The Mass or Weight of a Sphere calculator computes the mass or weight of a sphere 
based on the radius (r) and the mean density (ρ).
INSTRUCTIONS: Choose units and enter the following:
- (r) Radius of Sphere
- (ρ) Density of Sphere
Mass of Sphere (m) : The calculator returns the mass of the sphere in kilograms (kg). However, this can be automatically converted to other mass or weight units (e.g., pounds, tons) via the pull-down menu next to the answer. NOTE: To find the mean density (ρ) of many common substances, elements, liquids and materials, CLICK HERE (e.g., the density of water is 1,000 kg/m³).
The Math / Science
The formula for the mass of a sphere:
M = 4/3⋅π⋅r³⋅mD
where:
- M is the mass of the sphere
- r is the radius of the sphere
- mD is the mean density of the material
The mass of a sphere calculator first computes the volume of the sphere based on the radius. With the computed volume, this formula then executes the simple equation below to compute the approximate mass of the object.
See the mean density (ρ) of many common substances
Above the formula for mass and volume of a sphere are combined.
| Common Mean Densities | |
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Fluids
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.
Sphere Calculators:
- Sphere Surface Area based radius (r)
- Sphere Surface Area from Volume
- Sphere Volume from Radius
- Sphere Volume from Circumference
- Sphere Volume from Surface Area
- Sphere Volume from Mass and Density
- Sphere Radius from Volume
- Sphere Radius from Surface Area
- Sphere Weight (Mass) from volume and density
- Sphere Density
- Area of Triangle on a Sphere
- Distance between Two Points on a Sphere
- Sphere Cap Surface Area
- Sphere Cap Volume
- Sphere Cap Weight (Mass)
- Sphere Segment Volume
- Sphere Segment Weight (Mass)
- Sphere Segment Wall Surface Area (without the circular top and bottom ends)
- Sphere Segment Full Surface Area (with the top and bottom circles, aka ends)
- Volume of Spherical Shell
- Mass of Spherical Shell
A word on Mass and Weight
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 unit conversion engine can be assumed to be fairly accurate unless you require weight at very high altitudes or in space.