`M = 4/3 * pi * ( "r" ^3 - ( "r" - "t" )^3)* "mD" `

Enter a value for all fields

The Mass or Weight of a Spherical Shell calculator computes the volume of a spherical shell with an outer radius (r) and a thickness (t).    Spherical Shell INSTRUCTIONS: Choose your units (e.g. centimeters, inches or kilometers) and enter the following parameters:

• (r) Outer Radius of Sphere
• (t) Thickness of Sphere Shell
• (mD) Mean Density of Material in Shell

Mass of the Spherical Shell (M): The mass is returned in kilograms.  However the user can automatically convert the mass to other mass and weight units (e.g. grams, ounces, pound and tons) via the pull-down menu.  To compute the Volume of a Spherical Shell, CLICK HERE.

Uses

The mass of a spherical shell can compute the amount of materials needed to coat any spherical object from a candy gumball to a submarine bathysphere.  
To look-up the Mean Density of over 500 substances,CLICK HERE.

The Math

The equation calculate the Volume of a Sphere is V = 4/3•π•r³. This formula computes the difference between two spheres to represent a spherical shell, and can be algebraically reduced as as follows:

 V = 4/3 π (r³ - (r-t)³)

where:

• r is the outer radius and
• t is the thickness

Once the volume of the shell is known, this calculator then uses that volume with the mean density as follows:

• mass = mD • volume

The mean density (mD, μD or ρ) of many common substances, elements, liquids and materials can be found by clicking HERE (e.g. the μD_(water) is 1000.0 kg/m³).

Common Mean Densities

Metals Aluminum - 2700.0 kg/m³ Brass - 8530.0 kg/m³ Bronze - 8150.0 kg/m³ Chromium - 7190 kg/m3 Cobalt - 8746 kg/m3 Copper - 8920.0 kg/m³ Gallium - 5907 kg/m3  Gold - 19300.0 kg/m³ Iron - 7847.0 kg/m³  Lead - 11340.0 kg/m³ Nickle - 8908  kg/m3  Palladium -  12160.0 kg/m³ Platinum - 21450.0 kg/m³ Steel - 7850.0 kg/m³ Silver - 10490.0 kg/m³ Titanium - 4500.0 kg/m³ Tungsten - 19600.0 kg/m³ Zinc - 7135.0 kg/m³ Zirconium - 6570.0 kg/m³

Fluids Pure Water - 1,000 kg/m³  Seawater - 1,022 kg/m³  Milk - 1,037 kg/m³  Olive Oil - 860 kg/m³ Diesel Fuel - 885 kg/m³  Crude Oil - 870 kg/m³  to 920 kg/m³  Fuel Oil -  890 kg/m³  Ethanol - 789 kg/m³  Gasoline (petrol) - 737 kg/m³  Cement Slurry - 1,442 kg/m³

Sphere Calculators:

• Sphere Surface Area from Radius
• 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