Radius of a Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

circle 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:

 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 \(\large{\frac{ft}{sec}}\)  \(\large{\frac{m}{s}}\)