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.
- 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.
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.
where:
- rho is the mean density
| Common Mean Densities | |
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Fluids
Fuels
Market-Ready Grains |
Metals
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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/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.