Common equations for area:
| Shape |
Equation |
Variables |
| Square |
s^2\,\! |
s is the length of the side of the square. |
| Regular triangle |
\frac{\sqrt{3}}{4}s^2\,\! |
s is the length of one side of the triangle. |
| Regular hexagon |
\frac{3\sqrt{3}}{2}s^2\,\! |
s is the length of one side of the hexagon. |
| Regular octagon |
2(1+\sqrt{2})s^2\,\! |
s is the length of one side of the octagon. |
| Any regular polygon |
\frac{1}{2}a p \,\! |
a is the apothem, or the radius of an inscribed circle in the polygon, and p is the perimeter of the polygon. |
| Any regular polygon |
\frac{P^2/n} {4 \cdot \tan(\pi/n)}\,\! |
P is the Perimeter and n is the number of sides. |
| Any regular polygon (using degree measure) |
\frac{P^2/n} {4 \cdot \tan(180^\circ/n)}\,\! |
P is the Perimeter and n is the number of sides. |
| Rectangle |
lw \,\! |
l and w are the lengths of the rectangle's sides (length and width). |
| Parallelogram (in general) |
bh\,\! |
b and h are the length of the base and the length of the perpendicular height, respectively. |
| Rhombus |
\frac{1}{2}ab |
a and b are the lengths of the two diagonals of the rhombus. |
| Triangle |
\frac{1}{2}bh \,\! |
b and h are the base and altitude (measured perpendicular to the base), respectively. |
| Triangle |
\frac{1}{2} a b \sin C\,\! |
a and b are any two sides, and C is the angle between them. |
| Circle |
\pi r^2 ,\,\! or \pi d^2/4 \,\! |
r is the radius and d the diameter. |
| Ellipse |
\pi ab \,\! |
a and b are the semi-major and semi-minor axes, respectively. |
| Trapezoid |
\frac{1}{2}(a+b)h \,\! |
a and b are the parallel sides and h the distance (height) between the parallels. |
| Total surface area of a Cylinder |
2\pi r^2+2\pi r h \,\! |
r and h are the radius and height, respectively. |
| Lateral surface area of a cylinder |
2 \pi r h \,\! |
r and h are the radius and height, respectively. |
| Total surface area of a Cone |
\pi r (l + r) \,\! |
r and l are the radius and slant height, respectively. |
| Lateral surface area of a cone |
\pi r l \,\! |
r and l are the radius and slant height, respectively. |
| Total surface area of a Sphere |
4\pi r^2\,\! or \pi d^2\,\! |
r and d are the radius and diameter, respectively. |
| Total surface area of an ellipsoid |
|
See the article. |
| Circular sector |
\frac{1}{2} r^2 \theta \,\! |
r and \theta are the radius and angle (in radians), respectively. |
| Square to circular area conversion |
\frac{4}{\pi} A\,\! |
A is the area of the square in square units. |
| Circular to square area conversion |
\frac{1}{4} C\pi\,\! |
C is the area of the circle in circular units. |
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