`V = 1/3 * pi * "h2" ( "a" ^2+ "a" * "b" + "b" ^2) + pi * "b" ^2 * "h1" `

Enter a value for all fields

The Volume of a Bottle calculator computes the volume of a bottle shaped object (see diagram).  

INSTRUCTIONS: Choose units and enter the following: 

• (a) Neck Radius
• (h₂) Neck Height (tapered neck section)
• (b) Base Radius
• (h₁) Base Height

Bottle Volume (V): The volume is returned in liters (L).  However, this volume can be automatically converted to compatible via the pull-down menu.

The Math / Science

Geometrically, a bottle shaped object is the combination of right circular cone with a frustum defined by base radius (a) and top radius (b) and height (h₂) in between and a cylinder of radius (b) and height (h₁).  See diagram. 

The formula for the volume of a bottle is:

   `V = (pi/3)*h2*(a^2+a*b+b^2) +  pi * b^2 * h1`

where:

• V = volume of the bottle
• h1 = height of cone
• h2 = height of cylinder
• b = radius of base and bottom of cone
• a = radius of top of cone

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Bottle Calculators

• Surface Area of a Bottle
• Mass of the Contents of a Bottle
• Volume of a Bottle

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Volume is a three dimensional measurement of the amount of space taken up by an object.  Volume units are cubic measurements for solid objects such as cubic inches and cubic meters.  Fluid objects have separate units such as fluid ounces, gallons, barrel and liters. 

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape.  Many such calculations are available in the following list of calculators. 

In many cases, the calculators are for a column with a geometric shaped base and vertical sides.  The most basic form is an Area times a Height.

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Volume Calculators

• Volume of a Cube 
• Volume of a Box
• Volume of a Cone
• Volume of a Cone Frustum
• Volume of a Cylinder
• Volume of a Slanted Cylinder
• Volume of a Triangular 
• Volume of a Quadrilateral 
• Volume of a Pentagon 
• Volume of a Hexagon 
• Volume of a Heptagon
• Volume of a Octagon
• Volume of a Nonagon
• Volume of a Decagon
• Volume of a Hendecagon
• Volume of a Dodecagon
• Volume of a Paraboloid
• Volume of a Polygon based Pyramid
• Volume of a Pyramid Frustum
• Volume of a Sphere
• Volume of a Sphere Cap
• Volume of a Sphere Segment
• Volume of a Sphere Shell
• Volume of a Oblate Spheroid
• Volume of a Ellipsoid
• Volume of a Torus
• Volume of a Bottle
• Volume of a Chamfer