Calculators
Triangular Pyramid Frustum Calculator
Calculate right equilateral triangular pyramid frustum volume, face slant height, and lateral and total surface areas in your browser.
Measure a frustum with equilateral triangular bases.
A right triangular pyramid frustum has parallel equilateral triangular bases centered on the same perpendicular axis, with corresponding edges aligned. Enter base sides a and b and perpendicular height h. Base areas are √3a²/4 and √3b²/4. Volume V = √3h(a² + ab + b²)/12. Face slant height s = √(h² + (a − b)²/12); lateral area L = 3(a + b)s/2. Total area adds both bases to L. The slant height joins corresponding edge midpoints, rather than corners. For a = 6, b = 2, and h = 3, volume is 13√3 ≈ 22.5166604984 cubic units and slant height is √(31/3). Either base may be larger; equal sides give a right equilateral triangular prism. Use positive lengths from 1e-50 to 1e50 in one consistent unit; scientific notation is accepted. Results use browser floating-point arithmetic rounded to 12 significant digits. This solid model does not account for wall thickness or hollow container capacity. Inputs remain in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Which shapes does this calculator support?
The bases must be equilateral triangles in parallel planes, aligned without rotation, with their centers on the same perpendicular axis. Oblique frustums and irregular triangular bases are outside this model.
How is volume calculated?
V = h(B₁ + √(B₁B₂) + B₂)/3. For equilateral base sides a and b this becomes √3h(a² + ab + b²)/12.
What does total surface area include?
Total area includes the three trapezoidal side faces and both triangular bases. Lateral area includes only the three side faces.
Can the bases be equal or entered in reverse order?
Yes. Either base can be larger. Equal side lengths give a right equilateral triangular prism, with slant height equal to perpendicular height.
Which units and input sizes are supported?
Use the same length unit for all inputs, from 1e-50 to 1e50. Areas are in square units and volume is in cubic units. Scientific notation is supported and results are rounded to 12 significant digits.