Sector

Sector formula

Area: \(\; A= \frac {1}{2} \phi r^2 = \frac {1}{2} ar\)

Angle: \(\; \phi = \frac {a}{r} \)

Length: \(\; a= \phi r \)

Length: \(\; b= 2r \;sin\; \frac { \phi } {2} \)

Where:

\(A\) = area

\(r\) = radius

\(a\) = arc length

\(\phi \) = vertex angle in radius

\(b\) = length

\(sin\) = sine

circle segment formula

Area: \(\; A= \frac {1}{2} r^2 \left( \phi - sin\phi \right)     \)

\(\phi\) : \(\; \phi= \frac {c}{r} = 2 \left( arccos \frac {r-e} {r}   \right)     \)

Length: \(\; d= 2r \;sin\; \frac { \phi } {2} \)

Where:

\(A\) = area

\(r\) = radius

\(c\) = arc length

\(\phi \) = vertex angle in radius

\(d\) = length

\(e\) = height

\(sin\) = sine

\(arcos\) = arccosine