Conical Frustum Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The volume of a conical frustum is calculated with V = (πh ÷ 3) × (R² + Rr + r²), where R is the large radius (at the base), r the small radius (at the truncated top), and h the height between them. For a frustum with a large radius of 5 cm, small radius 3 cm, and height 6 cm, the volume is about 307.88 cm³.
Explanation
A conical frustum is what remains of a cone once its tip has been cut off by a plane parallel to its base — the characteristic shape of a bucket, a lampshade, or a paper cup. Its volume formula directly generalizes that of the full cone, and can be checked by two notable limiting cases: when the small radius r becomes zero, the formula reduces exactly to (πh/3)×R², the formula for the full cone — confirmed exactly by this calculator's second test case, identical to the first example of our cone volume calculator. At the other extreme, when the two radii become equal (R = r, no reduction in radius between base and top), the formula reduces exactly to π×R²×h, the formula for a cylinder — confirmed by the third test case, which incidentally gives the same numerical value (113.097... cm³) as this site's emblematic example of a sphere of radius 3 cm, a numerical coincidence specific to that particular radius rather than a general property. The conical frustum appears frequently in practice: a bucket, a flared flowerpot, a fries cone, or the cross-section of a truncated-cone dam.
Example: large radius 5 cm, small radius 3 cm, height 6 cm
Inputs
Large radius: 5 cm. Small radius: 3 cm. Height: 6 cm.
Calculation
V = (π × 6 ÷ 3) × (5² + 5×3 + 3²) = 2π × (25 + 15 + 9) = 2π × 49 = 98π ≈ 307.88 cm³.
Result
The volume of this conical frustum is about 307.88 cm³.
Frequently asked questions
What happens if the small radius is zero?
The frustum becomes a full cone again, with no truncation: the formula simplifies exactly to that of the cone, V = (πh/3)×R², since all terms containing r vanish. This is exactly what this calculator's second test case verifies, identical to the result of our cone volume calculator for the same dimensions.
What happens if the two radii are equal?
The frustum becomes a perfect cylinder, with no taper between base and top: the formula reduces exactly to V = π×R²×h, the usual formula for the volume of a cylinder — a result confirmed directly by this calculator's third test case.
How do you calculate the lateral surface area of a conical frustum?
That lateral area is calculated with a different formula, π×(R+r)×g, where g is the slant height of the frustum (the length of the oblique side, computable by the Pythagorean theorem from the difference of the radii and the height). This calculator focuses on the volume; the lateral area follows logic similar to that already presented for the full cone.