How to find a semicircle's area
A semicircle is half a circle, so its area is half the full circle's: A = (1/2) × π × r². For a radius of 4, A = (1/2) × π × 16 = about 25.13 square units. The straight edge (the diameter) is 2r.
The derivation needs no new ideas: work out the full circle's area, πr² = π × 16 ≈ 50.27, then take half of it. Doubling the answer is a quick way to check your work, and it also shows why the radius matters so much — because r is squared, doubling the radius from 4 to 8 does not double the area but quadruples it to about 100.53. A semicircle is simply half of what the area of a circle calculator returns for the same radius.
How to use this calculator
Enter the radius. If you only know the diameter, halve it first (radius = diameter ÷ 2). The result is in square units of your length unit — square inches, cm², m², and so on.
- Diameter for radius is the most common mistake and inflates the area four times over.
- Area is not perimeter. The distance around a semicircle is πr + 2r, a separate calculation.
- Keep one unit throughout, since the answer comes out squared.
Half, wedge, or whole
A semicircle is just a 180° sector. For other angles use the sector area calculator, and for the distance around the curved edge use the circle circumference calculator (the arc is half the full circumference).
Frequently asked questions
- What is the formula for a semicircle's area?
- A = (1/2) × π × r², which is half the area of the full circle.
- What is the area of a semicircle with radius 4?
- About 25.13 square units.
- How do I find it from the diameter?
- Halve the diameter to get the radius, then use A = (1/2) × π × r².
- Is a semicircle the same as a 180° sector?
- Yes — a semicircle is a sector with a 180° central angle, exactly half the circle.
- How do I find the perimeter of a semicircle?
- Add the curved arc to the straight edge: perimeter = πr + 2r. For a radius of 4 that is about 12.57 + 8 = 20.57 units. Halving the full circumference alone leaves out the diameter and gives too small an answer.