# Thin Wall 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 thin wall circle is a structural shape used in construction.

## area of a Thin Walled Circle formulas

 $$\large{ A = 2\; \pi \;r\; t }$$ $$\large{ A = \pi \;D\; t }$$

### Where:

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

## Perimeter of a Thin Walled Circle formulas

 $$\large{ P = 2\; \pi \;r }$$ (outside) $$\large{ P = 2\; \pi \; \left( r - t \right) }$$ (inside)

### Where:

 Units English Metric $$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Radius of a Thin Walled Circle formula

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

### Where:

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

## Distance from Centroid of a Thin Walled 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 Thin Walled Circle formula

 $$\large{ S = \frac { 2\; \pi \;r \;t } { 3 } }$$

### Where:

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

## Plastic Section Modulus of a Thin Walled Circle formula

 $$\large{ Z = \pi \;r^2 \;t }$$

### Where:

 Units English Metric $$\large{ Z }$$ = plastic section modulus $$\large{ in^4 }$$ $$\large{mm^4 }$$ $$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$ $$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ $$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$

## Polar Moment of Inertia of a Thin Walled Circle formulas

 $$\large{ J_{z} = 2\; \pi \;r^3 \;t }$$ $$\large{ J_{z1} = 6\; \pi \;r^3 \;t }$$

### Where:

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

## Radius of Gyration of a Thin Walled Circle formulas

 $$\large{ k_{x} = \frac { \sqrt {2} } { 2 } \; r }$$ $$\large{ k_{y} = \frac { \sqrt {2} } { 2 } \; r }$$ $$\large{ k_{z} = r }$$ $$\large{ k_{x1} = \frac { \sqrt {6} } { 2 } \; r }$$ $$\large{ k_{y1} = \frac { \sqrt {6} } { 2 } \; r }$$ $$\large{ k_{z1} = \sqrt {3} \; r }$$

### Where:

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

## Second Moment of Area of a Thin Walled Circle formulas

 $$\large{ I_{x} = \pi \;r^3 \;t }$$ $$\large{ I_{x1} = 3\; \pi \;r^3 \;t }$$ $$\large{ I_{y1} = 3\; \pi \;r^3 \;t }$$

### Where:

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

## Torsional Constant of a Thin Walled Circle formula

 $$\large{ J = 2\; \pi \;r^3 \; t }$$

### Where:

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