`m = [4/3 * pi * "r" ^3] * 7850.0 `

Enter a value for all fields

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). NEW: Default units have been updated to millimeters.  ALSO NEW: Default density has been updated to 7,850 kg/m3 for density of steel.

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 grams (g).  However, this can be automatically converted to other mass or weight units (e.g., kilograms, 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.

         Mass = Volume ⋅ Density

See the mean density (ρ) of many common substances

Above the formula for mass and volume of a sphere are combined.

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Mean Density Table

Common Mean Densities in Kilograms per Meter Cubed (kg/m3)
Fluids Pure Water - 1,000   Seawater - 1,022   Milk - 1,037  Olive Oil - 860 Cement Slurry - 1,442  Fuels Diesel Fuel - 885  Crude Oil - 870 to 920   Fuel Oil -  890   Ethanol - 789   Gasoline (petrol) - 737  Propane - 493  Liquid Natural Gas - 430 to 470  Market-Ready Grains Corn - 721 (56 lb/bu) Wheat - 772 (60 lb/bu) Barley - 618 (48 lb/bu) Oats - 412 (32 lb/bu) Rye - 721 (56 lb/bu) Soybean - 772 (60 lb/bu)	Metals Density of Aluminum - 2,700 Density of Brass - 8,530  Density of Bronze - 8,150  Density of Chromium - 7,190  Density of Cobalt - 8,746  Density of Copper - 8,940   Density of Gallium - 5907  Density of Gold - 19,300 Density of Iron - 7,847 Density of Lead - 11,340 Density of Nickle - 8,908  Density of Palladium -  12,023 Density of Platinum - 21,450  Density of Steel - 7,850  Density of Silver - 10,490  Density of Tin - 7,280 Density of Titanium - 4,500  Density of Tungsten - 19,600  Density of Uranium - 19,050 Density of Zinc - 7,135  Density of Zirconium - 6,570	Earthen Concrete - 2,371 Dirt - 1,250 Fire Clay - 1,362 Glass - 2,500 Granite - 2,691 Sand (dry) - 1,602 Sand (wet) - 2,082 Sandstone - 2,323 Synthetic Bakelite - 1,362 Carbon Fiber - 2,000 Organic Balsa - 170 Cork - 240 Mahogany - 545 Oak - 760 Pine - 539 Rubber - 1,522
Mean Density Lookup Function

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)

If you want to identify a material by its density, use the Density Within Range tool.

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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

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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.
• Ellipsoid Cap - Volume computes the volume of a section of an ellipsoid.
• 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.
• Circular - Volume: Computes the volume of a column with a circular top and bottom and vertical sides.
• Circular - Mass: Computes the mass/weight of circular volume based on its dimensions and mean density.
• Elliptical Volume: Computes the volume of a column with an elliptical top and bottom and vertical sides. 
• Elliptical - Mass: Computes the mass/weight of an elliptical volume based on its dimensions and mean density.
• Ellipse Vertical Chord from Edge (VE): Computes the length of the vertical chord of an ellipse based on distance from the edge.
• Ellipse Vertical Chord from Center (VC): Computes the length of the vertical chord of an ellipse based on distance from the center.
• Ellipse Horizontal Chord from Edge (HE): Computes the length of the horizontal chord of an ellipse based on distance from the edge.
• Ellipse Horizontal Chord from Center (HC): Computes the length of the vertical chord of an ellipse based on distance from the center.
• Common Mean Density: Provides a lookup function to find the mean density of hundreds of materials (woods, metals, liquids, chemicals, food items, soils, and more)

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.