Square Pyramid Volume Calculator
Enter the base edge and the vertical height of a right square pyramid to get its volume in one step. The calculator also reports the slant height, the lateral area of the four triangular faces, the square base area and the total surface area. Every value uses the same length unit you type, so results follow inches, centimetres or metres automatically.
How to find the volume of a square pyramid
- Type the length of one square base edge into the Base edge field.
- Type the vertical height from the base to the apex into the Height field.
- Read the Volume and Total surface area cards at the top of the results.
- Check the Slant height, Lateral area and Base area cards below them.
- Click Copy result to grab all five values as plain text.
Examples
Base edge 6, height 4
base edge = 6, height = 4
volume = 48, slant height = 5, lateral area = 60, base area = 36, total area = 96
Base edge 10, height 12
base edge = 10, height = 12
volume = 400, slant height = 13, lateral area = 260, base area = 100, total area = 360
Base edge 8, height 3
base edge = 8, height = 3
volume = 64, slant height = 5, lateral area = 80, base area = 64, total area = 144
Frequently asked questions
What is the formula for the volume of a square pyramid?
Volume equals the base area times the height divided by three. Because the base is square, the base area is the base edge squared, so volume is base edge squared times height, all over three.
Why is the height divided by three?
A pyramid fills exactly one third of the prism that shares its base and height. That one third factor holds for every pyramid and cone, which is why the height is divided by three.
How is the slant height calculated?
The slant height runs from the apex down the middle of a triangular face to the base edge. It is the square root of the height squared plus half the base edge squared, so for base 6 and height 4 it comes to 5.
What is the difference between slant height and vertical height?
Vertical height is the straight up distance from the base centre to the apex, which is what you enter. Slant height is the slanted distance along a face and is always the larger of the two.
What does the lateral area include?
The lateral area is the four triangular side faces only, without the base. It equals two times the base edge times the slant height, which for base 6 and slant height 5 gives 60.
How is the total surface area found?
Add the square base area to the lateral area. That is the base edge squared plus two times the base edge times the slant height, so base 6 with a slant height of 5 totals 96.
Does this work for pyramids that are not square?
No. This calculator assumes a right pyramid with a square base and the apex directly above the centre. Rectangular, triangular or oblique pyramids follow different area formulas.
What units does it use?
It is unit agnostic. Volume comes out in your length unit cubed and the areas in that unit squared, so metre inputs give cubic metres and square metres. Do not mix units in one calculation.
Do my numbers stay private?
Yes. The math runs in your browser with no server call, so nothing you type is uploaded or stored anywhere.
Learn more
- Square pyramid volume and surface area explained
How the volume, slant height, lateral area and total surface area of a right square pyramid are derived, with worked numbers you can check.
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