Pyramid Volume Calculator
Calculate the volume of square, rectangular, triangular, and hexagonal pyramids. Enter the base dimensions and height to get instant results with formulas and a step-by-step breakdown. Perfect for students, teachers, and professionals.
What Is a Pyramid?
A pyramid is a three-dimensional geometric shape with a polygonal base and triangular faces that meet at a single point called the apex. The base can be any polygon — square, rectangle, triangle, hexagon, or other shapes. The volume of a pyramid is calculated using the formula:
V = ⅓ × Base Area × Height
Where:
Base Area = Area of the polygonal base
Height = Perpendicular distance from the apex to the base
How Does the Pyramid Volume Calculator Work?
The calculator uses the following formulas for different pyramid types:
- Square Pyramid: Base Area = s², Volume = ⅓ × s² × h
- Rectangular Pyramid: Base Area = l × w, Volume = ⅓ × l × w × h
- Triangular Pyramid: Base Area = ½ × b × b_h, Volume = ⅓ × ½ × b × b_h × h
- Hexagonal Pyramid: Base Area = ½ × P × a (where P is perimeter and a is apothem)
The calculator also computes the slant height, lateral surface area, total surface area, and edge length for square and rectangular pyramids.
Why Use This Pyramid Volume Calculator?
- Four Base Shapes: Supports square, rectangular, triangular, and hexagonal pyramids.
- Complete Measurements: Calculates volume, base area, slant height, lateral and total surface area.
- Unit Flexibility: Switch between metric and imperial units.
- Visual Representation: A diagram shows the pyramid with labeled dimensions.
- Free & Private: No registration, no data storage.
❓ Pyramid Volume Calculator FAQ
What is a pyramid?
A pyramid is a 3D shape with a polygonal base and triangular faces that meet at a single point called the apex. The base can be square, rectangular, triangular, hexagonal, or other polygons.
What is the formula for the volume of a pyramid?
The volume of any pyramid is V = ⅓ × Base Area × Height. The base area depends on the shape of the base.
How do I calculate the volume of a square pyramid?
V = ⅓ × s² × h, where s is the side length of the square base and h is the height.
How do I calculate the volume of a rectangular pyramid?
V = ⅓ × l × w × h, where l is the length, w is the width, and h is the height.
How do I calculate the volume of a triangular pyramid?
V = ⅓ × ½ × b × b_h × h, where b is the base of the triangle, b_h is the triangle's height, and h is the pyramid height.
How do I calculate the volume of a hexagonal pyramid?
V = ⅓ × (½ × P × a) × h, where P is the perimeter of the hexagon, a is the apothem, and h is the height.
What is the slant height of a pyramid?
The slant height is the distance from the apex to the midpoint of a base edge along the triangular face. It is used to calculate the lateral surface area.
What is the difference between lateral surface area and total surface area?
Lateral surface area is the sum of the areas of the triangular faces only. Total surface area includes the base area as well: TSA = Base Area + Lateral Area.
What is the edge length of a pyramid?
The edge length is the distance from the apex to a corner of the base. It is the length of the triangular face edges.
Can I use this calculator for a hexagonal pyramid?
Yes. The calculator supports hexagonal pyramids. You need to enter the side length, apothem, and height.
How do I convert pyramid volume from cubic meters to liters?
1 cubic meter = 1000 liters. The calculator can automatically convert volume to liters or gallons if you select the output unit option.
What is the volume of a pyramid with base area 25 and height 10?
V = ⅓ × 25 × 10 = 83.33 cubic units.
How is a pyramid different from a prism?
A prism has two parallel congruent bases and rectangular faces. A pyramid has one base and triangular faces that meet at an apex.
What is the apothem of a hexagonal pyramid?
The apothem is the distance from the center of the hexagon to the midpoint of any side. It is used to calculate the area of the hexagonal base.
Can I use this calculator for a tetrahedron?
A tetrahedron is a triangular pyramid where all faces are equilateral triangles. This calculator supports triangular pyramids with any base triangle dimensions.
What is the Great Pyramid of Giza's volume?
The Great Pyramid of Giza has a square base with side length about 230.4 m and original height about 146.6 m, giving a volume of about 2.6 million cubic meters.