Pyramid Calculator — Surface Area & Volume

Regular pyramids (square, triangular, …). Private by design — runs locally in your browser.

Diagram & Inputs

Tip: Provide a and n, plus at least one of h, ℓ, S, or V. The calculator fills in the rest and flags inconsistencies.

Results

How the Pyramid Calculator Works

This pyramid calculator helps you find missing dimensions for a regular pyramid—a pyramid whose base is a regular polygon (triangle, square, pentagon, and so on). If you know the base edge length and how many sides the base has, the calculator can work out the height, slant height, surface area, and volume using standard geometry formulas. It is a fast way to solve homework problems, check designs, or plan materials without digging through a textbook.

Key ideas in simple terms

A pyramid has a flat base and triangular faces that meet at the top. The height is the straight vertical distance from the base to the tip. The slant height runs along a triangular face. The surface area adds up the base area and the areas of the triangular faces. The volume measures how much space the pyramid encloses. These pieces are connected, so if you provide a few of them, the rest can be calculated.

How to use the pyramid calculator

  1. Enter the base edge length a and select the number of sides n for the base.
  2. Provide at least one more value: the height h, slant height ℓ, total surface area S, or volume V.
  3. Choose a length unit and decimal precision.
  4. Click Calculate to see all remaining dimensions and checks for consistency.

Formulas used (for reference)

  • Base perimeter: p = n·a
  • Base inradius: r = a / (2·tan(π/n))
  • Base area: B = n·a² / (4·tan(π/n))
  • Surface area: S = B + ½·p·ℓ
  • Volume: V = (1/3)·B·h
  • Relation: ℓ² = h² + r²
  • From S: ℓ = 2(S - B)/p (requires a and n)
  • From V: h = 3V/B (requires a and n)

Where it’s useful

Regular pyramids show up in architecture, packaging, art, and 3D modeling. A square pyramid is common in roof designs, while triangular pyramids (tetrahedrons) appear in structural frames and engineering models. If you are building a scale model, designing a decorative pyramid, or estimating material for a project, the surface area and volume outputs provide practical guidance.

Units: a, h, and ℓ use a length unit (for example, cm); S uses the squared unit (such as cm²); and V uses the cubed unit (such as cm³). The calculator runs locally in your browser, so your inputs remain private.

5 Fun Facts about Pyramids

Volume plays thirds

Any pyramid’s volume is ⅓ of a prism with the same base and height: V = (1/3)·B·h. Cones obey the same one‑third rule.

Prism sibling

Slant vs true height

Slant height ℓ and vertical height h meet via ℓ² = h² + r², where r is the inradius of the base polygon—Pythagoras hiding in the side face.

Pythagoras link

Square-base shortcut

For a square pyramid, each face is an isosceles triangle. Its altitude is √(ℓ² − (a/2)²), so total area splits neatly into four equal faces plus the base.

Face geometry

Egyptian slope

The Great Pyramid’s original slope was close to a 14:11 rise-run (~51.8°). Its height-to-base ratio almost matches a circle’s radius to half-circumference.

Historic curiosity

n-gon continuum

Change the base: triangle, pentagon, decagon—regular polygons all work. As n grows large, a regular pyramid approaches a cone.

Shape spectrum

Pyramid Calculator: FAQs

Which inputs are valid to solve a pyramid?

Provide a and n plus one of h, ℓ, S, or V. Two or more values are fine; the tool checks consistency.

What formulas are used?

B = n·a²/(4·tan(π/n)), S = B + ½·n·a·ℓ, V = (1/3)·B·h, and ℓ² = h² + r² with r = a/(2·tan(π/n)).

Does the calculator keep my data private?

Yes. Computation is entirely client-side; nothing is uploaded.

Can I change units or decimal places?

Yes. Choose a length unit for a, h, and ℓ. Surface area uses the squared unit; volume uses the cubed unit.

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