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.
Everyday Uses
Tent and canopy sizing
Pyramid tents need slant-height math for fabric — compute it from base and height.
Packaging design
Pyramid boxes and displays — get surface area for material and volume for contents.
Models and replicas
Scale-model pyramids for school projects with correct proportions and paint coverage.
Solid geometry homework
Volume, slant height, and surface area with the formulas visible.
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.