About the Pyramid Calculator
A pyramid has a flat base and triangular faces that rise to a single point. This calculator is for right pyramids with a square or rectangular base, where the tip sits directly above the centre. Enter the base sides and the vertical height and it gives you the volume, which is one third of the base area times the height, along with the area of the base, the area of the sloping faces and the total surface area. It also reports the slant heights of the two pairs of faces and the length of the edge from a base corner to the tip, which you need when cutting material for roofs, tents, paperweights or models.
Updated October 2026
How to use the Pyramid Calculator
- 1Choose a square or a rectangular base.
- 2Enter the base side, or the length and width.
- 3Enter the vertical height from the base to the tip.
- 4Read the volume and total surface area.
- 5Check the slant heights and edge length for cutting and building.
Worked example
Suppose you are making a pyramid-shaped planter with a 40 cm square base and a height of 30 cm. The volume is ⅓ × 1,600 × 30 = 16,000 cubic centimetres, or 16 litres. The slant height is the square root of 30² + 20², about 36.06 cm. Each face has an area of 20 × 36.06 = 721 square centimetres, so the four faces use 2,884 square centimetres of material, and the base adds 1,600.
Useful facts
- Doubling the height doubles the volume.
- Doubling every length multiplies the volume by 8.
- A pyramid has exactly one third the volume of a prism with the same base and height.
- A square pyramid has 5 faces, 8 edges and 5 vertices.
- The lateral faces are triangles.
Using the results
For roofing, the slant height gives the rafter length and the lateral area the amount of covering, before waste. For paper models, the faces are triangles with a base equal to the base edge and a height equal to the slant height. For packaging and casting, the volume tells you how much material fills the shape.
Related tools
The Volume Calculator and Surface Area Calculator cover boxes and prisms, the Cone Calculator is the round cousin of the pyramid, the Roofing Calculator turns slopes into roof areas and the Pythagorean Theorem Calculator finds slant lengths.
Features
- Square and rectangular bases
- Volume, base area, lateral area and total area
- Both slant heights shown
- Edge length from corner to tip
- Works in any consistent unit
- Free and private
Frequently asked questions
What is the volume formula for a pyramid?
Volume equals one third of the base area times the height. A pyramid with a 6 by 4 base and a height of 9 has a volume of ⅓ × 24 × 9 = 72 cubic units.
What is the slant height?
It is the height of a sloping triangular face measured along its centre line, from the middle of a base edge to the tip. For a square pyramid it is the square root of the height squared plus half the base side squared.
How do I find the surface area of a pyramid?
Add the base area to the areas of the triangular faces. Each face is half its base edge times its slant height. The calculator adds all four faces for you.
What is a right pyramid?
One whose tip lies straight above the centre of the base. If the tip is off to one side, the pyramid is oblique and the face formulas here no longer apply, though the volume formula still holds.
Does this work for the Great Pyramid?
Roughly. The Great Pyramid of Giza had a base of about 230 metres and a height of about 139 metres, giving a volume near 2.45 million cubic metres. Weathering has changed its current size slightly.
What is the edge length for?
It is the length of the sloping edge where two faces meet, from a base corner to the tip. You need it for the edge pieces of a frame, a tent or a roof hip.