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Process Design

Cone-Bottom Tank Volume Calculator

Cone-bottom (conical-bottom) tanks are common in process and mineral-processing service because the cone promotes complete drainage of solids and slurry. The total volume is the straight-side cylinder plus the conical bottom, and the volume at a given level depends on whether the liquid sits inside the cone or above it. This calculator estimates the cylinder volume, cone volume, total geometric volume, and the liquid volume at a fill level measured from the cone tip. It is a preliminary geometric estimate assuming a right circular cone — not a calibrated strapping table and not a mechanical or pressure-vessel design.

TypeInteractive engineering calculator

Calculator

m
m
m
Result
Cylinder volume35.3429 m³
Cone volume3.53429 m³
Total geometric volume38.8772 m³
Cone fraction of total9.09091 %

Preliminary geometric estimate — right circular cone bottom. Ignores fillets, nozzles, dished transitions, and internal equipment. Not a calibrated strapping table or mechanical design.

Formulas

Cylinder volume
V_cyl = π·D²/4 · H_cyl
Cone volume
V_cone = (1/3)·π·D²/4 · H_cone
Total volume
V_total = V_cyl + V_cone
Within cone (level y ≤ H_cone)
V = (1/3)·π·r_y²·y, r_y = R·y/H_cone
Above cone (level y > H_cone)
V = V_cone + π·R²·(y − H_cone)

Diagram

Cone-bottom tank: V = V_cyl + V_coneDH_cylH_coneV = V_cyl + V_cone

Worked example

A cone-bottom tank has a diameter of 3.0 m, a straight-side cylinder height of 5.0 m, and a cone height of 1.5 m. What is the total geometric capacity?

  1. 01V_cyl = π·D²/4 · H_cyl = π × 3²/4 × 5 = π × 11.25 = 35.34 m³
  2. 02V_cone = (1/3)·π·D²/4 · H_cone = (1/3) × π × 2.25 × 1.5 = 3.53 m³
  3. 03V_total = V_cyl + V_cone = 35.34 + 3.53 = 38.88 m³
  4. 04Cone fraction = 3.53 / 38.88 ≈ 9.1%
Result

Cylinder volume ≈ 35.34 m³; cone volume ≈ 3.53 m³; total volume ≈ 38.88 m³.

FAQ

Why does the cone add so little volume?
A cone holds one-third of the cylinder of the same diameter and height. For a shallow cone bottom the cone height is usually much smaller than the straight side, so the cone is a small fraction of the total — typically under 10–15% — even though it dominates the drainage behaviour.
How is the fill level measured?
In the partial-fill mode the level is measured from the cone tip (the lowest point). Below the cone height the liquid fills the cone and the wetted radius grows linearly; above the cone height the liquid fills the straight cylinder at the full diameter.
Does this handle a truncated (frustum) cone bottom?
No. This assumes a full right circular cone to a point. A truncated cone (frustum) with a flat bottom outlet has a different volume and is not covered here.
Can I use this for inventory or custody transfer?
No. It is a preliminary geometric estimate. Inventory, custody, and design work require the vendor drawings and a calibrated strapping table for the actual vessel.

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