Area Calculator

This calculator allows you to compute the area of 15 popular shapes rapidly and accurately. Below is a list of the shapes we offer and information about computing their areas.

How to Use This Calculator

1. Choose the shape to find the area of
2. Enter the required values

Some area calculators offer various methods of computing the area. For example, the triangle area calculator allows you to find the area given different values such as:

• Base & height
• Three sides
• Two sides & angle between them
• Two angles & side between them
• 2D vertex coordinates

Table of Area Formulas

• Square
• Rectangle
• Triangle
• Circle
• Ellipse
• Sector of a circle
• Parallelogram
• Rhombus
• Kite
• Trapezoid
• Regular pentagon
• Regular hexagon
• Regular octagon
• Regular n-gon
• Annulus

Area Formulas

Square Area Formula

Side length: $A = s^2$ where s is the side length.

Diagonal length: $A = \frac{d^2}{2}$ where d is the diagonal length.

Rectangle Area Formula

$A = l \times w$ where l is length and w is width.

Triangle Area Formula

Base and height: $A = \frac{1}{2} b h$

Three sides (Heron's formula): $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a + b + c}{2}$

Two sides and included angle: $A = \frac{1}{2} ab \sin(C)$

One side and two angles: $A = \frac{1}{2} \cdot \frac{a^2 \sin(B) \sin(C)}{\sin(A)}$

Coordinates: $A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$

Circle Area Formula

$A = \pi r^2$ where r is the radius.

Ellipse Area Formula

$A = \pi a b$ where a and b are the semi-major and semi-minor axes.

Sector of a Circle Area Formula

$A = \frac{\theta}{360^\circ} \pi r^2$ where θ is in degrees and r is the radius.

Parallelogram Area Formula

Base and height: $A = b h$

Two sides and included angle: $A = ab \sin(\theta)$

Diagonals and angle between: $A = \frac{1}{2} d_1 d_2 \sin(\theta)$

Rhombus Area Formula

Diagonals: $A = \frac{1}{2} d_1 d_2$

Side and height: $A = s h$

Side and angle: $A = s^2 \sin(\theta)$

Kite Area Formula

Diagonals: $A = \frac{1}{2} d_1 d_2$

Two unequal sides and included angle: $A = ab \sin(\theta)$

Trapezoid Area Formula

$A = \frac{1}{2} (a + b) h$ where a and b are the parallel sides, and h is the height.

Regular Pentagon Area Formula

$A = \frac{5}{4} s^2 \cot\left(\frac{\pi}{5}\right)$ where s is the side length.

Regular Hexagon Area Formula

$A = \frac{3\sqrt{3}}{2} s^2$ where s is the side length.

Regular Octagon Area Formula

$A = 2(1 + \sqrt{2}) s^2$ where s is the side length.

Regular N-gon Area Formula

$A = \frac{n s^2}{4} \cot\left(\frac{\pi}{n}\right)$ where n is the number of sides and s is the side length.

Annulus Area Formula

$A = \pi(R^2 - r^2)$ where R is the outer radius and r is the inner radius.