Frustum (Truncated Cone) Calculator

Volume, slant height and surface area of a conical frustum (truncated cone) such as a bucket, planter or lampshade, from both radii and the height.

Half the diameter of one end.
Half the diameter of the other end. Enter 0 for a full cone.
Perpendicular distance between the two ends, not the slant.
Volume
4.1344
Slant height
12.166
Lateral (side) area
382.19
Total surface area (sides + both ends)
545.55
Surface area, open top (sides + bottom)
495.29

Estimate generated with SortedSums: https://sortedsums.com/frustum-calculator/. For informational purposes only; verify before relying on it.

How it’s calculated

A frustum is a cone with its tip cut off parallel to the base. Its volume is the big cone minus the small cone, which simplifies to:

V = (π h / 3) × (R² + R r + r²) Slant height l = √((R − r)² + h²) Lateral area = π (R + r) l Total area = π (R + r) l + π R² + π r²

Example (a tapered bucket): R = 6 in, r = 4 in, h = 12 in. V = (π × 12 / 3) × (36 + 24 + 16) = 304π ≈ 955.0 in³ ≈ 4.13 US gal. l = √(4 + 144) ≈ 12.166 in; lateral area = π × 10 × 12.166 ≈ 382.2 in².

Frequently asked questions

What is a frustum?

The part of a cone (or pyramid) left between the base and a cut parallel to it. Buckets, flower pots, lampshades and some tanks are frustums.

Can I use average radius × height?

No, π × ((R + r)/2)² × h underestimates the volume. The exact formula adds the R·r term: V = πh(R² + Rr + r²)/3.

What if the top is wider than the bottom?

The formulas are symmetric in R and r, so just enter the two radii in either field.

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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