`M = pi a b ((2 c)/3 - x + x^3/(3c^2))*mD`

Enter a value for all fields

The Mass or Weight of an Ellipsoid Cap calculator computes the mass or weight of an ellipsoid cap where the semi-axes of the ellipsoid are a, b, and c, and the height of the cap is h.  The mean density is also used.

INSTRUCTIONS:  Choose units and enter the following:

• (a)  semi-axis a.
• (b)  semi-axis b.
• (c)  semi-axis c.
• (h) height of the cap
• (mD) mean density of the cap material [CLICK HERE ]

Mass or Weight of an Ellipsoid Cap (M): The mass is returned in kilograms. However, the volume can be automatically converted to compatible units via the pull-down menu. 

The Math / Science

his calculator first computes the volume of an ellipsoid cap  based on the following formula:

           `V = π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))`

where:

• V is the volume of the ellipsoid cap
• a, b and c are the lengths of the semi-axes
• x = c - h and h is the height of the ellipsoid cap

With the volume of the ellipsoid cap, this formula then executes the simple equation below to compute the approximate mass of the object.

        Mass = Volume ⋅ Density

To query the mean density (mD or μD) of many common substances, elements, liquids and materials, CLICK HERE (e.g. the density of water is 1,000 kg/m³.

When the formula for mass and volume of a Ellipsoid Cap are combined, one has formula for the mass of an ellipsoid cap is:

    M = `π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))⋅mD`

where:

• M is the mass of the ellipsoid cap 
• a, b and c are the lengths of the semi-axes
• x = c - h and h is the height of the ellipsoid cap
• mD is the mean density of the material

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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.

Related Calculators:

• Volume of an Ellipsoid Cap
• Mass of an Ellipsoid Cap
• Volume of a Ellipsoid
• Weight or Mass of an Ellipsoid
• Surface Area of an Ellipsoid
• Volume of a Sphere
• Volume of a Oblate Spheroid