pir. The perimeter includes both the curved arc and the straight diameter edge: P = pir + 2r = r(pi + 2). So the perimeter is always larger than the arc length by exactly the diameter (2r).
How do I calculate the area of a semicircle if I only know the diameter?
First divide the diameter by 2 to get the radius, then apply the area formula A = pir^2/2. For example, a semicircle with diameter 10 has radius 5, so the area is pi x 25 / 2 ≈ 39.27 square units. This calculator accepts radius input -- just halve your diameter first.