Radius of a Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

circle diameter 4circle 10Radius, abbreviated as r, of a circle is a line segment between the center point and a point on a circle or sphere.

 

Radius of a Circle formulas

\(\large{ r = \frac{D}{2} }\)

\(\large{ r = \frac{C}{2 \; \pi} }\) 

\(\large{ r = \frac{ 2 \; A }{ C } }\)

\(\large{ r = \sqrt{ \frac{A}{\pi} }  }\)

\(\large{ r = \sqrt{ \frac{G \; m}{g} } }\)

\(\large{ r = \frac{ l_a }{ \theta } }\)

\(\large{ r = \sqrt{ \frac{ 2 \; A_s }{ \theta \; - \; sin \; \theta } }  }\)

\(\large{ r = \sqrt{ \frac{ c^2 }{ 4 }  +  h_c^2  } }\)

\(\large{ r = h_s + h_c }\)

\(\large{ r = \sqrt{ \frac{ 2 \; A_{se} }{ \theta }  } }\)

\(\large{ r = \frac{ v^2 }{ a_c }   }\)     (centripetal acceleration)

\(\large{ r = \frac { v_c \; t  }{ 2 \; \pi  }   }\)     (circular velocity)

\(\large{ r = \frac{ 2 \; g \; m }{ v_e }   }\)     (escape velocity)

\(\large{ r = \sqrt{  \frac{t_s^2 \;G\; m}{4\; \pi^2}  }  }\)     (Kepler's third law)

Where:

\(\large{ r }\) = radius

\(\large{ l_a }\) = arc length

\(\large{ A }\) = area

\(\large{ \theta }\)  (Greek dymbol theta) = central angle

\(\large{ a_c }\) = centripetal acceleration

\(\large{ v_c }\) = circular velocity

\(\large{ C }\) = circumference

\(\large{ c }\) = cord

\(\large{ h_c }\) = chord circle center to midpoint distance

\(\large{ d }\) = diameter

\(\large{ v_e }\) = escape velocity

\(\large{ g }\) = gravitational acceleration

\(\large{ m }\) = mass

\(\large{ \pi }\) = Pi

\(\large{ A_{se} }\) = sector area

\(\large{ A_s }\) = segment area

\(\large{ h_s }\) = segment height

\(\large{ t }\) = time

\(\large{ t_s }\) = time (satellite orbit period)

\(\large{ G }\) = universal gravitational constant

\(\large{ v }\) = velocity