Pyramid Calculator
Find the volume, surface area, slant height, and lateral edge of a regular pyramid with any number of sides
Volume
Measurements
Base Area
Lateral Surface Area
Total Surface Area
Face Area (per face)
Slant Height
Lateral Edge Length
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Pyramid Calculator Formula
Volume of a regular pyramid:
V = (1/3) × A_base × h
A_base = area of the regular polygon base, h = perpendicular height.
Base area of a regular n-gon:
A_base = (n × s²) / (4 × tan(π / n))
n = number of sides, s = base side length.
Slant height (apex to midpoint of a base edge):
l = sqrt(h² + (s / (2 × tan(π / n)))²)
The term s / (2 × tan(π / n)) is the base apothem.
Lateral edge (apex to a base vertex):
e = sqrt(h² + (s / (2 × sin(π / n)))²)
The term s / (2 × sin(π / n)) is the base circumradius.
Lateral surface area (all triangular faces):
A_lateral = (1/2) × n × s × l
n = number of sides, s = base side length, l = slant height.
How to Use This Calculator
- Enter the number of sides of the base (3 for a triangular pyramid, 4 for a square pyramid, and so on). Defaults to 4.
- Enter the base side length — every side of the regular polygon base has this same length.
- Enter the height of the pyramid (perpendicular distance from base to apex).
- Click Calculate to see the volume, base area, lateral surface area, slant height, and lateral edge length.
Frequently Asked Questions
How do you calculate the volume of a pyramid?
The volume of any pyramid is V = (1/3) × A_base × h, where A_base is the area of the base and h is the perpendicular height. For a regular polygon base, the base area is (n × s²) / (4 × tan(π / n)). The 1/3 factor means a pyramid holds exactly one-third of the prism that shares its base and height.
How is the surface area of a pyramid calculated?
This calculator reports the lateral surface area — the combined area of the triangular side faces — as A_lateral = (1/2) × n × s × l, where l is the slant height. To get the total surface area, add the base area shown in the results to the lateral surface area.
What is the difference between slant height and lateral edge length?
The slant height (l) runs from the apex down to the midpoint of a base edge, so it is the height of each triangular face. The lateral edge (e) runs from the apex to a base corner (vertex). The lateral edge is always the longer of the two because a base vertex is farther from the center than an edge midpoint.
Does this calculator work for triangular, pentagonal, and hexagonal pyramids?
Yes. Set the number of sides to 3 for a triangular pyramid, 5 for a pentagonal pyramid, 6 for a hexagonal pyramid, and so on. The base must be a regular polygon — every side the same length. For a circular base, use the cone volume calculator instead.
What units does this calculator use?
It is unit-agnostic. Enter all lengths in the same unit: lengths (slant height, lateral edge) come back in that unit, areas in the unit squared, and volume in the unit cubed. For example, meters in gives square meters for area and cubic meters for volume.
What is the volume of the Great Pyramid of Giza?
The Great Pyramid is a square pyramid (4 sides) with a base side of about 230.4 meters and a height of about 146.5 meters. Entering n = 4, s = 230.4, and h = 146.5 gives a volume of roughly 2.6 million cubic meters.
How do I find the height from the slant height?
Rearrange the slant-height formula: h = sqrt(l² − a²), where a is the base apothem s / (2 × tan(π / n)). For a square base this simplifies to h = sqrt(l² − (s/2)²). Our Pythagorean theorem calculator can solve this right-triangle relationship for you.
Can I share my calculation?
Yes. After clicking Calculate, the URL updates with your number of sides, base side, and height. Copy and share the URL to let anyone open the same pre-filled form and results.