Pyramid Volume Calculator
Determine the volume of any pyramid with a regular polygonal base — from a triangular pyramid (tetrahedron) to an octagonal pyramid. Choose whether to enter the side length of the base polygon or provide the base area directly. Results appear instantly in both metric (mm³, cm³, m³, L) and US/Imperial units (in³, ft³, yd³, US gal, fl oz).
Pyramid Volume Formula
A pyramid is a polyhedron formed by connecting a polygonal base and a single apex point. The volume formula is the same for every type of pyramid — regular or oblique:
V = (1/3) × A × h
where A is the base area and h is the perpendicular height from the base to the apex.
For a regular n-sided polygon with side length s, the base area is:
A = (n × s²) / (4 × tan(π/n))
Combining these gives a single formula for the volume of a regular pyramid:
V = (n × h × s²) / (12 × tan(π/n))
How to Calculate Pyramid Volume — Square Pyramid Example (Cheops)
- Select the base shape. The Great Pyramid of Giza (Khufu / Cheops) has a square base — choose Square.
- Select the unit system. Choose Metric and set the unit to m.
- Enter the side length. The average edge of the Cheops pyramid is 230.3 m.
- Enter the height. The original height was 146.6 m; today it stands at 138.5 m.
- Click Calculate. The original volume is ≈ 2,591,795 m³; the current volume is ≈ 2,448,592 m³.
Pyramid Types and Names
| Faces | Edges | Vertices | Base Shape | Pyramid Name |
|---|---|---|---|---|
| 4 | 6 | 4 | Triangle | Tetrahedron / Triangular Pyramid |
| 5 | 8 | 5 | Square | Square Pyramid |
| 6 | 10 | 6 | Pentagon | Pentagonal Pyramid |
| 7 | 12 | 7 | Hexagon | Hexagonal Pyramid |
| 8 | 14 | 8 | Heptagon | Heptagonal Pyramid |
| 9 | 16 | 9 | Octagon | Octagonal Pyramid |
Tetrahedron Volume Calculation
A triangular pyramid (tetrahedron) has a triangular base. For a regular tetrahedron — where all four faces are equilateral triangles — a special simplified formula applies:
V = a³ / (6√2)
where a is the edge length. The height of a regular tetrahedron is:
h = a × √(2/3) ≈ 0.8165 × a
Example — tea pyramid bag (regular tetrahedron, edge = 1.5 in, h ≈ 1.2 in):
- Select Triangle as the base shape.
- Switch to US / Imperial units and select in.
- Enter the side length: 1.5 in.
- Enter the height: 1.2 in (≈ 1.5 × 0.8165).
- Click Calculate → Volume ≈ 0.39 in³.
Measurement Systems
The calculator fully supports both metric and US customary (imperial) systems:
- Metric: millimeters (mm), centimeters (cm), meters (m)
- US / Imperial: inches (in), feet (ft), yards (yd)
The results panel always shows conversions in both systems simultaneously — cubic centimeters, liters, cubic feet, US gallons, and fluid ounces — so you never need a separate unit converter.
Frequently Asked Questions
How do I find the volume of a pyramid?
- Calculate (or measure) the base area.
- Multiply the base area by the pyramid's perpendicular height.
- Divide the result by 3.
This works for all pyramid types — right, oblique, regular, or irregular — as long as the base area and height are known.
How do I find the volume of a hexagonal pyramid?
For a regular hexagonal pyramid with side length a and height h:
V = (√3 / 2) × a² × h
Alternatively, use the calculator: select Hexagon, enter a and h, and click Calculate.
What is the volume of the Great Pyramid of Giza?
The original Great Pyramid of Giza (Khufu) had a volume of approximately 2.59 million m³ (≈ 91.5 million ft³). Today, after millennia of erosion, its volume is roughly 2.45 million m³ (≈ 86.5 million ft³). These figures assume a right square pyramid with a 230.3 m base edge and heights of 146.6 m (original) / 138.5 m (current).
What is the difference between a prism and a pyramid?
A prism has two parallel, congruent polygon bases connected by rectangular faces; its volume is simply base area × height. A pyramid has one polygonal base tapering to a single apex, so its volume is one-third that of the corresponding prism with the same base and height.