Written by Jerry Ratzlaff on . Posted in Plane Geometry

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 formula

$$\large{ r = \frac{D}{2} }$$

$$\large{ r = \frac{C}{2 \; \pi} }$$

$$\large{ r = \frac{ 2 \; A }{ C } }$$

$$\large{ r = \sqrt{ \frac{A}{\pi} } }$$

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

$$\large{ r = \frac{ l_a }{ \theta } }$$

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

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

$$\large{ r = h_s + h_c }$$

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

$$\large{ r = \frac{ v^2 }{ a_c } }$$     (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