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`V = "n" * "h" /12 * ( "b" ^2 + "b" * "B" + "B" ^2) * cot(pi/ "n" )`

Enter a value for all fields

The **Volume of a Polygon Based Pyramid Frustum** calculator computes the volume of the frustum of right pyramid with two regular polygon bases (top and bottom) with the same number of sides (n) separated by a height (h).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**n**) Number of Polygon Sides - (
**b**) Length of Top Sides - (
**B**) Length of Bottom Sides - (
**h**) Height between Top and Bottom polygons

**Pyramid Volume (V):** The calculator returns the volume in cubic meters (m^{3}). However, this can be automatically converted to other volume units (e.g. cubic feet, gallons or liters) via the pull-down menu.

The top and base polygons are regular polygons with equal length sides and angles. The polygons are defined by the number of sides (n) and the equal side lengths of **b** and **B** of the two polygons respectively (see diagram).

The formula for the volume of a polygon pyramid frustum is:

V = n⋅h/12⋅(b^{2}+b⋅B+B^{2})⋅cot(π/n)

where:

- V is the volume of the polygon pyramid frustum
- n is the number of sides of the polygon
- b is the length of the sides on the top polygon
- B is the length of the sides on the bottom polygon

- Volume of a Pyramid
- Mass or Weight of a Pyramid
- Volume of a Frustum of a Pyramid
- Mass of a Frustum of a Pyramid
- Volume of a Polygon Based Pyramid
- Mass of a Polygon Based Pyramid
- Volume of a Frustum of a Polygon Based Pyramid
- Mass of a Frustum of a Polygon Based Pyramid
- Mean Density of Many Substances: The Mean Density Lookup equation provides the mean density of hundreds (650+) substances from metals to gases, woods, food, liquids and much more. The results of the Mean Density look-up are in kg/m
^{3}. Use the answer for the substance you choose in the mass equation to approximate the mass or weight of the pyramid shaped object based on its shape, dimensions and the mean density of its composition.

**Volume **is a three dimensional measurement of the amount of space taken up by an object. Volume units are cubic measurements for solid objects such as cubic inches and cubic meters. Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel.

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape. Many such calculations are available in the following list of calculators.

In many cases, the calculators are for a column with a geometric shaped base and vertical sides. One basic formula for volume is area times a Height when the volume has vertical sides.

- Volume from Area and Height
- Volume of a Cube
- Volume of a Box
- Volume of a Cone
- Volume of a Cone Frustum
- Volume of a Cylinder
- Volume of a Slanted Cylinder
- Volume of a Semicircle
- Volume of a Triangular
- Volume of a Quadrilateral
- Volume of a Pentagon
- Volume of a Hexagon
- Volume of a Heptagon
- Volume of a Octagon
- Volume of a Nonagon
- Volume of a Decagon
- Volume of a Hendecagon
- Volume of a Dodecagon
- Volume of a Paraboloid
- Volume of a Polygon based Pyramid
- Volume of a Pyramid Frustum
- Volume of a Sphere
- Volume of a Sphere Cap
- Volume of a Sphere Segment
- Volume of a Sphere Shell
- Volume of a Oblate Spheroid
- Volume of a Ellipsoid
- Volume of a Torus
- Volume of a Bottle
- Volume of a Chamfer