Square Pyramid Calculator: Volume, Slant Height and Surface Area
Enter the side of the square base and the vertical height. You get the volume, the slant height of each face, the edge length and the surface areas.
- Nothing you type is stored
- Free
- No signup
Volume
400m³
- Slant height (s)
- 13 m
- Sloping edge
- 13.9284 m
- Lateral surface area (LSA)
- 260 m²
- Total surface area (TSA)
- 360 m²
Show working
- V = ⅓ × a² × h = ⅓ × 10² × 12 = 400 m³
- s = √(h² + (a/2)²) = √(12² + 5²) = 13 m
- e = √(h² + a²/2) = 13.9284 m
- LSA = 2as = 2 × 10 × 13 = 260 m²
- TSA = a² + 2as = 360 m²
How to use
- Enter the base side a and the height h.
- Choose a length unit.
- Read the volume, slant height and surface areas.
Good to know
Volume = ⅓ × a² × h, one third of a cuboid with the same base and height. The slant height of each triangular face is s = √(h² + (a/2)²) and each sloping edge is √(h² + a²/2).
Lateral surface area = 2as (four triangles of base a and height s) and total surface area = a² + 2as. With a = 10 and h = 12, s = 13 and TSA = 360.
Height here means the vertical height from the tip to the centre of the base, not the slant height. For a rectangular base, use the volume calculator.
Questions
What is the volume of a square pyramid?
⅓ × base side² × height.
What is the slant height of a pyramid?
The height of each triangular face, from the middle of a base edge to the tip: √(h² + (a/2)²).
What is the difference between height and slant height?
Height goes straight down from the tip to the centre of the base. Slant height runs down the middle of a face.
What is the total surface area?
Base a² plus the four triangular faces 2as.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.