Semicircle - Math Word Definition

Math Open Reference Home Contact About Subject Index Semicircle 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.

Area of a semicircle

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 πR2, 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

Perimeter of a semicircle

The perimeter of a semicircle is not half the perimeter of a circle*. From the figure above, you can see that the perimeter is the curved part, which is half the circle, plus the diameter line across the bottom.

Recall that the perimeter of a circle is 2πR, (See Perimeter of a circle). So the curved part is half that, or πR, 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

By factoring out R, this simplifies slightly to

Angle inscribed in a semicircle

The angle inscribed in a semicircle is always 90°. See Angle inscribed in a semicircle.

Alternative definition*

An alternative definition of a semicircle is that it is simply an arc - a curved line that is half the circumference of a circle, without the straight line linking its ends. This means it is not a closed figure, and so:

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

To avoid confusion, it is best to refer to this as a "semicircular arc".

Other circle topics

General

• 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)

Equations of a circle

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

Angles in a circle

• Inscribed angle
• Central angle
• Central angle theorem

Arcs

• 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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