▸ processconvert
Process Design

Tank Diameter & Height Calculator

This calculator works the vertical cylindrical tank volume relation in three directions. It can compute the geometric volume from diameter and straight-side height, or solve for the diameter or height needed to reach a target working volume. An optional fill (working) fraction converts between geometric volume and the usable working volume. It is a preliminary sizing estimate only — it covers the straight side of a flat-bottomed cylinder and does not size dished heads, cones, freeboard, internals, or mechanical design.

TypeInteractive engineering calculator

Calculator

m
m
%
Result
Geometric volume35.3429 m³
Working volume28.2743 m³
Diameter3 m
Straight-side height5 m
Fill fraction80 %

Preliminary geometric estimate — straight side only. Not a final vessel design.

Formulas

Geometric volume
V = π × D² / 4 × H
Working volume
V_working = V × fill fraction
Diameter from volume
D = √(4V / (π × H))
Height from volume
H = 4V / (π × D²)

Diagram

Tank Diameter & Height: V = πD²/4 × HworkingvolumeD (diameter)H (straight side)V = πD²/4 × H

Worked example

A vertical cylindrical tank has an internal diameter of 3.0 m and a straight-side height of 5.0 m, operated at an 80% working fill fraction. What are the geometric and working volumes?

  1. 01V = π × D² / 4 × H
  2. 02V = π × 3.0² / 4 × 5.0
  3. 03V = π × 11.25
  4. 04V = 35.34 m³ (geometric)
  5. 05V_working = 35.34 × 0.80 = 28.27 m³
Result

Geometric volume ≈ 35.34 m³; working volume at 80% fill ≈ 28.27 m³.

FAQ

Does this include dished heads or a conical bottom?
No. Only the straight-side cylindrical volume is calculated. Dished heads (torispherical, ellipsoidal, hemispherical) and conical bottoms add volume that is not included here.
What is the difference between geometric and working volume?
Geometric volume is the full internal capacity of the straight side. Working volume is the portion actually used in operation, set by the fill fraction. Tanks are rarely run full — freeboard, surge allowance, and control range mean the working volume is typically 70–90% of geometric volume.
Can I use this as a final tank design?
No. This is a preliminary sizing estimate. Final vessel design requires mechanical design (wall thickness, heads, supports), freeboard and surge allowances, agitation and nozzle layout, and review against applicable standards and project specifications.
How does this differ from the Tank Volume calculator?
The Tank Volume calculator computes the geometric volume of rectangular, vertical, and horizontal tanks in the forward direction only. This calculator adds inverse sizing — solving for the diameter or height needed to reach a target working volume — plus a fill-fraction working-volume step.

Related conversions