`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

Bottle Calculators

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

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 - 3 sided column
• Volume of a Quadrilateral - 4 sided column
• Volume of a Pentagon - 5 sided regular column
• Volume of a Hexagon - 6 sided regular column
• Volume of a Heptagon - 7 sided regular column
• Volume of a Octagon - 8 sided regular column
• Volume of a Nonagon - 9 sided regular column
• Volume of a Decagon - 10 sided regular column
• Volume of a Hendecagon  - 11 sided regular column
• Volume of a Dodecagon  - 12 sided regular column
• Volume of a Paraboloid
• Volume of a Polygon based Pyramid
• Volume of a Pyramid Frustum
• Volume of a Sphere
• Volume of a Oblate Spheroid
• Volume of a Ellipsoid
• Volume of a Torus
• Volume of a Bottle
• Volume of a Chamfer