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Weight and Volume Calc

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Calculator / Last modified by KurtHeckman on 2017/04/25 13:06
Cube - Weight by KurtHeckman, last modified
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`m = ` ` "s" ^3 * "mD" `
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Paraboloid - Weight by KurtHeckman, last modified
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`m = ` `1/2 * pi * "b" ^2 * "a" * "mD" `
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Box - Weight by KurtHeckman, last modified
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`"Box"_"volume" = ` ` "l" * "h" * "d" * "mD" `
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Pyramid - Weight by KurtHeckman, last modified
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`"Pyramid"_"(weight)" = ` `[1/3 * "A" * "h" ] * "mD" `
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Cone - Weight by KurtHeckman, last modified
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`W = ` `[1/3 * pi * "r" ^2 * "h" ] * "mD" `
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Pyramid Frustum - Weight by KurtHeckman, last modified
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`Mass (M) = ` `[1/3 * "h" *( "R" ^2+ "R" * "r" + "r" ^2)] * "mD" `
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Cone - Frustum Weight by KurtHeckman, last modified
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`M = ` `[1/3 * pi * "h" ( "a" ^2+ "a" * "b" + "b" ^2)]* "mD" `
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Sphere - Weight by KurtHeckman, last modified
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`"Sphere"_"(weight)" = ` `[4/3 * pi * "r" ^3] * "mD" `
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Cylinder - Weight by KurtHeckman, last modified
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`"Weight"_"cylinder" = ` `[pi * "r" ^2 * "h" ] * "mD" `
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Sphere - Cap Weight by KurtHeckman, last modified
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`[1/3 pi * "h" ^2 (3* "r" - "h" )] * "mD" `
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Cylinder Slanted - Weight by KurtHeckman, last modified
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`[pi * "r" ^2* "l" *sin( theta )] * "mD" `
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sphere - segment weight by KurtHeckman, last modified
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`m = ` ` "mD" * pi* "h" /6 * ( 3* "r1" ^2 +3* "r2" ^2 + "h" ^2)`
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Ellipsoid - Weight by KurtHeckman, last modified
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`m = ` `[4/3 * pi * "a" * "b" * "c" ]* "mD" `
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Triangular - Weight by KurtHeckman, last modified
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`"Triangular"_"(weight)" = ` ` "height" * sqrt(( "a" + "b" + "c" )/2(( "a" + "b" + "c" )/2- "a" )(( "a" + "b" + "c" )/2- "b" )(( "a" + "b" + "c" )/2- "c" )) * "mD" `
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Capsule - weight by KurtHeckman, last modified
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`M = ` ` "mD" * pi* "r" ^2 *( l - 2/3* "r" )`
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Torus - Weight by KurtHeckman, last modified
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`"Torus"_"(weight)" = ` `[1/4 pi^2 ( r + R )( R - r )^2]* "mD" `
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Bottle - mass by KurtHeckman, last modified
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`Volume = ` ` "mD" * [1/3 * pi * "h2" ( "a" ^2+ "a" * "b" + "b" ^2) + pi * "b" ^2 * "h1" ]`
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Cone - cored frustum weight by KurtHeckman, last modified
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`Mass = ` `(1/3 * pi * "h" ( "a" ^2+ "a" * "b" + "b" ^2) - "h" * pi * "b" ^2) * "mD" `
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Weight of Volume by KurtHeckman, last modified
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`"Weight"_"volume" = ` ` "V" * "mD" `
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meanDensity Lookup by KurtHeckman, last modified
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`muD = ` `f( "Name" )`
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Box - Volume by KurtHeckman, last modified
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`V = ` ` "l" * "h" * "d" `
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Cube - Volume by KurtHeckman, last modified
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`V = ` ` "s" ^3`
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Triangular - Volume by KurtHeckman, last modified
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`"Trianglar"_"(volume)" = ` ` "height" * sqrt(( "a" + "b" + "c" )/2(( "a" + "b" + "c" )/2- "a" )(( "a" + "b" + "c" )/2- "b" )(( "a" + "b" + "c" )/2- "c" )) `
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Bottle - volume by KurtHeckman, last modified
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`Volume = ` `1/3 * pi * "h2" ( "a" ^2+ "a" * "b" + "b" ^2) + pi * "b" ^2 * "h1" `
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Conic cylinder - volume by KurtHeckman, last modified
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`Volume = ` `V( d_1 , l_1 , d_2 , l_2 , d_3 , l_3 )`
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Pyramid - Volume by KurtHeckman, last modified
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`"Pyramid"_"(volume)" = ` `1/3 * "A" * "h" `
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Capsule - volume by KurtHeckman, last modified
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`V = ` `pi* "r" ^2 *( "l" - 2/3* "r" )`
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Cylinder - Volume by KurtHeckman, last modified
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`V = ` `pi * "r" ^2 * "h" `
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Pyramid Frustum - Volume by KurtHeckman, last modified
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`Volume = ` `1/3 * "h" *( "R" ^2+ "R" * "r" + "r" ^2)`
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Cone - Volume by KurtHeckman, last modified
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`V = ` `1/3 * pi * "r" ^2 * "h" `
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Cylinder Slanted - Volume by KurtHeckman, last modified
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`Vol = ` `pi * "r" ^2* "l" *sin( theta )`
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Sphere - Volume by KurtHeckman, last modified
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`V = ` `4/3 * pi * "r" ^3 `
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Cone - Frustum Volume by KurtHeckman, last modified
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`V = ` `1/3 * pi * "h" ( "a" ^2+ "a" * "b" + "b" ^2)`
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Ellipsoid - Volume by KurtHeckman, last modified
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`V = ` `4/3 * pi * "a" * "b" * "c" `
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Sphere - Cap Volume by KurtHeckman, last modified
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`V = ` `1/3 pi * "h" ^2 (3* "r" - "h" )`
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Hexagon Volume by KurtHeckman, last modified
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`Hexagon_"volume" = ` `3/2 * sqrt(3) * "s" ^2 * "h" `
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Paraboloid - Volume by KurtHeckman, last modified
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`V = ` `1/2 * pi * "b" ^2 * "a" `
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sphere - segment volume by KurtHeckman, last modified
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`V = ` `pi* "h" /6 * ( 3* r_1 ^2 +3* r_2 ^2 + "h" ^2)`
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pipe volume by KurtHeckman, last modified
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`"Pipe"_(volume) = ` `pi * ( d /2)^2 * l `
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Octagon Volume by KurtHeckman, last modified
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`V_"oct" = ` `2 (1 + sqrt(2)) * "s" ^2 * "h" `
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Sphere Tank Volume by KurtHeckman, last modified
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`Volume = ` `f( R , D )`
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V = A * d by KurtHeckman, last modified
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`V = ` ` "A" * "d" `
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Torus - Volume by KurtHeckman, last modified
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`V = ` `1/4 pi^2 ( "a" + "b" )( "b" - "a" )^2`
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Weight of Shapes Formula
Cube Paraboloid
Box Pyramid
Cone Pyramid - Frustum
Cone - Frustum Sphere
Cylinder Sphere - Cap
Cylinder Slanted Sphere - Segment
Ellipsoid Prism
Capsule Torus
Bottle Chamfer
Weight of Volume meanDensities
Box Cube Prism (Triangular)
Bottle Conic cylinder Pyramid
Capsule Cylinder Pyramid Frustum
Cone Cylinder Slanted Sphere
Cone - Frustum Ellipsoid Sphere - Cap
Hexagon Column Paraboloid Sphere - Segment
Pipe Octagon Column Spherical Tank
V = A * d Torus
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The Weight and Volume Calculator ShapeColumn1.pngShapeColumn2.png contains volume and mass / weight equations for a variety of geometric shapes and provides the mean density for a large number of substances.   

Description

The Weight and Volume Calculator Volume and Weight/Mass equations in this calculator let the user:

  1. Choose a geometric shape or container type,
  2. enter the dimensions of the object to determine the Volume, and
  3. enter a mean density to calculate the object's approximate mass.  Assuming nominal Earth gravity, the mass can be converted to nominal Earth surface weight (e.g. pounds from kilograms).  

vCalc provides a lookup function that contains the mean density in kilograms per cubic meter of hundreds of substances from farm commodities (e.g. grains, woods, etc) to quary items (types of stone and sand) to commonly transported liquids (e.g. water, diesel). 

The basic formula for all of the equations is this: Shapes - Ellipsoid etc.pngvarious frustums

                           ` "mass" = mu"Density" * "volume"`

Geometric Shapes or Containers

The mass equations in this calculator are based on three dimensional (3D) shapes and equations to calculate their volume.  The geometric shapes included in this calculator are:

  • Cube, Box, Cone, Cone (frustum), Cylinder, Slanted Cylinder,
  • Ellipsoid, Capsule, Bottle, Paraboloid, Pyramid, Pyramid Frustum, 
  • Sphere, Sphere Cap, Sphere Segment, Prism, Torus, Chamfer  

Mean Density

At the bottom of the Weight tab, Spheres.pngspheresvCalc provides a look-up function for many mean densities which can be used with the container shape to determine the weight of the contents of the container (e.g. water, grain, oil).  Using the meadDensity Lookup, the user can choose any of hundreds of substances and vCalc will return the mean density:

  • Basic Elements
  • Farm commodities 
  • Metals and Alloys
  • Minerals, Rocks, Sands and Soils
  • Oils and various industrial liquids
  • Types of Wood
This calculator, Weight and Volume Calc, references 43 equations/constants.

Equations and Constants