Triangular Pyramid Volume Calculator
Enter the base side length, the altitude of the triangular base and the perpendicular height of the pyramid to compute its volume — V = ⅓ × base area × height.
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units
units
V = ⅓ × base area × height
- 1
Base triangle area
½ × 6 × 5 = 15Area of the triangular base using the standard ½ × base × altitude formula. - 2
Volume
⅓ × 15 × 8 = 40
How does this calculator work?
A triangular pyramid's volume = ⅓ × base area × perpendicular height, where base area = ½ × base side × base altitude. All inputs must share the same unit; volume is in cubic units. The factor ⅓ applies to all pyramid shapes regardless of the base.
Formula
How this is calculated
A triangular pyramid (also called a tetrahedron in its general form) has a triangular base and three triangular lateral faces meeting at a single apex. Its volume follows the universal pyramid formula: V = ⅓ × base area × perpendicular height. This factor of one-third arises because three congruent pyramids fill one prism of the same base and height.
The triangular base area is computed as A = ½ × base_side × base_altitude, the standard triangle area formula. The perpendicular height H is the distance from the apex straight down to the base plane — not the slant height along a face. Multiplying: V = ⅓ × (½ × b × h_b) × H.
This calculator gives an exact volume for any triangular-base pyramid as long as you know the base dimensions and the perpendicular apex height. Lateral surface area requires knowing the full 3-D position of the apex relative to the base triangle and is not computed here without additional geometry.
Frequently asked questions
A triangular pyramid is a solid with a triangular base and three triangular lateral faces, all meeting at a single point called the apex. When all four faces are equilateral triangles of the same size it is called a regular tetrahedron, which is one of the five Platonic solids.
Three identical pyramids can always be assembled to fill a prism with the same triangular base and height. Because the prism volume is base area × height, each pyramid is exactly one-third of that. This proof works for any pyramid regardless of the base shape, making V = ⅓ · A · H universal.
The formula requires the perpendicular (true) height — the straight-line distance from the apex to the base plane, measured at a right angle to the base. Slant height is the distance along a lateral edge or lateral face and gives a larger (incorrect) value if substituted directly.
Also known as
TG we-Calculate Editorial Team. (2026). Triangular Pyramid Volume Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangular-pyramid-volume-calculator
TG we-Calculate Editorial Team. "Triangular Pyramid Volume Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangular-pyramid-volume-calculator.
TG we-Calculate Editorial Team, "Triangular Pyramid Volume Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangular-pyramid-volume-calculator
@misc{wecalculate_triangular_pyramid_volume_calculator, title = {Triangular Pyramid Volume Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangular-pyramid-volume-calculator}}, year = {2026}, note = {TG we-Calculate} }
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