Right Square Pyramid Calc: find A, A_l, V, A_F
Use this right square pyramid calculator to find the lateral face area, total lateral area, total surface area, and volume of any right or regular square pyramid.
The formula
V = ⅓s²h, slant l = √(h² + (s/2)²)
Volume scales with the cube
Double every length and the surface area quadruples while the volume grows eightfold. This is why doubling a container’s dimensions gives eight times the capacity but only four times the material — and why scaling models up rarely works the way intuition suggests.
The one-third family
Cones and pyramids are always exactly one third of the prism or cylinder that would enclose them, whatever the base shape. A sphere sits at two thirds of its enclosing cylinder — the result Archimedes asked to have carved on his tomb.
Units
Enter every dimension in the same unit; volume comes out cubed and surface area squared. If you work in centimetres, one litre is 1,000 cm³, which is why the capacity row is shown on the box and cylinder pages.