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`V = 1/4 * sqrt( 5*(5 + 2* sqrt(5)))* s^2 * h`

Enter a value for all fields

This **Volume of a Pentagon** calculator computes the volume of a regular pentagon shaped objects with 5 equal sides of length (**s**) and a height (**h**).

**INSTRUCTIONS:** Choose units and enter the following:

- (
**s**) Length of Pentagon Sides - (
**h**) Height of Pentagon Shape

**Volume of a Pentagon (V):** The volume is returned in cubic meters. However, this can be automatically converted to other volume units (e.g. gallons, cubic feet) via the pull-down menu.

The calculator first computes the Area of a Pentagon shaped surface, CLICK HERE, and then multiplies that area by the height to determine the volume of the pentagon shape.

The formula for the volume of a pentagon is:

V =¼•√(5+2•√5)•s^{2}•h

where:

- V = Volume of Pentagon
- s = Side Length
- h = Height

A regular pentagon has five equal sides and equal angles. * The U.S. Pentagon * A pentagon volume is a pentagon shaped object with a regular pentagon cross-section (area) and perpendicular height.

One famous pentagon shaped object is the U.S. Pentagon, home of the U.S. military. The Pentagon has side lengths (**s**) of 921 feet, and a height (**h**) of 77 feet. Use the calculator and compute the volume.

- Polygon Area from Number of Sides and Length of Sides
- Polygon Area from Number of Sides and Outer Radius
- Area of Polygon Segment from Number of Sides and Inner Radius
- Area of Polygon from Number of Sides and Inner Radius
- Length of the Sides of a Polygon based on the Outer Radius and Number of Sides
- Length of a Side of a Polygon from Inner Radius and Number of Sides
- Perimeter of a Polygon from Number of Sides and Length of Sides
- Polygon Perimeter from Outer Radius and Number of Sides
- Polygon Perimeter from Inner Radius and Number of Sides
- Polygon Perimeter from the Area and Number of Sides

**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. Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel.

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. One basic formula for volume is area times a Height when the volume has vertical sides.

- Volume from Area and Height
- 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 Semicircle
- 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