VolLab

Square Pyramid Volume Calculator

A third of the box that contains it — same idea as a cone.

Base side

Height

Volume

Surface area: 138.528
Slant height: 8.544

What you entered

Base side: 6Height: 8

1
Volume = ⅓ × base area × height
(1/3) × 6² × 8= 96
2
Slant height (apex to base-edge midpoint)
√(8² + (6/2)²)= 8.544
3
Surface area = base + 4 triangular faces
6² + 2 × 6 × 8.544= 138.528

Result

Volume: 96

A square pyramid with base side 6 and height 8 has a volume of 96 and a surface area of 138.528.

Square pyramid volume, surface area and slant height

Volume is one third of the base area times the height. Surface area includes the square base plus four triangular faces.

Base side x Height	Volume	Total surface area	Slant height
4 x 6	32.00	66.60	6.325
5 x 8	66.67	108.82	8.382
6 x 10	120.00	161.28	10.440
8 x 12	256.00	266.39	12.649
10 x 15	500.00	416.23	15.811
12 x 20	960.00	645.13	20.881

As with a cone, the one third factor means a pyramid holds a third of the prism that would enclose it. The slant height is always slightly greater than the vertical height, because it runs up the middle of a triangular face rather than straight up the axis - it is the hypotenuse of a right triangle formed by the height and half the base side. Use the vertical height in the volume formula and the slant height only for surface area; swapping them is the common error.

The same ⅓ rule as a cone

Just like a cone is a third of its enclosing cylinder, a pyramid's volume is exactly a third of the rectangular box sharing its base and height: V = ⅓ × base area × height.

Real pyramids, real math

This is the same formula engineers and archaeologists use to estimate the volume of stone in structures like the Great Pyramid of Giza.

Frequently asked questions

How do I calculate the volume of a pyramid?

Volume = ⅓ × base area × height. For a square-base pyramid with base side 10 and height 12: V = ⅓ × 100 × 12 = 400 cubic units. This ⅓ rule applies to any pyramid, regardless of base shape.

What is the slant height of a pyramid?

The slant height is the distance from the apex to the midpoint of a base edge, measured along a face. For a square pyramid: slant height = √(h² + (s/2)²), where h is the vertical height and s is the base side length.

How much stone is in the Great Pyramid?

The Great Pyramid has a base of about 230 m and height of 146 m. V = ⅓ × 230² × 146 = 2,574,467 m³. At ~2,500 kg per cubic meter of limestone, that's roughly 6.4 million tonnes of stone.