Geometrical Properties of Circular Sector

Radius - r =   m

Angle - α =   °

k = π180

a =  2·r²·(1 – cos(α)) m

Area

A = α2·k·r² m²

Centroid

y_c = a2 m

z_c = 4·r·sin(α2)3·α·k m

Perimeter

P = (α·k + 2)·r m

Second moments of area

I_y = r⁴·[α·k + sin(α)8 – 8·sin(α2)²9·α·k] m⁴

I_z = r⁴·(α·k – sin(α))8 m⁴

Polar moment of area

I_x = I_y + I_z m⁴

Radii of gyration

r_y =  I_yA m

r_z =  I_zA m

r_x =  I_xA m