The Mass of a Bottle calculator computes the mass based on the dimensions of the bottle and the mean density of the material. 
INSTRUCTIONS: Choose the length units you wish (e.g. centimeters or inches) and enter the following:
- (a) neck radius at the top of the bottle
- (h2) height of the tapered neck section
- (b) base section's radius
- (h1) height of the bottle's base that is a constant diameter along it's length from the bottom base to the beginning of the taper.
- (mD) mean density of material.
Mass of the Bottle (M): The calculator returns the mass in grams. However, this can be automatically converted to compatible units via the pull-down menu.
Bottle Calculators
The Math / Science
The formula for the mass of a bottle shaped object is the volume of the bottle times the density of the material. Assuming normal gravity, this also provides the weight. Geometrically, a bottle shaped object is the combination of right circular cone with a frustum defined by base radius (a) and top radius (b) and height (h2) in between and a cylinder of radius (b) and height (h1). The volume is calculated and then multiplied by a mean density (mD) to provide the mass of the shape. See diagram. KEY WORDS: container
| 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.
CLICK HERE for a pop-up function that provides the mean density (mD or μD) of many common substances, elements, liquids and materials.
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.