a square pyramid
- Base length
- 4
- Base width
- 4
- Vertical height
- 3
Volume16
16 x 3 / 3; slant from Pythagoras on 3 and 2
Open this exampleMath & Statisticsgeometry
Pyramid Calculator
Pyramid volume and surface for a rectangular base. A pyramid holds exactly one third of the prism enclosing it, and the face slant and edge slant are different lengths that are easy to confuse.
Also called: pyramid volume calculator, square pyramid.
Volume
16
Volume 16, which is a third of the 48 the enclosing prism holds. Total surface 44.84, of which 28.84 is the sloping faces. The edge slant is 4.12 and the face slant 3.61.
Base area
16
Sloping face area
28.84
Total surface area
44.84
Face slant height
3.61
Edge length
4.12
Enclosing prism volume
48
Method and background
How this is calculated
The volume is a third of the base area times the height, the same relationship a cone has with its cylinder. The two slant measurements catch people out: the face slant runs from the apex to the midpoint of a base edge and is what the triangular faces are built on, while the edge slant runs from the apex to a corner and is longer. Cladding needs the first and framing needs the second.
a pyramid is one third of its prism, the same ratio a cone has to its cylinder- l, w, h
- Base length, base width, height
Worked examples
Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.
the edge is longer than the face slant
- Base length
- 4
- Base width
- 4
- Vertical height
- 3
Volume16
boundary: the corner is further than the edge midpoint
Open this exampleMethod and limits
What it assumes
- A right pyramid with the apex above the centre of the base.
What it deliberately does not model
- An oblique pyramid has the same volume and different face areas.
Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator
Frequently asked questions
- What is the difference between slant height and edge length?
- Slant height goes from the apex to the middle of a base edge, edge length goes to a corner. The corner is further away, so the edge is always longer.