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Pyramid Surface Area Calculator

Enter the base edge and height of a square pyramid to find its surface area.

How it is calculated

The tool is built for a pyramid with a square base. Inputs are the base edge b and the vertical height h (apex straight down to the centre of the base), both greater than zero. Step 1, slant height: l = √((b ÷ 2)² + h²), the distance from the apex to the midpoint of a base edge. Step 2, lateral area: L = 2 × b × l, the four triangles together. Step 3, total area: S = b² + L. Results are rounded to two decimals and labelled in metres and square metres, so enter both lengths in metres, or in any single unit and read the numbers in that unit. Rectangular-base or oblique pyramids need a different formula.

Worked example

A square pyramid has a base edge of 6 and a vertical height of 4. Slant height: half the base is 3, so l = √(3² + 4²) = √25 = 5.00 m. Lateral area: 2 × 6 × 5 = 60, shown as 60.00 m². Base area: 6² = 36. Total surface area: 36 + 60 = 96.00 m². This is the amount of covering needed if the base is closed as well.

Try this example →

Common mistakes

  • Using the vertical height in place of the slant height in the triangle formula. The slant height is always longer than the vertical height, and using the wrong one understates the area.
  • Entering the edge of the lateral face, the sloping edge from corner to apex, as the base edge. The tool wants the side of the square base.
  • Mixing units, such as a base in centimetres and a height in metres. Both must use the same unit.
  • Including the base when only the roof or cover is needed. For a roof or tent skin, read the lateral area, not the total.

About this calculator

For a square pyramid, total surface area is the base square plus four congruent triangular faces. The tricky part is that the triangles’ height isn’t the pyramid’s vertical height — it’s the slant height, the distance from the apex down the middle of a triangular face, found with the Pythagorean theorem as l = √(h² + (s/2)²), where h is the vertical height and s is the base edge.

Once you have the slant height, the lateral surface area (the four triangular faces only, excluding the base) is 2 × s × l, and the total surface area adds the base: s² + 2sl. Architects, engineers and construction estimators use these formulas when calculating material for pyramid-shaped roofs, tent structures, or packaging, and they’re a staple of solid-geometry coursework. Using the base edge and the vertical height of a square pyramid, it finds the slant height first and then the lateral and total surface areas.

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Comments (1)

  • Editorial team

    This assumes a square base and a vertical height, so the apex sits straight above the centre. For a 4 by 6 pyramid the tool gives a slant of 6.32, a lateral area of 50.60 and a total of 66.60. The slant is not the height, and mixing them up in a painting or cladding estimate means you under-order. Measure the actual sloping face to confirm. Which material will you cover it with?

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