# Hollow Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Two circles each having all points on each circle at a fixed equal distance from a center point.
• Center of a circle having all points on the line circumference are at equal distance from the center point.
• A hollow circle is a structural shape used in construction.

## area of a Hollow Circle formula

 $$\large{ A = \pi \; \left( R^2 - r^2 \right) }$$

### Where:

 Units English Metric $$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Circumference of a Hollow Circle formulas

 $$\large{ C = 2 \; \pi \; R }$$ (outside) $$\large{ C = 2 \; \pi \; r }$$ (inside)

### Where:

 Units English Metric $$\large{ C }$$ = circumference $$\large{ in }$$ $$\large{ mm }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

### Where:

$$\large{ C }$$ = circumference

$$\large{ r }$$ = inside radius

$$\large{ R }$$ = outside radius

$$\large{ \pi }$$ = Pi

## Distance from Centroid of a Hollow Circle formulas

 $$\large{ C_x = r}$$ $$\large{ C_y = r}$$

### Where:

 Units English Metric $$\large{ C_x, C_y }$$ = distance from centroid $$\large{ in }$$ $$\large{ mm }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$

## Elastic Section Modulus of a Hollow Circle formula

 $$\large{ S = \frac{ \pi \; \left( R^4 \;-\; r^4 \right) }{ 4\;R } }$$

### Where:

 Units English Metric $$\large{ S }$$ = elastic section modulus $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Plastic Section Modulus of a Hollow Circle formula

 $$\large{ Z = \frac { 4 \; \left( R^3 \;-\; r^3 \right) } { 3 } }$$

### Where:

 Units English Metric $$\large{ Z }$$ = plastic section modulus $$\large{ in^4 }$$ $$\large{mm^4 }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$

## Polar Moment of Inertia of a Hollow Circle formulas

 $$\large{ J_{z} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) }$$ $$\large{ J_{z1} = \frac { \pi }{2} \; \left( R^4 - r^4 \right) + 2\; \pi \; R^2 \left( R^2 - r^2 \right) }$$

### Where:

 Units English Metric $$\large{ J }$$ = torsional constant $$\large{ in^4 }$$ $$\large{mm^4 }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Radius of a Hollow Circle formula

 $$\large{ r = \sqrt {\frac {2 \; A } {\pi} } }$$

### Where:

 Units English Metric $$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{mm^2 }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Radius of Gyration of a Hollow Circle formulas

 $$\large{ k_{x} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }$$ $$\large{ k_{y} = \frac {1}{2} \; \sqrt { R^2 + r^2 } }$$ $$\large{ k_{z} = \frac { \sqrt { 2 } }{2} \; \sqrt { R^2 + r^2 } }$$ $$\large{ k_{x1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }$$ $$\large{ k_{y1} = \frac {1}{2} \; \sqrt { 5 \; R^2 + r^2 } }$$ $$\large{ k_{z1} = \frac { \sqrt { 2 } }{2} \; \sqrt { 5 \; R^2 + r^2 } }$$

### Where:

 Units English Metric $$\large{ k }$$ = radius of gyration $$\large{ in }$$ $$\large{mm }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$

## Second Moment of Area of a Hollow circle formulas

 $$\large{ I_{x} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }$$ $$\large{ I_{y} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) }$$ $$\large{ I_{x1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }$$ $$\large{ I_{y1} = \frac { \pi }{4} \; \left( R^4 - r^4 \right) + \pi \; R^2 \left( R^2 - r^2 \right) }$$

### Where:

 Units English Metric $$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{mm^4 }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Sector of a Hollow Circle formula

 $$\large{ A = \frac{\pi \; \Delta \; \left( r^2 \;-\; R^2 \right) }{360} }$$

### Where:

 Units English Metric $$\large{ A }$$ = sector area $$\large{ in^2 }$$ $$\large{mm^2 }$$ $$\large{ \Delta }$$ = angle $$\large{ deg }$$ $$\large{rad }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Torsional Constant of a Hollow Circle formulas

 $$\large{ J = \frac { \pi \; \left( R^4 \;-\; r^4 \right) } { 2 } }$$ $$\large{ J = \frac { \pi \; \left( D^4 \;-\; d^4 \right) } { 32 } }$$

### Where:

 Units English Metric $$\large{ J }$$ = torsional constant $$\large{ in^4 }$$ $$\large{mm^4 }$$ $$\large{ d }$$ =  inside diameter $$\large{ in }$$ $$\large{mm }$$ $$\large{ D }$$ =  outside diameter $$\large{ in }$$ $$\large{mm }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ R }$$ = outside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$ 