How this calculator works
The apex sits above the centre of the square. A face slant reaches an edge midpoint; a corner edge reaches a vertex. Their horizontal runs differ. Once either sloping length is recovered, the Pythagorean theorem gives the vertical height. Surface modes subtract the base when needed and divide the remaining area among four equal faces.
Formula
B=a²; diagonal=a√2; l²=h²+a²/4; e²=h²+a²/2; face=al/2; lateral=2al; total=a²+2al; V=a²h/3; a=√(3V/h).
Worked example
A base side of 6 m and height of 4 m give slant 5 m and corner edge √34 m. Each face has area 15 m², all four have 60 m² and the total including the 36 m² base is 96 m². Volume is 48 m³.
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Frequently asked questions
Is lateral edge the slant height?
No. The corner edge ends at a base vertex; the slant ends at an edge midpoint and is shorter.
Which area belongs in face mode?
Only one triangular face. Lateral mode takes the sum of all four, while total surface mode also includes the square base.
Can volume and height determine the base?
Yes. The square base area is 3V/h and its side is the square root of that area.