A circular sector is a wedge obtained by taking a portion of a disk with central angle 
, illustrated above as the shaded region. Its curved
boundary is a circular arc. The sector is a quarter-disk
when 
and a half-disk when 
. Its curved boundary is then a quarter
circle or semicircle, respectively. Let 
be the radius of the circle, 
the chord length,
the arc length,
the sagitta
(height of the arced portion), and 
the apothem (height of the triangular
portion). Then
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(1)
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(2)
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(3)
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(4)
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(5)
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(6)
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(7)
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(8)
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(9)
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The angle 
obeys the relationships
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(10)
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(11)
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(12)
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(13)
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The area of the sector is
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(14)
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(15)
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(Beyer 1987). The area can also be found by direct integration as
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(16)
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It follows that the weighted mean of the 
is
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(17)
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(18)
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so the geometric centroid of the circular sector is
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(19)
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(20)
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(21)
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(Gearhart and Schulz 1990). Checking shows that this obeys the proper limits 
for a semicircle (
) and 
for an isosceles
triangle (
).
A circular sector with opening angle 
and its two radial edges kept separate gives a full radial
slit disk, whose boundary
conditions differ from those of the uncut disk.
." College Math. J. 21,
90-99, 1990.Harris, J. W. and Stocker, H. "Sector." §3.8.4
in