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

Enter a value for all fields

The Volume of the Frustum of a Cone calculator computes the volume of a frustum (slice) of a cone based on the top radius (a), bottom radius (b) and height (h) in between. 

INSTRUCTION: Choose units and enter the following:

• (a) - radius of top surface
• (b) - radius of bottom surface
• (h) - height in between top and bottom

Volume of the Cone Section (V):  The calculator computes the volume (V) in cubic meters (m³).  However this can be automatically converted to many other volume units (e.g. gallons or cubic feet) via the pull-down menu.  

The Math

The frustum of a cone is a section of a cone also known as a truncated cone. The frustum of a cone is created by parallel planes that go through the cone and are normal (perpendicular) to the center axis of the cone.  The shape of the top and bottom are perfect circles whose centers are directly aligned.  The planes are separated by the height (h). The formula for the Volume of the Frustum of a cone is as follows:

         V = ¹/₃ • π • h(a²+a•b+b²)    

where: 

• V is the volume of the frustum (section) of a cone
• a is the radius of one end
• b is the radius of the other end
• h is the height

Cone Calculators: 

1. Surface Area:  cone surface area based on cone height and cone base radius
2. Volume: cone volume based on cone height and cone base radius
3. Mass: cone mass or weight as a function of the volume and mean density
4. Frustum Surface Area: cone frustum surface area based on the two heights and two radii
5. Frustum Volume: cone frustum volume based on the two heights and two radii 
6. Frustum Mass: cone frustum weight or mass based on the cone frustum volume and mean density
7. Shell Volume: cone shell volume a.k.a. hollow cone volume
8. Shell Mass: cone shell mass or weight a.k.a. hollow cone mass.
9. Compute the total surface are of the frustum of a cone:  This includes the top and bottom surfaces.
10. Compute the lateral surface area (using L) of the frustum of a cone.

See Also

• Frustum Calculator - Equations for volume, mass and surface areas for various frustums.
• Planter Calculator - Equations for home and garden planters.
• Volume Calculator - Volume equations for various geometric shapes
• Mass Weight Calculator - Equations for the mass and weight of objects based on their mean density and shape

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

Reference

• Equation 4.42 Spiegel, Murray R. "Chapter 4." Mathematical Handbook of Formulas and Tables. New York: McGraw-Hill, 1968. N. pag. Print.