Pyramid
Find the volume, slant height, lateral edge and surface area of a regular pyramid, a frustum and a regular tetrahedron.
What is known:
Number of base sides n
x
Base edge a
x
Height h
x
Units:
The number of sides is a whole number from 3 (triangular pyramid) to 1000; lengths are positive numbers.
The pyramid calculator finds the volume, slant height (apothem), lateral edge, base, lateral and total surface areas of a regular n-gonal pyramid and of a regular frustum, the volume of any pyramid, and all elements of a regular tetrahedron.
Pyramid formulas
| Value | Formula |
|---|---|
| Volume of any pyramid | V = ⅓ · Sbase · h |
| Slant height of a regular pyramid | l = √(h² + r²), r is the inradius of the base |
| Lateral edge | e = √(h² + R²), R is the circumradius of the base |
| Lateral area of a regular pyramid | Slat = ½ · Pbase · l |
| Total surface area | S = Slat + Sbase |
Example. A regular square pyramid, a = 6, h = 4.
r = 3, l = √(16 + 9) = 5, Sbase = 36
V = ⅓ · 36 · 4 = 48, Slat = ½ · 24 · 5 = 60, S = 96.
Frustum of a pyramid
V = h/3 · (S1 + S2 + √(S1S2)), Slat = ½ · (P1 + P2) · l
Regular tetrahedron
All six edges equal a, the faces are equilateral triangles: V = a³√2 / 12, S = a²√3, h = a√(2/3).
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