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:^[1][2][3]

Three-dimensional shapes

Illustration of the shapes' equation terms

Cube

Cuboid

Prism

Parallelepiped

Pyramids

Tetrahedron

Cone

Cylinder

Sphere

Ellipsoid

This is a list of volume formulas of basic shapes:^{[4]: 405–406}

• 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:

$${\displaystyle {\begin{alignedat}{4}S&=4\pi r^{2}\\[0.3ex]&={\frac {1}{\pi ))C^{2}\\[0.3ex]&={\sqrt[{3}]{\pi (6V)^{2))}\\[0.3ex]\end{alignedat))}$$

Volume:

$${\displaystyle {\begin{alignedat}{4}V&={\frac {4}{3))\pi r^{3}\\[0.3ex]&={\frac {1}{6\pi ^{2))}C^{3}\\[0.3ex]&={\frac {1}{6{\sqrt {\pi ))))S^{3/2}\\[0.3ex]\end{alignedat))}$$

Radius:

$${\displaystyle {\begin{alignedat}{4}r&={\frac {1}{2\pi ))C\\[0.3ex]&={\sqrt ((\frac {1}{4\pi ))S))\\[0.3ex]&={\sqrt[{3}]((\frac {3}{4\pi ))V))\\[0.3ex]\end{alignedat))}$$

Circumference:

$${\displaystyle {\begin{alignedat}{4}C&=2\pi r\\[0.3ex]&={\sqrt {\pi S))\\[0.3ex]&={\sqrt[{3}]{\pi ^{2}6V))\\[0.3ex]\end{alignedat))}$$