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 tool solves any regular pyramid (base is a regular n-gon). Enter the base edge a and choose n. From there, give either the height h, the slant height ℓ, the total surface S, or the volume V. The calculator infers the rest, checks consistency within a small tolerance, and labels units for you.

  • 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)

Units: a, h, and ℓ use a length unit (e.g., cm); S uses the squared unit (e.g., cm²); V uses the cubed unit (e.g., cm³).

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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