Flat Top Cone Calculator

Measure frustum volume, areas, and patterns. Check slopes, surfaces, capacities, weights, and layout blanks fast. Enter top, base, and height values for precise outputs.

Enter Flat Top Cone Details

Formula Used

For a flat top cone, also called a frustum, the main volume formula is:

V = πh / 3 × (R² + Rr + r²)

Here, R is the bottom radius, r is the top radius, and h is the vertical height.

The slant height is:

s = √(h² + (R - r)²)

The lateral surface area is:

A = π(R + r)s

The full surface area adds top and bottom circular areas:

Total area = lateral area + πr² + πR²

For a sheet layout, the annular sector angle is:

Angle = 360 × |R - r| / s

How to Use This Calculator

  1. Select whether your top and bottom values are radii or diameters.
  2. Enter the bottom size, top size, and a known vertical or slant height.
  3. Select the measurement unit used for those dimensions.
  4. Add quantity, material thickness, density, and waste allowance if weight matters.
  5. Choose whether top and bottom faces are part of the material estimate.
  6. Press calculate to view the result above the form.
  7. Use the CSV or PDF button to save the output.

Example Data Table

Bottom Radius Top Radius Height Unit Use Case
12 6 10 in Small hopper
30 15 40 cm Reducer shell
2.5 1.25 3 ft Tank transition

What Is a Flat Top Cone?

A flat top cone is a cone with its tip cut away. It is also called a conical frustum. The shape has a large circular base, a smaller circular top, and a sloped side. It appears in hoppers, buckets, reducers, lampshades, funnels, tanks, and sheet metal transitions. A good calculator saves time because each result depends on several connected dimensions.

Why Accurate Inputs Matter

Small input errors can create large changes in volume and surface area. The top radius, bottom radius, height, and slant height must describe the same shape. If height is known, the slant height is found from a right triangle. If slant height is known, the vertical height can be reversed when the slant is long enough. Units also matter. A value entered in inches gives very different capacity than the same number entered in centimeters.

Useful Outputs

This tool gives volume, slant height, lateral area, end cap areas, total material area, capacity, layout radii, sector angle, and optional weight. These outputs help with design, estimating, cutting, and checking. For sheet work, the annular sector data is especially useful. It gives the inside radius, outside radius, and angle needed for a flat pattern. For a cylinder case, the layout becomes a rectangle instead.

Planning Material

Material estimates need more than geometry. Thickness, density, quantity, end caps, and waste allowance change the final weight and area. The calculator lets you include or exclude the top and bottom faces. That makes it suitable for open vessels, closed reducers, and simple display models. Waste allowance helps cover trimming, seams, and handling loss.

Practical Checks

Always confirm which value is radius and which value is diameter. Use the same unit for every length input. Keep the top size smaller than or equal to the base size for a normal flat top cone. Review the diagram in your own plan before cutting. The result table can be exported, stored, or shared with a fabricator.

Common Uses

Use this calculator during early planning and final checking. It supports makers, builders, students, and estimators. You can compare several sizes, then choose the best balance between capacity, surface area, and material demand before ordering stock or making a template.

FAQs

What is a flat top cone?

A flat top cone is a cone with the pointed tip removed. It has two circular ends and one sloped side. It is also called a frustum.

Can I use diameter instead of radius?

Yes. Select diameter from the input type menu. The calculator will convert each diameter into radius before applying the formulas.

What happens if both ends are the same size?

The shape becomes a cylinder. The volume and area still work, but the sheet pattern changes from an annular sector to a rectangle.

What is slant height?

Slant height is the straight distance along the side wall. It is longer than vertical height when the two radii are different.

Why add material thickness?

Thickness helps estimate weight. The calculator multiplies selected material area by thickness and density, then applies quantity and waste allowance.

Should I include top and bottom faces?

Include them when the part has closed ends. Leave them unchecked for an open funnel, hopper, sleeve, or side wall only estimate.

What does the sector angle mean?

The sector angle describes the flat sheet pattern for the side wall. It helps create a cutting template for fabrication work.

Can I export the results?

Yes. After calculation, use the CSV button for spreadsheet data or the PDF button for a simple printable report.

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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.