Mass of Shapes and Containers
The Mass of Shapes and Containers calculator contains the mass / weight equations for a variety of geometric shapes and provides the mean density for a large number of substances. 
spheres
Description
The Mass of Shapes and Containers equations in this calculator let the user:
- Choose a geometeric shape or container type,
- enter the dimensions of the object, and
- enter a mean density to calculate the object's approximate mass. Assuming nominal Earth gravity, the mass can be converted to nominal Earth surface weight (e.g. pounds from kilograms).
vCalc provides a lookup function that contains the mean density in kilograms per cubic meter of hundreds of substances from farm commodities (e.g. grains, woods, etc) to quary items (types of stone and sand) to commonly transported liquids (e.g. water, diesel).
The basic formula for all of the equations is this:
mass=μDensity⋅volume
Geometric Shapes or Containers
The mass equations in this calculator are based on three dimensional (3D) shapes and equations to calculate their volume. The geometric shapes included in this calculator are:
- Cube, Box, Cone, Cone (frustum), Cylinder, Slanted Cylinder,
- Ellipsoid, Capsule, Bottle, Paraboloid, Pyramid, Pyramid Frustum,
- Sphere, Sphere Cap, Sphere Segment, Prism, Torus, Chamfer
various frustums
Mean Density
| Material | Mean Density (mD) |
|---|---|
| Water | 1,000 kg/m³ |
| Ice | 916.7 kg/m³ |
| Aluminum | 2,700.0 kg/m³ |
| Brass | 8,530.0 kg/m³ |
| Chromium | 8,150.0 kg/m³ |
| Cobalt | 7,190 kg/m3 |
| Copper | 8,746 kg/m3 |
| Gallium | 8,920.0 kg/m³ |
| Gold | 19,300.0 kg/m³ |
| Iron | 7,847.0 kg/m³ |
| Lead | 11,340.0 kg/m³ |
| Nickle | 8,908 kg/m3 |
| Palladium | 12,160.0 kg/m³ |
| Platinum | 21,450.0 kg/m³ |
| Steel | 7,850.0 kg/m³ |
| Silver | 10,490.0 kg/m³ |
| Titanium | 4,500.0 kg/m³ |
| Tungsten | 19,600.0 kg/m³ |
| Zinc | 7,135.0 kg/m³ |
| Zirconium | 6,570.0 kg/m³ |
This calculator also includes a function that provides the mean densities for some common substances. Use these functions to provide the mean density of a substance. The user can copy the answer and enter it into the volume calculations to determine the approximate mass or weight. Common substances have buttons with their weight including the following:
- air - benzene - water
- dirt - ethanol - ice
- concrete - glycerine - blood
- lead - aluminum - mercury
- brass - copper - steel
- gold - silver - iron
vCalc also provides a look-up function for many more mean densities. Using the meadDensity Lookup, the user can choose any of the following substances and vCalc will return the mean density:
Acetic Acid ,Acetone,Acetonitrile,Actinium,Afromosia,air,Alcohol - ethyl,Alcohol - methyl,Alcohol - propyl,Alfalfa - ground,Alum - lumpy,Alum - pulverized,Alumina,Aluminum - 1100, 
various shapes
See Also
- Moments of Inertia - calculator for the MoI of different shapes around different axes.
- Geometry (3D) - calculator for euclidean objects
- Volume - Volume calculator for various geometric shapes.
- Trucking calculator - Load calculator
