Pyramid Calculator
Calculate the volume, base area, lateral and total surface area, slant heights, and lateral edge length of a right square or rectangular pyramid.
Frequently Asked Questions
How do you calculate the volume of a pyramid?
V = (base area × height) ÷ 3 — any pyramid has exactly one third the volume of a prism with the same base and height. A square pyramid with base side 6 and height 9 has V = (36 × 9) ÷ 3 = 108.
What is the slant height of a pyramid and how is it found?
The slant height is the distance from the apex down the middle of a triangular face to the base edge — not the same as the vertical height. For a right pyramid: slant = √(h² + (side/2)²), using the base side perpendicular to that face. It is needed to compute the lateral surface area.
How do you find the surface area of a pyramid?
Total SA = base area + lateral area. For a square pyramid, lateral area = 2 × a × slant (four triangles, each ½ × a × slant). For a rectangular base, the two pairs of faces have different slant heights: lateral = a × slant_a + b × slant_b.
How do the Great Pyramid's proportions compare?
The Great Pyramid of Giza originally had a base side of about 230.3 m and height of 146.6 m, giving a volume of roughly 2.6 million cubic metres. Its slant height was ≈186.4 m, and the ratio of perimeter to height closely approximates 2π — a subject of much speculation and geometry classroom fun.