Radius of a Circle

Radius, 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:

Units	English	Metric
\(\large{ r }\) = radius	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ l_a }\) = arc length	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ A }\) = area	\(\large{ in^2 }\)	\(\large{ mm^2 }\)
\(\large{ \theta }\)  (Greek dymbol theta) = central angle	\(\large{ deg }\)	\(\large{ rad }\)
\(\large{ a_c }\) = centripetal acceleration	\(\large{\frac{deg}{sec^2}}\)	\(\large{\frac{rad}{s^2}}\)
\(\large{ v_c }\) = circular velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ C }\) = circumference	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ s }\) = chord	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ s }\) = chord circle centerto midpoint distance	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ C }\) = diameter	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ v_e }\) = escape velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)
\(\large{ g }\) = gravitational acceleration	\(\large{\frac{ft}{sec^2}}\)	\(\large{\frac{rad}{s^2}}\)
\(\large{ m }\) = mass	\(\large{lbm}\)	\(\large{kg}\)
\(\large{ \pi }\) = Pi	\(\large{3.141 592 653 589 793...}\)
\(\large{ A_{se} }\) = sector area	\(\large{ in^2 }\)	\(\large{ mm^2 }\)
\(\large{ A_s }\) = segment area	\(\large{ in^2 }\)	\(\large{ mm^2 }\)
\(\large{ h_s }\) = segment height	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ t }\) = time	\(\large{ sec }\)	\(\large{ s }\)
\(\large{ t_s }\) = time (satellite orbit period)	\(\large{ sec }\)	\(\large{ s }\)
\(\large{ G }\) = universal gravitational constant	\(\large{\frac{lbf-ft^2}{lbm^2}}\)	\(\large{\frac{N - m^2}{kg^2}}\)
\(\large{ v }\) = velocity	\(\large{\frac{ft}{sec}}\)	\(\large{\frac{m}{s}}\)