The Weight or Mass of an Ellipsoid calculator computes the weight or mass of an ellipsoid with semi-axes 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) semi-axis of the ellipsoid.
- (b) semi-axis of the ellipsoid.
- (c) semi-axis 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 pull-down 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 semi-axis a
- b = length of semi-axis b
- c = length of semi-axis 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 semi-axes (a, b, c)
- Ellipsoid - Surface Area computes the surface area of an ellipsoid based on the length of the three semi-axes (a, b, c)
- Ellipsoid - Mass or Weight computes the mass or weight of an ellipsoid based on the length of the three semi-axes (a, b, c) and the mean density.
- Oblate Spheroid - Volume computes the volume of an Oblate Spheroid based on the length of the two semi-axes (b, c)
- Oblate Spheroid- Surface Area computes the surface area of an Oblate Spheroid based on the length of the two semi-axes (b, c)
- Oblate Spheroid- Mass or Weight computes the mass or weight of an Oblate Spheroid based on the length of the two semi-axes (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.
- Common Mean Density provides a lookup capability to find the mean density of hundreds of materials (woods, metals, liquids, chemicals, food items, soils, and more)
Mean Density Units
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/m3
- Liquid Natural Gas - 430 to 470 kg/m3
Market-Ready Grains
- Corn - 56 lb/bu (721 kg/m3)
- Wheat - 60 lb/bu (772 kg/m3)
- Barley - 48 lb/bu (618 kg/m3)
- Oats - 32 lb/bu (412 kg/m3)
- Rye - 56 lb/bu (721 kg/m3)
- Soybean - 60 lb/bu (772 kg/m3)
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Metals
- Density of Aluminum - 2,700 kg/m3
- Density of Brass - 8,530 kg/m3
- Density of Bronze - 8,150 kg/m3
- Density of Chromium - 7190 kg/m3
- Density of Cobalt - 8746 kg/m3
- Density of Copper - 8,920 kg/m3
- Density of Gallium - 5907 kg/m3
- Density of Gold - 19,300 kg/m3
- Density of Iron - 7,847 kg/m3
- Density of Lead - 11,340 kg/m3
- Density of Nickle - 8,908 kg/m3
- Density of Palladium - 12,023 kg/m3
- Density of Platinum - 21,450 kg/m3
- Density of Steel - 7,850 kg/m3
- Density of Silver - 10,490 kg/m3
- Density of Titanium - 4,500 kg/m3
- Density of Tungsten - 19,600 kg/m3
- Density of Uranium - 19,050 kg/m3
- Density of Zinc - 7,135 kg/m3
- Density of Zirconium - 6,570 kg/m³
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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)
vCalc provides for automatic conversions between density units via the pull-down menus.