Calculators
Pentagonal Pyramid Frustum Calculator
Calculate right regular pentagonal pyramid frustum volume, face slant height, and lateral and total surface areas in your browser.
Measure a frustum with regular pentagonal bases.
A right pentagonal pyramid frustum has parallel regular pentagonal bases centered on the same perpendicular axis, with corresponding edges aligned. Enter base side lengths a and b and perpendicular height h. Let t = tan(π/5). Base areas are 5a²/(4t) and 5b²/(4t). Volume V = 5h(a² + ab + b²)/(12t). Face slant height s = √(h² + (a − b)²/(4t²)); lateral area L = 5(a + b)s/2. Total area adds both bases to L. Slant height joins corresponding edge midpoints, not corners. For a = 6, b = 2, h = 3, volume is 65/t ≈ 89.4648248301 cubic units. Either base may be larger; equal sides give a right regular pentagonal 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 estimate wall thickness or hollow 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 regular pentagons in parallel planes, aligned without rotation, with their centers on the same perpendicular axis. Oblique frustums and irregular pentagonal bases are outside this model.
How is volume calculated?
V = h(B₁ + √(B₁B₂) + B₂)/3. For regular pentagonal base sides a and b this becomes 5h(a² + ab + b²)/(12 tan(π/5)).
What does total surface area include?
Total area includes the five trapezoidal side faces and both pentagonal bases. Lateral area includes only the five side faces.
Can the bases be equal or entered in reverse order?
Yes. Either base can be larger. Equal side lengths give a right regular pentagonal 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.