Truncated Square Pyramid Calculator

Enter top, base, and height values with units. Review volume, surface area, cost, and ratios. Download clean reports for records, estimates, and audits today.

Calculator Inputs

Leave blank to calculate it.

Formula Used

Let top square side be T, base square side be B, vertical height be h, and slant height be s.

Top area = T². Base area = B².

Volume = h ÷ 3 × (T² + B² + T × B).

Calculated slant height = √(h² + ((B − T) ÷ 2)²).

Lateral area = 2 × (T + B) × s.

Total surface area = T² + B² + lateral area.

Side edge = √(h² + ((B − T)² ÷ 2)).

Taper angle = atan(|B − T| ÷ (2h)).

How to Use This Calculator

  1. Enter the top square side, base square side, and vertical height.
  2. Select the unit used for every length value.
  3. Enter a known slant height only when it is measured directly.
  4. Add quantity, density, cost, and waste allowance when needed.
  5. Paste repeated measurements when you want sample statistics.
  6. Submit the form and review the result above the inputs.
  7. Use CSV or PDF export for records and sharing.

Example Data Table

Top Side Base Side Height Unit Volume Total Surface Area Use Case
375m155.000 m³245.108 m²Concrete hopper
486ft336.000 ft³383.059 ft²Roof cap
122015cm5,200.000 cm³1,813.151 cm²Display mold
2.553in43.750 in³76.512 in²Packaging insert

About the Truncated Square Pyramid Calculator

A truncated square pyramid is also called a square frustum. It appears in bins, hoppers, roof caps, stone blocks, molds, and packaging inserts. The shape has two parallel square faces. The lower face is usually larger. The upper face may also be larger. The vertical height connects both planes.

This calculator helps you study that shape with practical details. It finds volume, lateral area, total surface area, slant height, side edge, taper angle, top area, base area, mass, and material cost. It also supports quantity and waste allowance. Those options make the result useful for estimating and reporting.

Why Statistics Can Help

Real measurements are rarely perfect. A side length may change across samples. A height reading may vary by tool or operator. The optional sample box lets you enter repeated top, base, and height readings. The calculator can use their mean values. It also reports standard deviation and coefficient of variation. These statistics show how stable the measurements are.

A low coefficient of variation means readings are close together. A high value suggests more checking is needed. For production, this helps compare batches. For design, it helps choose safer allowances. For costing, it reduces surprise material gaps.

Practical Uses

Use the tool when planning concrete forms, metal transitions, architectural caps, storage hoppers, lamp shades, and display stands. Enter dimensions in one chosen unit. Then add density when weight matters. Add cost per cubic unit when material pricing matters. Use the waste field for cutting loss, shrinkage, spillage, or breakage.

The surface area result helps estimate coating, paint, wrapping, or sheet coverage. The volume result helps estimate filling, casting, packing, or excavation needs. The slant height supports side panel layout. The side edge helps check corner members.

Good Measurement Tips

Measure the top side and base side along matching directions. Use vertical height, not sloped side height, unless you enter a known slant separately. Keep units consistent. Record several readings for better reliability. Review the formula section before using results in a quote. Round outputs only after checking the required tolerance. Export the CSV or PDF when you need a record.

This keeps estimates consistent across teams. It also supports clear purchase reviews later.

FAQs

What is a truncated square pyramid?

It is a pyramid frustum with two parallel square faces. The top and base squares are connected by four sloped trapezoid faces.

Is vertical height the same as slant height?

No. Vertical height is perpendicular distance between the square faces. Slant height is measured along the middle of a side face.

Can the top side be larger than the base side?

Yes. The formulas still work when the top square is larger. The shape is simply inverted compared with the usual layout.

Why is there a sample measurement option?

It helps when measurements vary. You can paste repeated readings, use their means, and review standard deviation and variation.

How is volume calculated?

The calculator uses height divided by three, multiplied by top area, base area, and their square-root relation. For square faces, that becomes T² + B² + T × B.

What does waste allowance mean?

Waste allowance increases total volume for cutting loss, breakage, spillage, shrinkage, or safety margin. It does not change the single frustum size.

How should density be entered?

Enter density in kilograms per selected cubic unit. For example, use kg per m³ when the length unit is meters.

Can I export the results?

Yes. After calculation, use the CSV or PDF buttons to download the main result table for records, estimates, and reports.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.