`m = 7850 * "n" * "h" /12 * ( "b" ^2 + "b" * "B" + "B" ^2) * cot(pi/ "n" )`

Enter a value for all fields

The Mass or Weight of the Frustum of a Polygon Pyramid calculator computes the mass or weight of a regular pyramid frustum based on the dimensions of the polygon base, the height of the frustum and the density of material.

INSTRUCTIONS: Choose units and enter the following:

• (n) Number of Polygon Sides
• (b) Length of Sides on Top
• (B) Length of Sides on Bottom
• (h) Height of Pyramid
• (mD) Density of Material (Default: 7,850 kg/m³ for steel)

Pyramid Frustum Mass or Weight (m): The calculator returns the mass in kilograms, and the volume in cubic meters. However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

This Weight of the Frustum of a a Polygon based Pyramid calculator computes the weight or mass of a right pyramid frustum based on the dimensions of the frustum, a height (h) and a (mD) mean density.  The base area (A) is defined by a polygon of (n) sides each of length (b).

The formula for the mass of a regular pyramid frustum is:

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

where:

• m = mass of the pyramid frustum
• mD = density of material
• h = height of pyramid
• b = length of top sides
• B = length of base sides
• n = number of sides

---

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:

1. 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.
2. 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.
3. 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.
4. 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).

---

Mean Density Table

Common Mean Densities in Kilograms per Meter Cubed (kg/m3)
Fluids Pure Water - 1,000   Seawater - 1,022   Milk - 1,037  Olive Oil - 860 Cement Slurry - 1,442  Fuels Diesel Fuel - 885  Crude Oil - 870 to 920   Fuel Oil -  890   Ethanol - 789   Gasoline (petrol) - 737  Propane - 493  Liquid Natural Gas - 430 to 470  Market-Ready Grains Corn - 721 (56 lb/bu) Wheat - 772 (60 lb/bu) Barley - 618 (48 lb/bu) Oats - 412 (32 lb/bu) Rye - 721 (56 lb/bu) Soybean - 772 (60 lb/bu)	Metals Density of Aluminum - 2,700 Density of Brass - 8,530  Density of Bronze - 8,150  Density of Chromium - 7,190  Density of Cobalt - 8,746  Density of Copper - 8,940   Density of Gallium - 5907  Density of Gold - 19,300 Density of Iron - 7,847 Density of Lead - 11,340 Density of Nickle - 8,908  Density of Palladium -  12,023 Density of Platinum - 21,450  Density of Steel - 7,850  Density of Silver - 10,490  Density of Tin - 7,280 Density of Titanium - 4,500  Density of Tungsten - 19,600  Density of Uranium - 19,050 Density of Zinc - 7,135  Density of Zirconium - 6,570	Earthen Concrete - 2,371 Dirt - 1,250 Fire Clay - 1,362 Glass - 2,500 Granite - 2,691 Sand (dry) - 1,602 Sand (wet) - 2,082 Sandstone - 2,323 Synthetic Bakelite - 1,362 Carbon Fiber - 2,000 Organic Balsa - 170 Cork - 240 Mahogany - 545 Oak - 760 Pine - 539 Rubber - 1,522
Mean Density Lookup Function

Mean density is scientifically volume divided by mass.  There are  various unit for density adopted by cultures and industries. Common units for density included the following:

• kilograms per cubic meter (kg/m³)
• grams per cubic centimeter (g/cm³)
• grams per liter (g/L)
• pounds per cubic feet (lb/ft³)
• ounces per cubic inch (oz/in³)
• pounds per barrel (lb/bbl)
• pounds per bushel (lb/bu)

If you want to identify a material by its density, use the Density Within Range tool.