Geometry Tool

Conical Frustum Calculator

Calculate the volume and surface area of a truncated cone (a cone with the top cut off).

Σ The Formula

V = (1/3)πh(R² + Rr + r²)

Real World Examples

Lampshade
Top r=4in, Bottom r=8in, h=10in → V=1172.86 in³
Bucket
Top r=15cm, Bottom r=10cm, h=30cm → V=15.1 liters

# About This Calculator

A Conical Frustum is a truncated cone. It is the portion of a cone that remains after its top is cut off by a plane parallel to its base. This shape is ubiquitous in everyday objects like buckets, flower pots, and lampshades.

Calculating its properties requires the radius of the larger base ($R$), the radius of the smaller base ($r$), and the vertical distance between them ($h$). Understanding the volume and area of this shape is essential for industrial design and construction.

How To Use

  1. Enter the **Top Radius** of the frustum.
  2. Enter the **Bottom Radius** (often the larger one).
  3. Enter the vertical **Height** between the two bases.
  4. Click **Calculate Frustum** to see the volume, total surface area, and the slant height.

Frequently Asked Questions

What happens if r1 equals r2?+

If the top and bottom radii are equal, the shape becomes a cylinder. The frustum formula naturally simplifies to the cylinder volume formula (πr²h) in this case.

Can I use diameter instead?+

No, this tool uses radii. If you have the diameter, simply divide it by 2 before entering the value.

Is Conical Frustum Calculator free to use?+

Yes, Conical Frustum Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

How accurate is Conical Frustum Calculator?+

We use standard mathematical formulas and high-precision computing algorithms to ensure results for Conical Frustum Calculator are accurate for academic and professional use.

Can I use Conical Frustum Calculator on my phone?+

Yes! Conical Frustum Calculator is fully responsive and optimized for all devices, including smartphones, tablets, and desktops.

Do you save my data?+

No. We prioritize your privacy. All calculations are performed in your browser or temporarily processed, and we do not store your personal input data.

About

A Conical Frustum is a truncated cone. It is the portion of a cone that remains after its top is cut off by a plane parallel to its base. This shape is ubiquitous in everyday objects like buckets, flower pots, and lampshades.

Calculating its properties requires the radius of the larger base ($R$), the radius of the smaller base ($r$), and the vertical distance between them ($h$). Understanding the volume and area of this shape is essential for industrial design and construction.

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