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.
Ellipsoid Calculators
 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.
 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.
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:
Common Mean Densities 
Fluids
 Pure Water  1,000 kg/m³
 Seawater  1,022 kg/m³
 Milk  1,037 kg/m³
 Olive Oil  860 kg/m³
 Cement Slurry  1,442 kg/m³
Fuels
 Diesel Fuel  885 kg/m³
 Crude Oil  870 kg/m³ to 920 kg/m³
 Fuel Oil  890 kg/m³
 Ethanol  789 kg/m³
 Gasoline (petrol)  737 kg/m³
 Propane  493 kg/m^{3}
 Liquid Natural Gas  430 to 470 kg/m^{3}
MarketReady Grains
 Corn  56 lb/bu (721 kg/m^{3})
 Wheat  60 lb/bu (772 kg/m^{3})
 Barley  48 lb/bu (618 kg/m^{3})
 Oats  32 lb/bu (412 kg/m^{3})
 Rye  56 lb/bu (721 kg/m^{3})
 Soybean  60 lb/bu (772 kg/m^{3})

Metals
 Aluminum  2700 kg/m³
 Brass  8530 kg/m³
 Bronze  8150 kg/m³
 Chromium  7190 kg/m3
 Cobalt  8746 kg/m3
 Copper  8920 kg/m³
 Gallium  5907 kg/m3
 Gold  19300 kg/m³
 Iridium  22560 kg/m^{3}
 Iron  7847.0 kg/m³
 Lead  11340 kg/m³
 Molybdenum  10280 kg/m^{3}
 Nickle  8908 kg/m3
 Palladium  12160 kg/m³
 Platinum  21450.0 kg/m³
 Rhodium  12410 kg/m^{3}
 Steel  7850 kg/m³
 Silver  10490 kg/m³
 Titanium  4500 kg/m³
 Tungsten  19600 kg/m³
 Zinc  7135 kg/m³
 Zirconium  6570 kg/m³

Mean Density is the average amount of mass within a volume for a substance. Note, volume of a material is often highly subject to the temperatures, since materials expand as they warm. For that reason, mean densities of substances are often cited with a set of nominal conditions such as temperature and barometric pressure.
The formula for mean density is:
μD = V / m
where:
 μD = mean density
 V = Volume in units like cubic meters or cubic inches
 m = Mass in units like kilograms or pounds
Mean density is also often indicated as the Greek symbol rho (ρ).
Mass and Weight
Density is a function of mass. However, converting from mass to weight is trivial under the right conditions. Fortunately those conditions are generally true anywhere on the surface of the Earth, so the conversions built into the vCalc engine can be assumed to be fairly accurate unless you require weight at very high altitudes or in space.
The mean density (mD or μD) of many common substances, elements, liquids and materials can be found by clicking HERE .
Mean Density Units
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)
vCalc provides for automatic conversions between density units via the pulldown menus.