Pyramid Calculator
Free pyramid calculator. Choose square or rectangular pyramid, enter base and height, and get volume, lateral area, total surface area, base area and slant height. Shows formulas and examples.
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Pyramid Calculator
Calculate volume, lateral surface area, total surface area, base area and slant height of a right pyramid. Supports square and rectangular bases. Suitable for math homework, DIY construction and 3D modeling.
Square & rectangular Formula-based Step-friendly
Height is measured perpendicular from base to apex.
Pyramid formulas used
This tool uses the general pyramid volume formula and specific surface-area formulas for square and rectangular bases.
1. Volume of a pyramid
\( V = \frac{1}{3} B h \)
where \( B \) is the base area and \( h \) is the vertical height.
2. Square pyramid
Base area: \( B = a^2 \)
Slant height: \( \ell = \sqrt{ \left(\frac{a}{2}\right)^2 + h^2 } \)
Lateral area: \( A_L = 2 a \ell \)
Total area: \( A_T = a^2 + 2 a \ell \)
3. Rectangular pyramid
Base area: \( B = a b \)
Slant height along side a: \( \ell_a = \sqrt{ \left(\frac{b}{2}\right)^2 + h^2 } \)
Slant height along side b: \( \ell_b = \sqrt{ \left(\frac{a}{2}\right)^2 + h^2 } \)
Lateral area: \( A_L = a \ell_a + b \ell_b \)
Total area: \( A_T = ab + a \ell_a + b \ell_b \)
Example
Example: Square pyramid with base side 6 m and height 9 m.
- Base area \( B = 6^2 = 36 \text{ m}^2 \)
- Volume \( V = \frac{1}{3} \times 36 \times 9 = 108 \text{ m}^3 \)
- Slant height \( \ell = \sqrt{(6/2)^2 + 9^2} = \sqrt{9 + 81} = \sqrt{90} \approx 9.487 \text{ m} \)
- Lateral area \( A_L = 2 \times 6 \times 9.487 \approx 113.84 \text{ m}^2 \)
- Total area \( A_T = 36 + 113.84 \approx 149.84 \text{ m}^2 \)
The calculator runs these steps automatically.
Pyramid Calculator – FAQ
Formula (LaTeX) + variables + units
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1. Volume of a pyramid \( V = \frac{1}{3} B h \) where \( B \) is the base area and \( h \) is the vertical height.
2. Square pyramid Base area: \( B = a^2 \) Slant height: \( \ell = \sqrt{ \left(\frac{a}{2}\right)^2 + h^2 } \) Lateral area: \( A_L = 2 a \ell \) Total area: \( A_T = a^2 + 2 a \ell \)
3. Rectangular pyramid Base area: \( B = a b \) Slant height along side a: \( \ell_a = \sqrt{ \left(\frac{b}{2}\right)^2 + h^2 } \) Slant height along side b: \( \ell_b = \sqrt{ \left(\frac{a}{2}\right)^2 + h^2 } \) Lateral area: \( A_L = a \ell_a + b \ell_b \) Total area: \( A_T = ab + a \ell_a + b \ell_b \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.