Enter your pyramid's base side length, height, and number of sides to calculate volume, total surface area, lateral surface area, slant height, and lateral edge length. The Pyramid Calculator supports triangular, square, pentagonal, hexagonal, and other regular polygon bases — just pick your shape and plug in the dimensions.
Volume (V)
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Total Surface Area (A)
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Lateral Surface Area (L)
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Base Area (B)
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Slant Height (s)
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Lateral Edge Length (e)
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The volume of any pyramid is V = (1/3) × base area × height. For a regular polygon base, the base area depends on the number of sides and side length. For example, a square pyramid with side length 6 m and height 9 m has a base area of 36 m² and a volume of (1/3) × 36 × 9 = 108 m³.
Total surface area = lateral surface area + base area. The lateral surface area equals (1/2) × perimeter of base × slant height. The slant height (s) is the distance from the midpoint of a base edge to the apex, calculated as √(h² + r²), where r is the apothem (inradius) of the base polygon.
The height (h) is the perpendicular distance from the base to the apex, measured straight up. The slant height (s) is the distance along the face from the midpoint of a base edge to the apex — it's always longer than the height. Slant height is used to calculate lateral surface area.
For a regular hexagonal pyramid, the base area is (3√3 / 2) × a², where a is the side length. Then apply V = (1/3) × base area × height. For example, with a = 4 m and h = 10 m, base area ≈ 41.57 m² and volume ≈ 138.56 m³.
The Great Pyramid of Giza has a square base with side length of approximately 230.4 m and an original height of about 146.5 m. Its volume is approximately (1/3) × 230.4² × 146.5 ≈ 2,583,283 m³, making it one of the largest man-made structures ever built.
The lateral edge (e) is the distance from a corner of the base polygon to the apex. For a square pyramid, e = √(h² + (a√2 / 2)²), where h is the height and a is the base side length. For a general regular polygon base, it uses the circumradius of the base polygon instead.
Yes — select '3 — Triangle' as the base shape. A triangular pyramid (tetrahedron) has an equilateral triangle as its base. The calculator will compute the base area as (√3 / 4) × a², then use that to find volume, lateral surface area, slant height, and lateral edge length.
A right pyramid has its apex directly above the centroid of the base, making the height perpendicular to the base. An oblique pyramid has its apex offset to one side. This calculator assumes a right regular pyramid, which is the most common type used in geometry and real-world construction.