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 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 $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$