Volume of Triangular Pyramid Calculator
A triangular pyramid (tetrahedron) is a pyramid on a triangular base. Enter the base triangle’s base and height plus the pyramid’s own height to get V = ⅓ × base area × height.
Example: with Base triangle: base (b) 12 · Base triangle: height (h) 9 · Pyramid height (H) 10 · Units centimeters (cm) → Pyramid volume: 180.00 cm³.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outTriangular pyramid volume formula
Every pyramid follows the same rule: V = ⅓ × base area × height. For a pyramid with a triangular base, the base area is ½ × b × h, so the full formula is V = ⅓ × (½bh) × H. With the defaults — a base triangle 12 cm wide and 9 cm tall under a pyramid 10 cm high — the base area is ½ × 12 × 9 = 54 cm², and ⅓ × 54 × 10 = 180 cm³.
Keep the two heights straight: the base triangle’s height h lies flat in the base, while the pyramid height H rises perpendicular from the base plane to the apex. A triangular prism with the same base and height would hold 3× as much — the ⅓ is what makes it a pyramid.
How it’s calculated
Volume = ⅓ × (½ × b × h) × H, where ½bh is the area of the triangular base and H is the perpendicular height from the base plane to the apex. Conversions: 1 US gallon = 231 in³ exactly, 1 ft³ = 7.48052 gal (NIST Handbook 44), 1 liter = 1,000 cm³, 1 m³ = 1,000 L.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Dropping the ⅓ — base area × height gives the prism’s volume, three times too big.
- Confusing the base triangle’s height with the pyramid’s height — they are different measurements in different directions.
- Using a slanted edge or face as the pyramid height — H must be perpendicular to the base.
Frequently asked questions
How do I find the volume of a triangular pyramid?
Multiply the base triangle’s area (½ × b × h) by the pyramid’s height and divide by 3. For a 12 × 9 base triangle and height 10: ⅓ × 54 × 10 = 180 cubic units.
What is the volume of a regular tetrahedron?
When all four faces are equilateral triangles with edge a, V = a³ ÷ (6√2) ≈ 0.11785a³. An edge of 10 cm gives about 117.85 cm³.
What is the difference between a triangular pyramid and a triangular prism?
A prism keeps the same triangular cross-section along its whole length (V = ½bh × L); a pyramid tapers to a point, so it holds exactly one-third of the matching prism.
Which height goes where in the formula?
The base triangle’s height h is used only to get the base area (½bh). The pyramid height H — measured straight up from the base plane to the apex — is what you multiply by before taking ⅓.