Hollow Circle

area of a Hollow Circle formula
\( A \;=\; \pi \cdot ( R^2 - r^2 ) \)
Symbol	English	Metric
\( A \) = area	\( in^2 \)	\( mm^2 \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\( R \) = outside radius	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)

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.

Circumference of a Hollow Circle formulas
\( C \;=\; 2 \cdot \pi \cdot r \) (inside) \( C \;=\; 2 \cdot \pi \cdot R \) (outside)
Symbol	English	Metric
\( C \) = circumference	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)

Distance from Centroid of a Hollow Circle formulas
\( C_x \;=\; r\) \( C_y \;=\; r\)
Symbol	English	Metric
\( C_x, C_y \) = distance from centroid	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)

Elastic Section Modulus of a Hollow Circle formula
\( S \;=\; \dfrac{ \pi \cdot ( R^4 - r^4 ) }{ 4\cdot R }\)
Symbol	English	Metric
\( S \) = elastic section modulus	\(in^3\)	\(mm^3\)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)

Plastic Section Modulus of a Hollow Circle formula
\( Z \;=\; \dfrac{ 4 \cdot ( R^3 - r^3 ) }{ 3 } \)
Symbol	English	Metric
\( Z \) = plastic section modulus	\( in^3 \)	\(mm^3 \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)

Polar Moment of Inertia of a Hollow Circle formulas
\( J_{z} \;=\; \dfrac{ \pi }{ 2 } \cdot ( R^4 - r^4 ) \) \( J_{z1} \;=\; \left( \dfrac{ \pi }{ 2 } \cdot ( R^4 - r^4 ) \right) + ( 2 \cdot \pi \cdot R^2 \cdot ( R^2 - r^2 ) \;) \)
Symbol	English	Metric
\( J \) = torsional constant	\( in^4 \)	\(mm^4 \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)

Radius of a Hollow Circle formula
\( r \;=\; \dfrac{ C }{ 2 \cdot \pi }\) \(R \;=\; \dfrac{ C }{ 2 \cdot \pi }\)
Symbol	English	Metric
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( C \) = circumference	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)

Radius of Gyration of a Hollow Circle formulas
\( k_{x} \;=\; \frac{1}{2} \cdot \sqrt { R^2 + r^2 } \) \( k_{y} \;=\; \frac{1}{2} \cdot \sqrt { R^2 + r^2 } \) \( k_{z} \;=\; \dfrac{ \sqrt{ 2 } }{ 2 } \cdot \sqrt{ R^2 + r^2 } \) \( k_{x1} \;=\; \frac{1}{2} \cdot \sqrt{ 5 \cdot R^2 + r^2 } \) \( k_{y1} \;=\; \frac{1}{2} \cdot \sqrt{ 5 \cdot R^2 + r^2 } \) \( k_{z1} \;=\; \dfrac{ \sqrt{ 2 } }{ 2 } \cdot \sqrt{ 5 \cdot R^2 + r^2 } \)
Symbol	English	Metric
\( k \) = radius of gyration	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)

Second Moment of Area of a Hollow circle formulas
\( I_{x} \;=\; \dfrac{ \pi }{ 4 } \cdot ( R^4 - r^4 ) \) \( I_{y} \;=\; \dfrac{ \pi }{ 4 } \cdot ( R^4 - r^4 ) \) \( I_{x1} \;=\; [ \; \dfrac{ \pi }{ 4 } \cdot ( R^4 - r^4 ) \; ] + [ \; \pi \cdot R^2 \cdot ( R^2 - r^2 ) \; ] \) \( I_{y1} \;=\; [ \; \dfrac{ \pi }{ 4 } \cdot ( R^4 - r^4 ) \; ] + [ \; \pi \cdot R^2 \cdot ( R^2 - r^2 ) \; ] \)
Symbol	English	Metric
\( I \) = moment of inertia	\( in^4 \)	\( mm^4 \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)

Sector of a Hollow Circle formula
\( A \;=\; \dfrac{ \pi \cdot \Delta \cdot ( r^2 - R^2 ) }{ 360 }\)
Symbol	English	Metric
\( A \) = sector area	\( in^2 \)	\(mm^2 \)
\( \Delta \) = angle	\( deg \)	\(rad \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)

Torsional Constant of a Hollow Circle formulas
\( J \;=\; \dfrac{ \pi \cdot ( R^4 - r^4 ) }{ 2 }\) \( J \;=\; \dfrac{ \pi \cdot ( D^4 - d^4 ) }{ 32 }\)
Symbol	English	Metric
\( J \) = torsional constant	\( in^4 \)	\(mm^4 \)
\( d \) = inside diameter	\( in \)	\( mm \)
\( D \) = outside diameter	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)