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This is a short list of some common mathematical shapes and figures and the formulas that describe them.

Two-dimensional shapes

Shape	Area	Perimeter/Circumference	Meanings of symbols
Square	${\displaystyle l^{2}}$	${\displaystyle 4l}$	${\displaystyle l}$ is the length of a side
Rectangle	${\displaystyle lb}$	${\displaystyle 2(l+b)}$	${\displaystyle l}$ is length, ${\displaystyle b}$ is breadth
Circle	${\displaystyle \pi r^{2}}$	${\displaystyle 2\pi r}$ or ${\displaystyle \pi d}$	where ${\displaystyle r}$ is the radius and ${\displaystyle d}$ is the diameter
Ellipse	${\displaystyle \pi ab}$		where ${\displaystyle a}$ is the semimajor axis and ${\displaystyle b}$ is the semiminor axis
Triangle	${\displaystyle {\frac {bh}{2}}}$	${\displaystyle a+b+c}$	${\displaystyle b}$ is base; ${\displaystyle h}$ is height; ${\displaystyle a,b,c}$ are sides
Parallelogram	${\displaystyle bh}$	${\displaystyle 2(a+b)}$	${\displaystyle b}$ is base, ${\displaystyle h}$ is height, ${\displaystyle a}$ is side
Trapezoid	${\displaystyle {\frac {a+b}{2}}h}$		${\displaystyle a}$ and ${\displaystyle b}$ are the bases

Sources:

Three-dimensional shapes

This is a list of volume formulas of basic shapes:

• Cone – ${\textstyle {\frac {1}{3}}\pi r^{2}h}$, where ${\textstyle r}$ is the base's radius
• Cube – ${\textstyle a^{3}}$, where ${\textstyle a}$ is the side's length;
• Cuboid – ${\textstyle abc}$, where ${\textstyle a}$, ${\textstyle b}$, and ${\textstyle c}$ are the sides' length;
• Cylinder – ${\textstyle \pi r^{2}h}$, where ${\textstyle r}$ is the base's radius and ${\textstyle h}$ is the cone's height;
• Ellipsoid – ${\textstyle {\frac {4}{3}}\pi abc}$, where ${\textstyle a}$, ${\textstyle b}$, and ${\textstyle c}$ are the semi-major and semi-minor axes' length;
• Sphere – ${\textstyle {\frac {4}{3}}\pi r^{3}}$, where ${\textstyle r}$ is the radius;
• Parallelepiped – ${\textstyle abc{\sqrt {K}}}$, where ${\textstyle a}$, ${\textstyle b}$, and ${\textstyle c}$ are the sides' length,${\textstyle K=1+2\cos(\alpha )\cos(\beta )\cos(\gamma )-\cos ^{2}(\alpha )-\cos ^{2}(\beta )-\cos ^{2}(\gamma )}$, and ${\textstyle \alpha }$, ${\textstyle \beta }$, and ${\textstyle \gamma }$ are angles between the two sides;
• Prism – ${\textstyle Bh}$, where ${\textstyle B}$ is the base's area and ${\textstyle h}$ is the prism's height;
• Pyramid – ${\textstyle {\frac {1}{3}}Bh}$, where ${\textstyle B}$ is the base's area and ${\textstyle h}$ is the pyramid's height;
• Tetrahedron – ${\textstyle {{\sqrt {2}} \over 12}a^{3}}$, where ${\textstyle a}$ is the side's length.

Sphere

The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables

• ${\displaystyle r}$ is the radius,
• ${\displaystyle C=2\pi r}$ is the circumference (the length of any one of its great circles),
• ${\displaystyle S}$ is the surface area,
• ${\displaystyle V}$ is the volume.

Surface area:

$${\displaystyle {\begin{alignedat}{4}S&=4\pi r^{2}\\&={\frac {1}{\pi }}C^{2}\\&={\sqrt{\pi (6V)^{2}}}\\\end{alignedat}}}$$

Volume:

$${\displaystyle {\begin{alignedat}{4}V&={\frac {4}{3}}\pi r^{3}\\&={\frac {1}{6\pi ^{2}}}C^{3}\\&={\frac {1}{6{\sqrt {\pi }}}}S^{3/2}\\\end{alignedat}}}$$

Radius:

$${\displaystyle {\begin{alignedat}{4}r&={\frac {1}{2\pi }}C\\&={\sqrt {{\frac {1}{4\pi }}S}}\\&={\sqrt{{\frac {3}{4\pi }}V}}\\\end{alignedat}}}$$

Circumference:

$${\displaystyle {\begin{alignedat}{4}C&=2\pi r\\&={\sqrt {\pi S}}\\&={\sqrt{\pi ^{2}6V}}\\\end{alignedat}}}$$

See also

• Arc length – Distance along a curve
• Area#Area formulas – Size of a two-dimensional surface
• Perimeter#Formulas – Path that surrounds an area
• List of second moments of area
• List of surface-area-to-volume ratios – Surface area per unit volume
• List of surface area formulas – Measure of a two-dimensional surface
• List of trigonometric identities
• List of volume formulas – Quantity of three-dimensional space

References

1. "Archived copy" (PDF). Archived from the original (PDF) on 2012-08-13. Retrieved 2011-11-29.{{cite web}}: CS1 maint: archived copy as title (link)
2. "Area Formulas".
3. "List of Basic Geometry Formulas". 27 May 2018.
4. Treese, Steven A. (2018). History and Measurement of the Base and Derived Units. Cham, Switzerland: Springer Science+Business Media. ISBN 978-3-319-77577-7. LCCN 2018940415. OCLC 1036766223.

• Elementary geometry
• Mathematics-related lists