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 (m3). However, this can be automatically converted to other volume units (e.g. cubic feet, gallons or liters) via the pull-down menu.
The Math / Science
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⋅(b2+b⋅B+B2)⋅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
Pyramid Calculators
- Pyramid Geometries
- 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
A regular pyramid is a type of pyramid that has the following characteristics:
- Base: The base of a regular pyramid is a regular polygon, meaning all sides of the polygon are equal in length, and all interior angles are equal. Examples of regular polygons include equilateral triangles, squares, and regular pentagons.
- Apex: The apex is the point directly above the center of the base. In a regular pyramid, the apex is aligned such that the line segment (height) from the apex to the center of the base is perpendicular to the base.
- Lateral Faces: The lateral faces of the pyramid are congruent isosceles triangles. Each triangle shares a side with the base of the pyramid and meets at the apex.
- Height: The height of the pyramid is the perpendicular distance from the apex to the center of the base.
Because of these properties, a regular pyramid is symmetric around its vertical axis (the line connecting the apex to the center of the base).
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 Calculators
- 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
- Gasket Volume