Square
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.
- a ∥ c
- b ∥ d
- a = b = c = d
- ∠A = ∠B = ∠C = ∠D = 360°
- 4 interior angles are 90°
- 2 diagonals
- 4 edges
- 4 vertex
Article Links
Area of a Square formulas |
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\( \large{ A_{area} = a^2 }\) \( \large{ A_{area} = \frac{D'^2}{2} }\) \( \large{ A_{area} = 4 \; r^2 }\) \( \large{ A_{area} = 2 \; R^2 }\) |
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Symbol | English | Metric |
\(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
\(\large{ D' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{ mm }\) |
Circumcircle Radius of a Square formulas |
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\(\large{ R = \frac{a}{ \sqrt {2} } }\) \(\large{ R = \frac{D'}{2} }\) |
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Symbol | English | Metric |
\(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ D' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Diagonal of a Square formulas |
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\(\large{ D' = a \; \sqrt {2} }\) \(\large{ D' = \sqrt {2 \; A_{area} } }\) \(\large{ D' = 2 \; R }\) \(\large{ D' = 2 \; r \; \sqrt{2} }\) \(\large{ D' = 2\;R }\) \(\large{ D' = \frac{P}{ 2\; \sqrt{2} } }\) |
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Symbol | English | Metric |
\(\large{ D' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
Distance from Centroid of a Square formulas |
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\(\large{ C_x = \frac { a } { 2 } }\) \(\large{ C_y = \frac { a } { 2} }\) |
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Symbol | English | Metric |
\(\large{ C }\) = distance from centroid | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Elastic Section Modulus of a Square formulas |
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\(\large{ S = \frac { a^3 } { 6 } }\) | ||
Symbol | English | Metric |
\(\large{ S }\) = elastic section modulus | \(\large{in^3}\) | \(\large{mm^3}\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Inscribed Circle Radius of a Square formulas |
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\(\large{ r = \frac{a}{2} }\) \(\large{ r = \frac{P}{8} }\) \(\large{ r = \frac{D'}{2\; \sqrt{2} } }\) \(\large{ r = \frac{ \sqrt{A_{area} } }{2} }\) \(\large{ r = \frac{R}{ \sqrt{2} } }\) |
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Symbol | English | Metric |
\(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
\(\large{ D' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
Perimeter of a Square formulas |
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\(\large{ P = 4\;a }\) \(\large{ P = 4\; \sqrt{A_{area} } }\) \(\large{ P = 2\;D'\; \sqrt{2} }\) \(\large{ P = 4\;R\; \sqrt{2} }\) \(\large{ P = 8\;r }\) |
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Symbol | English | Metric |
\(\large{ P }\) = perimeter | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
\(\large{ D' }\) = diagonal | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ R }\) = outside radius | \(\large{ in }\) | \(\large{ mm }\) |
Side of a Square formulas |
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\(\large{ a = \sqrt{ A_{area} } }\) | ||
Symbol | English | Metric |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ A_{area} }\) = area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
Plastic Section Modulus of a Square formulas |
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\(\large{ Z = \frac{ a^3 }{ 4 } }\) | ||
Symbol | English | Metric |
\(\large{ Z }\) = plastic section modulus | \(\large{ in^3 }\) | \(\large{ mm^2 }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Polar Moment of Inertia of a Square formulas |
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\(\large{ J_{z} = \frac {a^4}{6} }\) \(\large{ J_{z1} = \frac {2\;a^4}{3} }\) |
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Symbol | English | Metric |
\(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Radius of Gyration of a Square formulas |
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\(\large{ k_{x} = \frac { a } { 2\; \sqrt 3 } }\) \(\large{ k_{y} = \frac { a } { 2\; \sqrt 3 } }\) \(\large{ k_{z} = \frac { a } { \sqrt 6 } }\) \(\large{ k_{x1} = \frac { a } { \sqrt 3 } }\) \(\large{ k_{y1} = \frac { a } { \sqrt 3 } }\) \(\large{ k_{z1} = \sqrt { \frac {2}{3} \;a } }\) |
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Symbol | English | Metric |
\(\large{ k }\) = radius of gyration | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Second Moment of Area of a Square formulas |
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\(\large{ I_{x} = \frac {a^4}{12} }\) \(\large{ I_{y} = \frac {a^4}{12} }\) \(\large{ I_{x1} = \frac {a^4}{3} }\) \(\large{ I_{y1} = \frac {a^4}{3} }\) |
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Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(\large{ in^4 }\) | \(\large{ mm^4 }\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Radius of Gyration of a Square formulas |
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\(\large{ J = 2.25 \; \left( \frac { a } { 2 } \right) ^4 }\) | ||
Symbol | English | Metric |
\(\large{ J }\) = torsional constant | \(\large{ in^4 }\) | \(\large{ }mm^4\) |
\(\large{ a, b, c, d }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Inertia Structural Steel Modulus