Truncated cone volume calculator

Enter the parameters of the truncated cone, choose the calculation option, specify the precision and click "Calculate" — the calculator will instantly compute the volume.

Truncated cone surface area calculator

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What is a truncated cone (frustum)?

A truncated cone (or frustum) is a geometric solid formed by cutting off the top of a cone with a plane parallel to its base. It has two circular bases of different radii and a lateral surface.

Formula for the volume of a truncated cone

The volume of a truncated cone is calculated using the following formula:

V = 1 3 π h ( R 2 + R r + r 2 )

where:

  • R — radius of the larger base;
  • r — radius of the smaller base;
  • h — height of the truncated cone;
  • π ≈ 3.14159.

Real-world applications of the truncated cone

A truncated cone is a very common shape in real life, so calculating its volume is necessary in many areas:

  • Construction and Architecture. Towers, domes, bridge piers, and decorative columns often have the shape of a truncated cone. Knowing the volume helps calculate the consumption of concrete or other materials.
  • Manufacturing and Industry. Buckets, funnels, hoppers, and industrial tanks frequently take this shape — volume calculations help determine their capacity.
  • Agriculture. Silos and granaries often have a conical shape — calculating the volume helps determine the amount of grain or feed.
  • Landscape Design. When planning mounds, conical flower beds, or decorative hills, the volume of soil to be brought in is calculated.
  • Food Industry. Funnels, dispensers, containers for liquids and bulk products often have the shape of a truncated cone.
  • 3D Printing and Modeling. When designing parts, the volume must be known to calculate material consumption and the weight of the product.

How to use the calculator?

  1. Measure or take from the drawing the radius of the larger base R, the radius of the smaller base r, and the height h.
  2. Enter the values into the fields of the calculator.
  3. Choose the desired precision of the result.
  4. Click "Calculate" — the result will appear instantly.

Frequently Asked Questions

What is the difference between a cone and a truncated cone?
A regular cone has a single circular base and tapers to a point (apex). A truncated cone (frustum) is formed when the top is cut off with a plane parallel to the base, leaving two circular bases of different sizes.

What units does the calculator use?
The calculator works with any consistent units — centimeters, meters, inches, or feet. Just make sure all three values (R, r, h) use the same unit. The result will be in cubic units accordingly.

Can the radii be equal?
If R equals r, the shape becomes a cylinder, and the formula still works correctly — it simplifies to V = π·r²·h.