Pyramid Calculator
Solve square, rectangular and regular n-sided pyramids: volume, base area, slant height, lateral edge and surface area, or work backwards from a target volume.
Where each number came from
- Base apothem = s / (2·tan(π/n)) = 3 cm
- Base circumradius = s / (2·sin(π/n)) = 4.2426 cm
- Base area = n·s·apothem / 2 = 36 cm²
- Lateral edge = √(h² + circumradius²) = 5.831 cm
- Base perimeter = 24 cm
- Volume = base area × h / 3 = 48 cm³
- Lateral area = Σ (edge × slant / 2) = 60 cm²
- Total area = lateral + base = 96 cm²
Solved from the dimensions you entered.
Faces and shape
| Face group | Count | Slant height (cm) | Area (cm²) |
|---|---|---|---|
| All 4 triangular faces | 4 | 5 | 60 |
Slant height is measured up the middle of a face, from the base edge to the apex. The lateral edge is the longer distance along a corner.
What is the Pyramid Calculator?
The ByteTools Pyramid Calculator handles the three base shapes that cover almost every question: a square base, a rectangular base, and a regular polygon with any number of sides from 3 upwards.
- Square, rectangular and regular n-gon bases in one tool
- Volume, base area, lateral area and total surface area
- Base apothem, circumradius, slant height and lateral edge
- Rectangular pyramids report both slant heights, one per face pair
- Reverse solving: find the height or the base edge from a target volume
- Scaled sketch plus a face-by-face area table
How to use the Pyramid Calculator
- 1
Pick the base shape: square, rectangular, or a regular polygon with n sides.
- 2
Choose whether to solve from the dimensions, or backwards from a target volume.
- 3
Enter the base edge (and width for a rectangle), the height, and the number of sides if you chose a polygon.
- 4
Read the volume, base area, lateral area and total surface area in the summary tiles.
- 5
Check the per-face slant heights in the faces table, then click Copy results.
About the Pyramid Calculator
The ByteTools Pyramid Calculator handles the three base shapes that cover almost every question: a square base, a rectangular base, and a regular polygon with any number of sides from 3 upwards. Volume is always base area × height ÷ 3, and the tool works out the base area, the base apothem s ÷ (2·tan(π/n)), the circumradius, the slant height √(h² + apothem²) and the lateral edge √(h² + circumradius²).
Rectangular pyramids get special treatment because they have two different slant heights, one for each pair of opposite faces, so the tool reports each face group separately with its own slant height and area. It can also run the arithmetic backwards: give it a target volume and it will solve for the height, or for the base edge.
All the geometry runs locally in your browser using JavaScript, so nothing you enter ever leaves your device and the page keeps working offline once it has loaded. Choose your unit once and every figure — base area, slant height, lateral edge, volume — is reported in it, with the working shown line by line so you can check each step against your own textbook.
Frequently asked questions
What is the formula for the volume of a pyramid?
Volume = base area × perpendicular height ÷ 3, whatever the base shape. A square pyramid with a 6 cm base and a 4 cm height has a base area of 36 cm² and a volume of 48 cm³. The height must be measured straight down from the apex, not along a face.
What is the difference between slant height and lateral edge?
Slant height runs up the middle of a triangular face, from the midpoint of a base edge to the apex, and equals √(h² + apothem²). The lateral edge runs up a corner, from a base vertex to the apex, and equals √(h² + circumradius²). The lateral edge is always the longer of the two.
How do you find the surface area of a square pyramid?
Add the base area s² to the four triangular faces, each of area s × slant height ÷ 2. For a 6 cm base and 4 cm height the slant height is 5 cm, so the lateral area is 60 cm² and the total is 96 cm². The calculator shows the two figures separately.
Can this calculator handle a hexagonal or pentagonal pyramid?
Yes. Choose Regular n-sided base and set the number of sides to 5, 6 or anything up to 200. The tool derives the apothem and circumradius from the edge length using the standard regular-polygon relationships, then solves everything from there.
How do I find the height of a pyramid if I know its volume?
Rearrange the volume formula to h = 3V ÷ base area. Switch the Solve dropdown to Find the height from a target volume, enter the base and the volume you want, and the tool does it for you — and it can solve for the base edge the same way.
Related tools
Cone Calculator
Solve a right circular cone from any two of radius, height and slant height, with volume, lateral and total surface area, apex angle and a cutting template.
Cone Frustum Calculator
Calculate the volume, slant height and surface area of a truncated cone, and get the flat pattern radii and included angle for sheet metal or papercraft.
Polygon Area Calculator
Paste a list of vertex coordinates to get the area of any simple polygon by the shoelace formula, plus perimeter, centroid, winding order and a convexity check.
Hexagon Calculator
Solve a regular hexagon from any single measurement — side, area, perimeter, apothem, circumradius or either diagonal — and see how many tile a given area.
Area Calculator
Calculate the area of a rectangle, triangle, circle, trapezoid or ellipse from simple measurements, with the formula shown and results in m², ft² and more.