List of formulas in elementary geometry

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[]

Shape	Volume	Surface area	Meanings of symbols
Cube	${\displaystyle l^{3}}$	${\displaystyle 6l^{2}}$	${\displaystyle l}$ is the length of a side
Rectangular Prism	${\displaystyle lbh}$	${\displaystyle 2(lb+lh+bh)}$	${\displaystyle l}$ = length, ${\displaystyle h}$ = height, ${\displaystyle b}$ = breadth
Sphere	${\displaystyle {\frac {4\pi r^{3}}{3}}}$	${\displaystyle 4\pi r^{2}}$	${\displaystyle r}$ is the radius
Right circular cylinder	${\displaystyle \pi r^{2}h}$	${\displaystyle 2\pi r(h+r)}$	${\displaystyle r}$ is the radius and ${\displaystyle h}$ is the height

Sources:^[4]

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:

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

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 – Equalities that involve trigonometric functions
• List of volume formulas – Quantity of three-dimensional space

References[]