The Weight or Mass of an Ellipsoid calculator computes the weight or mass of an ellipsoid with semiaxes of lengths a, b, and c (see diagram), where the composition of the ellipsoid has a mean density (mD).
INSTRUCTIONS: Choose units and enter the following:
 (a) semiaxis of the ellipsoid.
 (b) semiaxis of the ellipsoid.
 (c) semiaxis of the ellipsoid.
 (mD) mean density of the sphere
Mass of Ellipsoid (m): The mass of the ellipsoid is returned in kilograms. However, this can be automatically converted to other mass and weight units (e.g. pounds, tons, grams) via the pulldown menu.
The Math / Science
The formula for the mass or weight of an ellipsoid is:
`m =[4/3 * pi *a*b*c]*mD`
where:
 m = mass of the ellipsoid
 a = length of semiaxis a
 b = length of semiaxis b
 c = length of semiaxis c
 mD = mean density of composition
The formula computes the volume of the geometric shape based on the input parameters. With the computed volume, this formula then executes the simple equation below to compute the approximate mass of the object.
mass = ρ * volume
where:
 Ellipsoid  Volume computes the volume of an ellipsoid based on the length of the three semiaxes (a, b, c)
 Ellipsoid  Surface Area computes the surface area of an ellipsoid based on the length of the three semiaxes (a, b, c)
 Ellipsoid  Mass or Weight computes the mass or weight of an ellipsoid based on the length of the three semiaxes (a, b, c) and the mean density.
 Ellipsoid Cap  Volume computes the volume of a section of an ellipsoid.
 Oblate Spheroid  Volume computes the volume of an Oblate Spheroid based on the length of the two semiaxes (b, c)
 Oblate Spheroid Surface Area computes the surface area of an Oblate Spheroid based on the length of the two semiaxes (b, c)
 Oblate Spheroid Mass or Weight computes the mass or weight of an Oblate Spheroid based on the length of the two semiaxes (b, c) and the mean density.
 Sphere  Volume computes the volume of a sphere based on the length of the radius (a)
 Sphere  Surface Area computes the surface area of a sphere based on the length of the radius (a)
 Sphere  Mass or Weight computes the mass or weight of a sphere based on the length of the radius (a) and the mean density.
 Circular  Volume: Computes the volume of a column with a circular top and bottom and vertical sides.
 Circular  Mass: Computes the mass/weight of circular volume based on its dimensions and mean density.
 Elliptical Volume: Computes the volume of a column with an elliptical top and bottom and vertical sides.
 Elliptical  Mass: Computes the mass/weight of an elliptical volume based on its dimensions and mean density.
 Ellipse Vertical Chord from Edge (VE): Computes the length of the vertical chord of an ellipse based on distance from the edge.
 Ellipse Vertical Chord from Center (VC): Computes the length of the vertical chord of an ellipse based on distance from the center.
 Ellipse Horizontal Chord from Edge (HE): Computes the length of the horizontal chord of an ellipse based on distance from the edge.
 Ellipse Horizontal Chord from Center (HC): Computes the length of the vertical chord of an ellipse based on distance from the center.
 Common Mean Density: Provides a lookup function to find the mean density of hundreds of materials (woods, metals, liquids, chemicals, food items, soils, and more)
Mean Density Table
Common Mean Densities in Kilograms per Meter Cubed (kg/m^{3}) 
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
MarketReady Grains

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/m^{3})
 grams per cubic centimeter (g/cm^{3})
 grams per liter (g/L)
 pounds per cubic feet (lb/ft^{3})
 ounces per cubic inch (oz/in^{3})
 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.
Weight is technically the downward force that a mass exerts based on the force of gravity and the mass of the object. On the surface of the Earth, mass and weight are often interchanged. In some places, objects are sold by the gram (mass), and in other locations, the same objects are sold by the ounce (weight).
The Weight Calculators use the dimensions of an object and its shape to compute the objects volume. They then apply a density associated with a material to estimate the objects weight.
Weight Calculators