Pyramid Frustum Calculator
Calculate surface area and volume of square and triangular pyramid frustums
Professional geometry calculator for pyramid frustums (truncated pyramids). Instantly compute surface area, volume, lateral area, and slant height with detailed step-by-step solutions and visual representations.
Frustum Parameters
Calculation Results
Enter Dimensions to Calculate
Input the frustum dimensions and click calculate to see detailed results
💡 Tip: Use Ctrl+Enter to quickly calculate results
When to Use Pyramid Frustum Calculator
Architecture & Construction
Calculate material requirements for truncated pyramid structures, roof designs, foundation work, and architectural elements with precise volume and surface area measurements.
Engineering Design
Design mechanical components, hoppers, funnels, and industrial equipment with frustum shapes. Calculate stress distribution and material optimization for engineering projects.
Educational Mathematics
Perfect for geometry students, teachers, and tutors working with 3D shapes. Verify homework solutions, create practice problems, and understand frustum properties with step-by-step calculations.
3D Modeling & CAD
Validate 3D model dimensions, calculate material volumes for 3D printing, and verify CAD design specifications for frustum-shaped objects and components.
Manufacturing & Production
Calculate material costs, production volumes, and surface treatments for manufactured frustum-shaped products like containers, decorative elements, and industrial components.
Research & Analysis
Support scientific research, geological studies, and mathematical analysis requiring precise frustum calculations. Generate data for academic papers and technical documentation.
Frequently Asked Questions
What is a pyramid frustum?
A pyramid frustum (or truncated pyramid) is a portion of a pyramid that remains after cutting off the top portion with a plane parallel to the base. It has two parallel bases of different sizes connected by slanted faces. Common examples include lamp shades, flower pots, and architectural elements.
How do you calculate the surface area of a pyramid frustum?
The surface area of a pyramid frustum equals the sum of the areas of both bases plus the lateral surface area. For a square frustum: SA = a₁² + a₂² + 2(a₁ + a₂)√[h² + ((a₁-a₂)/2)²], where a₁ and a₂ are the side lengths of the bases and h is the height. Our calculator handles all these complex calculations automatically.
What is the volume formula for a pyramid frustum?
The volume of a pyramid frustum is V = (h/3)(A₁ + A₂ + √(A₁×A₂)), where h is the height, A₁ is the area of the larger base, and A₂ is the area of the smaller base. This formula works for both square and triangular frustums, with the base areas calculated according to their respective shapes.
Can this calculator handle both square and triangular frustums?
Yes, our calculator supports both square pyramid frustums and triangular pyramid frustums. Simply select the frustum type and enter the appropriate dimensions. The calculator automatically applies the correct formulas and provides accurate results for both geometric shapes.
Is this pyramid frustum calculator free to use?
Yes, this pyramid frustum calculator is completely free to use. No registration required, no limits on calculations, and all computations are performed instantly in your browser. You can calculate as many frustums as needed without any restrictions.
What units can I use for measurements?
You can use any consistent unit of measurement (inches, feet, meters, centimeters, millimeters, etc.). The calculator will maintain the same units for all results. Just ensure all input dimensions use the same unit for accurate calculations.
How accurate are the calculations?
Our calculator provides highly accurate results with precision up to 6 decimal places. All calculations use standard geometric formulas and are verified for mathematical accuracy. The results are suitable for professional engineering, architectural, and educational applications.
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