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:
\(\large{ r }\) = 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