Tetrahedron Volume Calculator

A regular tetrahedron is a Platonic solid composed of four equilateral triangular faces, six straight edges, and four vertex corners. The primary driver for all geometric attributes of a regular tetrahedron is its edge length (a). The volume (V) is derived using the formula V = a^3 / (6 * sqrt(2)). Similarly, the total surface area depends on the face area, calculated as A = sqrt(3) * a^2. When calculating from alternative inputs like the circumsphere radius or height, the tool first isolates the edge length using inverse algebraic formulas before executing the final spatial computations.

Let us compute the volume of a regular tetrahedron with a given edge length of 6 centimeters. First, substitute a = 6 into the volume formula: V = 6^3 / (6 * sqrt(2)). Evaluating the cube gives 216 / (6 * 1.4142), which simplifies to 216 / 8.4853. This results in a final volume of approximately 25.46 cubic centimeters. To find its height, we apply the height formula h = sqrt(2/3) * a, yielding approximately 4.89 centimeters.

Always verify your input units before running calculations to ensure dimensional consistency. Keep in mind that formulas involving inspheres, midspheres, and circumspheres strictly apply to regular tetrahedrons where all four faces are congruent equilateral triangles. For irregular tetrahedrons, alternative methods such as scalar triple products using vector coordinates are required.