This Conical Frustum Volume Calculator helps you quickly calculate the volume of a frustum — a shape formed when a circular cone is sliced by two parallel planes, removing the smaller cone from the top.
Commonly used in geometry, engineering, and even computer science, a conical frustum appears in structures like buckets, lampshades, and funnels. This tool computes the volume using the formula involving both the base radius and the radius of the top surface, as well as the height of the frustum.
The calculator is based on the standard formula for the volume of a conical frustum:
Volume = (1/3) × π × h × (R² + Rr + r²)
Where:
R = base radius (bottom)
r = top radius (top surface)
h = vertical height (not the slant height)
π ≈ 3.1416
What Is a Conical Frustum?
A frustum is a cone with its top sliced off by a plane parallel to the base. It has a top and bottom circle, with different radii. This 3D shape is often called a truncated cone.
How It Works
- Enter the base radius (R): This is the radius of the larger, bottom circle.
- Enter the top radius (r): The radius of the smaller, upper circle.
- Enter the vertical height (h): This is the perpendicular distance between the two circular faces (not the slant height).
- Click "Calculate": The tool will apply the formula and return the volume of the cone that has been truncated.
Why Use This Cone Calculator?
- Instant and accurate results for the volume of a conical frustum
- Supports units for scientific or practical use
- Helpful for students, engineers, and anyone in computer science or design
Frequently Asked Questions
1. What’s the difference between slant height and vertical height?
The slant height is the diagonal side length of the frustum, while the vertical height is the perpendicular distance between the top and bottom surfaces — used in the volume calculation.
2. Can I use this to calculate the volume of a full cone?
This calculator is specifically for a truncated cone or frustum. For a full cone, use a standard cone calculator that uses the formula (1/3) × π × r² × h.
3. Why is the volume formula using 1/3 π?
The factor 1/3 π comes from the derivation of the volume of a cone. For frustums, it is applied to both radii and height to find the partial volume of what was once a whole cone.