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
- Enter the **Top Radius** of the frustum.
- Enter the **Bottom Radius** (often the larger one).
- Enter the vertical **Height** between the two bases.
- 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.