Half a circle. A closed shape consisting of half a circle and a diameter of that circle*****.

A semicircle is a half circle, formed by cutting a whole circle along a diameter line, as shown above. Any diameter of a circle cuts it into two equal semicircles.

*****
An alternative definition is that it is an open arc. See note at end of page.

The area of a semicircle is half the area area of the circle from which it is made.
Recall that the area of a circle is πR^{2}, where R is the radius.
(See Area of a circle).

So, the formula for the area of a semicircle is:
where:

*R* is the radius of the semicircle

*π* is Pi, approximately 3.142

The perimeter of a semicircle is * not* half the perimeter of a circle

Recall that the perimeter of a circle is *2πR*,
(See Perimeter of a circle).

So the curved part is half that, or *π*R, and the base line is twice the radius or *2R*.

So, the formula for the perimeter of a semicircle is:
where:

*R* is the radius of the semicircle

*π* is Pi, approximately 3.142

- Has no area
- Has no perimeter. Its length is the length of the arc, or πR.

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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