Sphere Cap Weight

The Mass or Weight of a Sphere Cap calculator computes the mass of a section of a sphere that includes the surface (i.e. a sphere cap - see diagram).  

INSTRUCTIONS: Choose units and enter the following:

• (r) Radius of Sphere
• (h) Height of the Sphere Cap
• (mD) Mean Density of Material (Default is 7,850 kg/m³ for steel)

Mass or Weight of Sphere Cap(M): The calculator returns the mass in grams.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Sphere Cap Weight (Mass) formula provides the weight of the cap of a sphere defined by a depth (h) from the surface in a sphere defined by a radius (r) with a mean density (mD) .

This formula computes the volume of the geometric shape based on the input parameters.  With the computed volume, this formula then executes the simple equation below to compute the approximate mass of the object.

mass = density * volume

The formula for the volume of a sphere cap is:

V = π•h²(3•r-h)/3

where:

• V is the volume of the sphere cap
• r is the radius of the sphere
• h is the height of the cap

Mean Density Table

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.

Weight is technically the downward force that a mass exerts based on the force of gravity and the mass of the object.  On the surface of the Earth, mass and weight are often interchanged.  In some places, objects are sold by the gram (mass), and in other locations, the same objects are sold by the ounce (weight).

The Weight Calculators use the dimensions of an object and its shape to compute the objects volume.  They then apply a density associated with a material to estimate the objects weight.

Weight Calculators

• Weight from Area, Height and Density
• Cube Weight 
• Box Weight
• Cone Weight
• Cone Frustum Weight
• Cylinder Weight
• Slanted Cylinder Weight
• Semicircle Weight
• Triangular Weight
• Quadrilateral Weight 
• Pentagon Weight 
• Hexagon Weight 
• Heptagon Weight
• Octagon Weight
• Nonagon Weight
• Decagon Weight
• Hendecagon Weight
• Dodecagon Weight
• Paraboloid Weight
• Polygon Pyramid Frustum Weight
• Sphere Mass
• Sphere Cap Weight
• Sphere Segment Weight
• Sphere Shell Mass
• Oblate Spheroid Mass
• Ellipsoid Weight
• Torus Weight
• Bottle Weight
• Bottle Content Weight
• Chamfer Weight
• Ring Weight

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