Polygon Volume

This Volume of a Polygon based column equation computes the volume of a column where the base is the area of a regular polygon with (n) equal sides of length (s) combined with the height (h) to compute the volume.

INSTRUCTIONS: Choose units and enter the following:

• n - the number of sides of the regular polygon
• s - the length of a side of the polygon
• h - height of the polygon column

Column Volume(V): The calculator returns the volume in cubic meters.  However, this can be automatically converted to other volume units via the pull-down menu.

The Math / Science

The formula for the volume of a polygon based shape is:

    `V = (1/4 * n * s^2 cot(pi/n)) * h`

where:

• V = Volume of the Polygon based column
• n = number of sides of the polygon
• s = length of the side of the polygon
• h = height of the polygon

A regular n-sided polygon is a polygon with n equal length sides and is a polygon which has n equal angles at the n vertices of the polygon.  A vertical column with a base of a regular polygon has a volume of V = Area of Base X Depth.  Where the depth is the height of the column.

Polygon Columns Calculators

• Surface area of a regular polygon column
• Volume of a polygon based column
• Mass of a polygon based column