How to use this square pyramid calculator
- Enter one side of the square base and the vertical, perpendicular height. Use the same length unit for both.
- Select Calculate. Volume is the main result; the other cells show total surface area, the four triangular faces, face slant height and base area.
- Editing either measurement removes the confirmed answer and disables Copy. Calculate again after every change.
- Copy creates a short text summary. Clear removes both inputs and the result.
Formulas and measurement meaning
This tool models a right square pyramid: the apex is directly above the centre of a square base. It does not model an oblique or irregular pyramid.
The face slant height runs from the midpoint of a base edge to the apex, so l = √(h² + (s/2)²). The four triangular faces total 2sl.
Volume is one third of base area times perpendicular height. Total surface area includes the square base as well as all four side faces.
l = √(h² + (s/2)²) · V = s²h/3 · L = 2sl · S = s² + L
Worked examples
Base side 4 cm, height 3 cm
The slant height is √13 ≈ 3.61 cm. Volume is 16 cm³, lateral area is about 28.84 cm², and total surface area is about 44.84 cm².
Base side 10 m, height 12 m
The slant height is 13 m. Volume is 400 m³, lateral area is 260 m², and total surface area is 360 m².
Limits and input notes
- Both inputs must be positive decimals with at most 12 decimal places; units and exponent notation are not accepted in fields.
- Use one consistent unit. The calculator does not convert mixed units.
- Surface figures assume a closed mathematical solid; seams, thickness, waste and openings are excluded.
- Displayed values use at most two decimals, while calculations retain greater internal precision.
Frequently asked questions
Is slant height the same as vertical height?
No. Vertical height is perpendicular to the base; slant height lies on a triangular face and is longer unless the base side tends to zero.
Does surface area include the base?
Yes. Total surface area includes the base. Lateral area lists only the four triangular faces.
Can I use a rectangular base?
No. This page is specifically for a square base with one shared side length.
Can I enter an edge from apex to corner?
No. That lateral edge is not the face slant height or vertical height required here.