Shape Area Calculator

Input	Shape & Size
Find the area of a	... Square Triangle Rectangle Circle Sphere Pentagon Hexagon Octagon Cube Cylinder

Output	Area
Area

Using This Calculator

This calculator can be used to quickly figure the area of a triangle, square, rectangle, circle, sphere, pentagon, hexagon, octogon, cube, or cylinder.

For 2 dimensional shapes it calculates the area of the shape & for 3 dimensional shapes it calculates their surface area.

Area Formulas

The formulas for each regular shape are shown below.

Triangle

triangle area = base lenght * height / 2

Square

square area = length²

Rectangle

rectangle area = length * width

Circle

circle area = π * Radius²

Sphere

sphere surface area = 4π * Radius²

Pentagon

• regular pentagon (without apothem): side² * 1/4* √(5 (5+2 √5))
• regular pentagon (where apothem is known): area = 5* side * apothem / 2
  • apothem = 1/2 side / tan 36°

Hexagon

hexagon area = side length² * 3 √3 / 2

Octagon

octagon area = 2(1+ √ 2) * side length²

Cube

cube surface area = 6 * length²

Cylinder

cylinder surface area = 2 π * height * Radius+ 2 π * Radius²

Incircle, Circumcircle, Radius & Apothem

Definitions

• Regular Polygon: A polygon with n sides where all sides have equal lengths.
• Radius: Line which connects the center of a polygot to one of its verticies.
• Circumcircle: Circle which fits outside a polygon and connects all verticies. The radius of this circle is the same as the radius of the poligon.
• Incircle: Circle which fits inside a polygon and connects the midpoint of each side.
• Apothem: Line connecting the midpoint of a polygon's side to its center.
• Perimeter: The distance around a polygon. For regular polygons with a fixed number of sides this is found by multiplying the length of a side by how many sides the polygon has.
• Area: The amount of space inside the boundary of flat 2-dimensional shapes or the surface of a solid 3-dimensional object.