Vessel Volume Calculator | Cylinder + Heads (hemispherical, ellipsoidal, torispherical)

Chemicaltweak Vessel Volume Calculator is an Easy online tool that helps chemical engineering students and process engineers to get ellipsoidal, spherical, torispherical & flat head vessel volumes just by entering data.

Chemical Engineering Vessel Volume Calculator

Calculate volume filled in various vessel types with different head shapes

Vessel Parameters

Horizontal Vertical
mm
mm
mm
mm

Results

Volume Calculation

Filled Volume:
0 m³
Total Volume:
0 m³
Fill Percentage:
0%

Vessel Diagram

Calibration Chart

Level % Level (mm) Volume (m³)

How to use Vessel volume calculator

Inputs the calculator uses:

  • Diameter (D) — inside diameter of the shell.
  • Straight length (L) — length of the cylindrical shell only.
  • Head type — hemispherical, ellipsoidal (2:1), torispherical approximations, flat.
  • Dish depth or parameters for torispherical heads when needed.
  • Liquid level (H) — measured from the lowest inside point of the vessel.

Units in the UI are mm. The calculator converts to meters for volume.

Outputs:

  • Cylinder volume, head volume (each), total vessel volume.
  • Filled volume at the given level
  • Fill percentage
  • Calibration table (levels vs volume)

You can also use the Unit Converter for Engineers (Free downloadable pdf) to convert pressure, volume, or length units while calculating vessel volume.

What is a Vessel Volume Calculator?

A vessel volume calculator is an online tool that helps chemical engineering students and process engineers calculate the volume of industrial vessels with different head types like ellipsoidal, spherical, torispherical, or flat head vessels. This calculator provides accurate volume measurements instantly.

Tank volume  formula

All the formulas used in the calculator are listed below.

Parameters

  • Diameter: D
  • Radius: r = \frac{D}{2}
  • Straight Length: L
  • Liquid Level: H

1. Ellipsoidal Head (2:1 Elliptical)

Dish Depth:

a = \frac{D}{4}

Head Volume:

V_{head} = \frac{\pi}{6}D^2 a

2. Spherical (Hemispherical) Head

Dish Depth:

a = \frac{D}{2} = r

Head Volume:

V_{head} = \frac{2\pi r^3}{3}

3. Torispherical (ASME F&D)

Parameters: f = 1.0, k = 0.1

Approximate Dish Depth:

a \approx 0.2D

Head Volume (approximation):

V_{head} = \frac{\pi D^2 a}{6}

Use the Pipe Volume Calculator to estimate the liquid volume inside pipes for hydrotest and passivation.

4. Torispherical (Standard F&D)

Parameters: f = 1.0, k = 0.06

Approximate Dish Depth:

a \approx 0.2D

Head Volume (approximation):

V_{head} = \frac{\pi D^2 a}{6}

5. Torispherical (80:10 F&D)

Parameters: f = 0.8, k = 0.1

Approximate Dish Depth:

a \approx 0.2D

Head Volume (approximation):

V_{head} = \frac{\pi D^2 a}{6}

6. Flat Head

Dish Depth:

a = 0

Head Volume:

V_{head} = 0

Total Volume (All Types)

Cylinder Volume:

V_{cylinder} = \pi r^2 L

Total Vessel Volume:

V_{total} = \pi r^2 L + 2V_{head}