# Thin Wall Circle

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.
• See Article Link  -  Geometric Properties of Structural Shapes ## area of a Thin Walled Circle formula

$$\large{ A = 2\; \pi \;r\; t }$$     (Area of a Thin Walled Circle)

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

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

### Solve for r

 area, A thickness, t

### Solve for t

Symbol English Metric
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ ## Perimeter of a Thin Walled Circle formula

$$\large{ P = 2\; \pi \;r }$$     (outside)

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

Symbol English Metric
$$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ ## Radius of a Thin Walled Circle formula

$$\large{ r = \sqrt{ \frac { 2 \; A }{ \pi } } }$$     (Radius of a Thin Walled Circle)

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

Symbol 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

$$\large{ C_x = r}$$

$$\large{ C_y = r}$$

Symbol 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

$$\large{ S = \frac{ 2 \; \pi \; r \; t }{ 3 } }$$     (Elastic Section Modulus of a Thin Walled Circle)

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

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

Symbol English Metric
$$\large{ S }$$ = elastic section modulus $$\large{in^3}$$ $$\large{mm^3}$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ ## Plastic Section Modulus of a Thin Walled Circle formula

$$\large{ Z = \pi \; r^2 \; t }$$     (Plastic Section Modulus of a Thin Walled Circle)

$$\large{ r = \sqrt{ \frac{ Z }{ \pi \; t } } }$$

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

Symbol English Metric
$$\large{ Z }$$ = plastic section modulus $$\large{ in^3 }$$ $$\large{mm^3 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ ## Polar Moment of Inertia of a Thin Walled Circle formulas

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

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

Symbol English Metric
$$\large{ J }$$ = torsional constant $$\large{ in^4 }$$ $$\large{mm^4 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ ## Radius of Gyration of a Thin Walled Circle formulas

$$\large{ k_{x} = \frac { \sqrt {2} } { 2 } \; r }$$

$$\large{ k_{y} = \frac { \sqrt {2} } { 2 } \; r }$$

$$\large{ k_{z} = r }$$

$$\large{ k_{x1} = \frac { \sqrt {6} } { 2 } \; r }$$

$$\large{ k_{y1} = \frac { \sqrt {6} } { 2 } \; r }$$

$$\large{ k_{z1} = \sqrt {3} \; r }$$

Symbol 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

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

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

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

Symbol English Metric
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{mm^4 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = inside radius $$\large{ in }$$ $$\large{mm }$$
$$\large{ t }$$ = thickness $$\large{ in }$$ $$\large{mm }$$ ## Torsional Constant of a Thin Walled Circle formula

$$\large{ J = 2\; \pi \;r^3 \; t }$$     (Torsional Constant of a Thin Walled Circle)

$$\large{ r = \left( \frac{ J }{ 2 \; \pi \; t } \right)^{ \frac{1}{3} } }$$

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

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