Square

Area of a Square formulas
\( A_{area} \;=\; a^2 \) \( A_{area} \;=\; \dfrac{ D'^2 }{ 2 }\) \( A_{area} \;=\; 4 \cdot r^2 \) \( A_{area} \;=\; 2 \cdot R^2 \)
Symbol	English	Metric
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( D' \) = diagonal	\( in \)	\( mm \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)

Square (a two-dimensional figure) is a quadrilateral with four equal side lengths and 90° interior angles.
Abbreviated as SQ
Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
Diagonal is a line from one vertices to another that is non adjacent.
Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
Quadrilateral (a two-dimensional figure) is a polygon with four sides.

Circumcircle Radius of a Square formulas
\( R \;=\; \dfrac{ a }{ \sqrt {2} }\) \( R \;=\; \dfrac{ D' }{ 2 }\)
Symbol	English	Metric
\( R \) = outside radius	\( in \)	\( mm \)
\( D' \) = diagonal	\( in \)	\( mm \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)

Diagonal of a Square formulas
\( D' \;=\; a \cdot \sqrt {2} \) \( D' \;=\; \sqrt {2 \cdot A_{area} } \) \( D' \;=\; 2 \cdot R \) \( D' \;=\; 2 \cdot r \cdot \sqrt{2} \) \( D' \;=\; 2 \cdot R \) \( D' \;=\; \dfrac{ P }{ 2 \cdot \sqrt{2} }\)
Symbol	English	Metric
\( D' \) = diagonal	\( in \)	\(\large{ mm }\)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( P \) = perimeter	\( in \)	\( mm \)

Distance from Centroid of a Square formulas
\( C_x \;=\; \dfrac{ a }{ 2 }\) \( C_y \;=\; \dfrac{ a }{ 2 }\)
Symbol	English	Metric
\( C \) = distance from centroid	\( in \)	\( mm \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)

Elastic Section Modulus of a Square formulas
\( S \;=\; \dfrac{ a^3 }{ 6 }\)
Symbol	English	Metric
\( S \) = elastic section modulus	\( in^3 \)	\( mm^3 \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)

Inscribed Circle Radius of a Square formulas
\( r \;=\; \dfrac{ a}{ 2 } \) \( r \;=\; \dfrac{ P}{ 8 } \) \( r \;=\; \dfrac{ D }{ 2\cdot \sqrt{2} } \) \( r \;=\; \dfrac{ \sqrt{A_{area} } }{ 2 } \) \( r \;=\; \dfrac{ R}{ \sqrt{2} }\)
Symbol	English	Metric
\( r \) = inside radius	\( in \)	\( mm \)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( D' \) = diagonal	\( in \)	\( mm \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)
\( P \) = perimeter	\( in \)	\( mm \)

Perimeter of a Square formulas
\( P \;=\; 4 \cdot a \) \( P \;=\; 4\cdot \sqrt{A_{area} } \) \( P \;=\; 2\cdot D'\cdot \sqrt{2} \) \( P \;=\; 4\cdot R\cdot \sqrt{2} \) \( P \;=\; 8\cdot r \)
Symbol	English	Metric
\( P \) = perimeter	\( in \)	\( mm \)
\( A_{area} \) = area	\( in^2 \)	\( mm^2 \)
\( D' \) = diagonal	\( in \)	\( mm \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)
\( r \) = inside radius	\( in \)	\( mm \)
\( R \) = outside radius	\( in \)	\( mm \)

Plastic Section Modulus of a Square formulas
\( Z \;=\; \dfrac{ a^3 }{ 4 } \)
Symbol	English	Metric
\( Z \) = plastic section modulus	\( in^3 \)	\( mm^3 \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)

Polar Moment of Inertia of a Square formulas
\( J_{z} \;=\; \dfrac{ a^4}{ 6 }\) \( J_{z1} \;=\; \dfrac{ 2\cdot a^4}{ 3 }\)
Symbol	English	Metric
\( J \) = torsional constant	\( in^4 \)	\( mm^4 \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)

Torsional Constant formulas
\( J \;=\; 2.25 \cdot \left( \dfrac{ a }{ 2 } \right)^4 \)
Symbol	English	Metric
\( J \) = torsional constant	\( in^4 \)	\( mm^4 \)
\( a, b, c, d \) = edge	\( in \)	\( mm \)

Lorentz Force

Number Density

Rotational Kinetic Energy