Triangular Pyramid (Regular Tetrahedron) — Volume + Surface Area
Regular tetrahedron: V = a³/(6√2), SA = √3·a², height = a√(2/3). All four faces are equilateral triangles.
Result
Volume
25.4558
a³/(6√2) = 25.4558. SA = √3·a² = 62.3538.
- Edge (a)6
- Volume (a³/6√2)25.455844
- Surface area (√3 a²)62.353829
- Each face area15.588457
- Height (a√(2/3))4.898979
- Inradius (a/(2√6))1.224745
- Circumradius (a√6/4)3.674235
Step-by-step
- Each face = equilateral triangle of side a; area = √3/4 × a² = 15.5885.
- SA = 4 × face area = 4 × 15.5885 = 62.3538.
- Height (apex to base) = a√(2/3) = 6 × 0.816497 = 4.8990.
- V = a³/(6√2) = 216 / 8.4853 = 25.4558. (Equivalent: ⅓ × base × height = 25.4558.)
How to use this calculator
- Enter the edge length (all 6 edges equal).
- Read volume, total surface area, and key radii.
About this calculator
A regular tetrahedron is the simplest Platonic solid: 4 vertices, 4 equilateral-triangle faces, 6 edges of equal length a. Volume V = a³ / (6√2) = (√2 / 12) a³. Surface area SA = 4 × (√3/4) a² = √3 a². Height (from one vertex to opposite face) h = a√(2/3) = a√6/3. Inradius (insphere) = a / (2√6). Circumradius (sphere through 4 vertices) = a√6 / 4. Source: Coxeter, "Regular Polytopes"; Stewart, "Calculus." Common as the molecular geometry of methane (CH₄), the d4 die, and the structural unit of diamond.
Frequently asked
Triangular pyramid = any pyramid with a triangular base. Regular tetrahedron = the special case where all 4 faces are congruent equilateral triangles. This calc handles the regular case.
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