Ellipsoidal Head Volume Calculator

Calculate 2:1 semi-ellipsoidal head volume and partial depth liquid capacity for pressure vessels.

⬭ Calculate Ellipsoidal Head Volume

What is an Ellipsoidal Head Tank?

An ellipsoidal head tank features dished ends shaped with a 2:1 elliptical cross-section. This standardized geometric shape offers optimum wall strength and volume for high-pressure boilers and chemical reactors.

Reference codes at ASME Boiler & Pressure Vessel Code.

How This Calculator Works

To use this calculator, enter the inside diameter (D) of your ellipsoidal head and optional straight flange height (sf). The calculator converts all dimensions to meters, applies the 2:1 semi-ellipsoidal volume equation, and outputs total liquid capacity in US Gallons, Litres, Cubic Feet, Cubic Meters, and Imperial Gallons. For complete tank calculations, see our dish-end tank volume calculator and fuel tank volume calculator.

How to Use the Ellipsoidal Head Volume Calculator

Easily determine 2:1 semi-ellipsoidal head capacity with these clear point-by-point steps:

  1. Enter Head Inside Diameter (D): Measure and input the internal diameter of the pressure vessel head.
  2. Enter Straight Flange Height (sf): Input the straight flange length (leave blank if zero).
  3. Choose Measurement Units: Select ft, in, m, or cm for accurate dimension conversion.
  4. Click "Calculate Volume": Submit the form to compute the 2:1 semi-ellipsoidal dome volume.
  5. Check Results Table: View total liquid capacity displayed in US Gallons, Litres, Cubic Feet, Cubic Meters, and UK Gallons.

ASME 2:1 Semi-Ellipsoidal Head Volume Formula

For a standard ASME 2:1 semi-ellipsoidal head, the minor axis depth equals one-fourth of the inside diameter (h = D / 4). The internal volume formula combines the semi-ellipsoid dome volume and straight flange cylinder volume:

2:1 Ellipsoidal Head Formula:

Volume = (π / 24) × D³ + (π / 4) × D² × sf

Where D is inside diameter and sf is straight flange length.

Advantages of 2:1 Ellipsoidal Dished Heads

Ellipsoidal heads provide smooth stress transitions under high internal pressures, reducing required wall thickness compared to flat or shallow dished ends while maintaining high liquid capacity. Scientific geometry reference: Wolfram MathWorld Ellipsoidal Geometry Reference.

Standard Tank Capacity & Volume Sizing Chart

Tank Sizing / Model Typical Dimensions Litres US Gallons
500 Litres (132 gal)0.86m × 0.95m (2.8ft × 3.1ft)500 L132 gal
1,000 Litres (264 gal)1.10m × 1.15m (3.6ft × 3.8ft)1,000 L264 gal
2,500 Litres (660 gal)1.45m × 1.60m (4.8ft × 5.2ft)2,500 L660 gal
5,000 Litres (1,320 gal)1.85m × 1.95m (6.1ft × 6.4ft)5,000 L1,320 gal
10,000 Litres (2,640 gal)2.35m × 2.40m (7.7ft × 7.9ft)10,000 L2,640 gal

Frequently Asked Questions

What does 2:1 ratio mean in ellipsoidal heads?

A 2:1 ellipsoidal head has an inside diameter that is exactly twice its internal dish depth (Dish Depth = Diameter / 4).

What is the volume formula for a 2:1 semi-ellipsoidal head?

The formula for dish volume is V = (π / 24) × D³. Adding straight flange gives V = (π / 24) × D³ + (π / 4) × D² × sf.

Why are 2:1 ellipsoidal heads preferred for high-pressure storage?

They provide optimal stress distribution, allowing thinner wall thickness compared to torispherical heads for the same pressure rating.

How does dish depth relate to inside diameter in 2:1 heads?

Internal dish depth equals 25% of the inside diameter (Depth = D / 4).

How do I calculate total vessel volume with two ellipsoidal heads?

Calculate the main cylinder shell volume (V = π × r² × L) and add the volume of the two ellipsoidal heads (2 × head volume).