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
Calculator
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:
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?
- Measure or take from the drawing the radius of the larger base R, the radius of the smaller base r, and the height h.
- Enter the values into the fields of the calculator.
- Choose the desired precision of the result.
- 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.