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) the 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.
Note: the mean density (mD, μD, ρ) of many common substances, elements, liquids and materials can be found by CLICKING HERE.
| Common Mean Densities |
| Metals
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| Fluids
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Ellipsoid Calculator
- 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
Density of Metals
- Density of Aluminum - 2700.0 kg/m³
- Density of Brass - 8530.0 kg/m³
- Density of Bronze - 8150.0 kg/m³
- Density of Chromium - 7190 kg/m3
- Density of Cobalt - 8746 kg/m3
- Density of Copper - 8920.0 kg/m³
- Density of Gallium - 5907 kg/m3
- Density of Gold - 19300.0 kg/m³
- Density of Iron - 7847.0 kg/m³
- Density of Lead - 11340.0 kg/m³
- Density of Nickle - 8908 kg/m3
- Density of Palladium - 12160.0 kg/m³
- Density of Platinum - 21450.0 kg/m³
- Density of Steel - 7850.0 kg/m³
- Density of Silver - 10490.0 kg/m³
- Density of Titanium - 4500.0 kg/m³
- Density of Tungsten - 19600.0 kg/m³
- Density of Zinc - 7135.0 kg/m³
- Density of Zirconium - 6570.0 kg/m³