Horizontal Dish End Tank Volume Calculator

This calculator works out the volume of a horizontal cylindrical tank with dish-shaped (torispherical or elliptical) ends. You enter the tank diameter, the straight shell length, and the dish depth, and it returns the total volume in litres, cubic metres, and US gallons.

Formula

The total volume of a horizontal tank with dished ends is the sum of the cylindrical shell volume and the two dish end volumes:

V_total = V_shell + 2 × V_dish

Where:

• V_shell = π × (d/2)² × L (the volume of the straight cylindrical part)
• V_dish = π × h × (3 × (d/2)² + h²) / 6 (the volume of one spherical-cap-shaped end)
• d = internal diameter of the tank (m)
• L = length of the straight shell, excluding the dish ends (m)
• h = depth of the dish (the distance the end protrudes from the straight shell, m)

This formula treats each dish end as a spherical cap. It is accurate for true spherical caps and a good approximation for standard torispherical (ASME F&D) and elliptical heads when the dish depth is known. For ASME heads, the dish depth is typically about 0.194 × diameter (for a 2:1 elliptical head, h = d/4).

Worked Example

Using the default values from the calculator: diameter d = 2.0 m, shell length L = 4.0 m, dish depth h = 0.3 m.

1. Calculate the shell volume: V_shell = π × (1.0)² × 4.0 = 12.566 m³
2. Calculate one dish volume: V_dish = π × 0.3 × (3 × 1.0² + 0.3²) / 6 = π × 0.3 × (3 + 0.09) / 6 = π × 0.3 × 3.09 / 6 = 0.4854 m³
3. Total volume: V_total = 12.566 + 2 × 0.4854 = 13.537 m³
4. In litres: 13.537 × 1000 = 13,537 L
5. In US gallons: 13.537 × 264.172 = 3,576 US gal

The calculator shows 13.54 m³, 13537 L, and 3576.1 US gal, matching the manual calculation.

Why Dish Ends Matter

Flat-ended tanks are cheaper to make but cannot withstand high internal pressure. Dished ends are curved to distribute stress more evenly, so they are used on pressure vessels, storage tanks, and heat exchangers. The dish depth (h) is the key extra dimension you need beyond the cylinder length. Many tank drawings list “length” as the overall length including the dishes, so you must subtract the two dish depths to get the straight shell length.

How to Read the Result

The calculator gives the total volume when the tank is completely full. For a horizontal tank, the liquid volume at a given fill level is not linear – it depends on the cross‑sectional area of a partially filled circle. That requires a separate calculation using the liquid height. The result here is useful for sizing, capacity planning, and estimating the total contents when full.

Common Mistakes

• Using overall length instead of shell length – always subtract the two dish depths from the overall length.
• Unit mix-ups – if you enter diameter in inches and length in feet, the volume will be wrong. Keep all dimensions in the same unit.
• Ignoring the dish depth – for a 2 m diameter tank, a 0.3 m dish adds about 4% to the volume. That can be significant for large tanks.
• Using the wrong dish volume formula – the spherical cap formula works for any dish as long as you know the depth, but some tables give the volume of a torispherical head differently. The difference is small for typical proportions.

Choosing the Right Dish Type

Common dish types include:

• Elliptical (2:1) – depth = d/4. Used for high pressures.
• Torispherical (ASME F&D) – depth ≈ 0.194 × d. A common compromise.
• Hemispherical – depth = d/2. The strongest but most expensive.
• Flat – depth = 0. No pressure rating.

If you only know the dish type, use the depth ratios above. For a 2 m diameter ASME head, h = 0.388 m; for a 2:1 elliptical, h = 0.5 m.

Frequently Asked Questions

What if my tank has elliptical heads – does the same formula work?

Yes, the spherical cap formula is a close approximation for elliptical heads as long as you use the actual dish depth. For a 2:1 elliptical head, the depth is d/4. The volume difference from the true elliptical formula is typically less than 1%.

How do I find the dish depth if I only have the overall length?

Subtract the straight shell length from the overall length, then divide by 2 (since there are two ends). For example, if overall length is 5 m and the straight shell is 4.4 m, each dish depth is (5 – 4.4)/2 = 0.3 m.

Can I use this for a vertical tank?

No. This calculator is for horizontal tanks. For a vertical tank with dished ends, the volume is the cylinder volume plus the two dish volumes, but the formula is the same – you just don’t need to worry about the horizontal orientation for total volume.

Why does the calculator ask for shell length, not overall length?

Because the dish ends add volume beyond the straight cylinder. If you enter overall length, you would double‑count the dish volume. The calculator needs the straight part only.

What units should I use?

Any consistent unit works, but the calculator defaults to metres. If you use feet, the volume will be in cubic feet – you can convert to gallons by multiplying by 7.48052. The calculator’s outputs are in m³, litres, and US gallons, so it’s easiest to enter metres.

Is the volume affected by the thickness of the tank wall?

Yes, the calculator uses internal dimensions. If you only have external dimensions, subtract the wall thickness twice from the diameter and once from the length (or use the internal dimensions directly). For thin walls the difference is small, but for thick vessels it matters.

Related

• Cylindrical Tank Volume Calculator: Formula & Examples
• Diesel Tank Volume Calculator: How to Estimate Gallons
• Yards to Square Feet Calculator: How to Convert

in d | Tank diameter | m | 2.0 | 0
in l | Shell length (straight side) | m | 4.0 | 0
in h | Dish depth (each end) | m | 0.3 | 0
out vol_total | Total volume | m³ | (pi * d^2 / 4) * l + 2 * (pi * h * (3 * (d/2)^2 + h^2) / 6) | 2
out vol_litres | Volume | L | vol_total * 1000 | 0
out vol_usgal | Volume | US gal | vol_total * 264.172 | 1