Dish End Tank Volume Calculator

A dish end tank volume calculator works out the total volume of a cylindrical tank with dished (curved) heads, using the cylinder length, the tank diameter, and the dish depth. You enter those three dimensions, and it returns the combined volume of the cylindrical shell and both dished ends in your chosen units. This page explains the formula, shows a worked example, and covers the practical details you need to measure a dished-end tank accurately.

Formula

The total volume of a dished-end tank is the sum of the cylindrical section and the two heads. For a standard 2:1 elliptical head (the most common type), the volume of one head is:

V_head = (π × h × (3 × (D/2)² + h²)) / 6

Where:

• V_head = volume of one dished head (m³, ft³, etc.)
• π ≈ 3.14159
• h = dish depth, the distance from the tangent line to the crown (m, ft)
• D = internal tank diameter (m, ft)

The cylindrical section volume is simply the area of the circle times the length:

V_cyl = (π × D² / 4) × L

Where L is the cylinder length between the tangent lines (the straight part, not including the heads). Total volume = V_cyl + 2 × V_head.

Worked Example

Using the default values from the calculator: D = 1.0 m, L = 2.0 m, h = 0.15 m.

1. Cylinder volume: (π × 1.0² / 4) × 2.0 = (3.14159 × 1 / 4) × 2 = 0.7854 × 2 = 1.5708 m³
2. One head volume: (π × 0.15 × (3 × (0.5)² + 0.15²)) / 6 = (3.14159 × 0.15 × (0.75 + 0.0225)) / 6 = (3.14159 × 0.15 × 0.7725) / 6 = (3.14159 × 0.115875) / 6 = 0.3640 / 6 = 0.0607 m³
3. Two heads: 2 × 0.0607 = 0.1214 m³
4. Total: 1.5708 + 0.1214 = 1.6922 m³

The calculator rounds to three decimals, giving 1.692 m³, which equals 1,692 liters.

When to Use This Calculator

Use this calculator when you need the full volume of a tank with dished ends – for example, to estimate how much liquid a storage tank holds, to size a pressure vessel, or to calculate the volume of a reactor or separator. It is also helpful for estimating the amount of liquid in a partially filled tank, though that requires a more complex formula that accounts for the fill level.

For horizontal tanks, the cylinder length is the straight side between the two heads. For vertical tanks, the same formula applies, but you would typically measure the height of the cylindrical section instead of length.

How to Measure the Dimensions

Accurate measurements are critical. Here are the key points:

• Diameter (D): Measure the internal diameter of the cylindrical shell. If you only have the outside diameter, subtract twice the wall thickness.
• Cylinder length (L): This is the distance between the tangent lines – the points where the straight cylinder meets the curved head. On a real tank, this is often measured from the weld seam or the start of the curvature. Do not include the heads.
• Dish depth (h): Measure from the tangent line to the deepest point of the head (the crown). For a 2:1 elliptical head, the depth is typically one-quarter of the diameter (h = D/4). For other shapes like torispherical or hemispherical, the depth differs.

Common Mistakes and Misconceptions

The most frequent error is using the overall tank length (including the heads) instead of the cylinder length. This overestimates the volume because the heads are not full cylinders. Another common mistake is using the wrong dish depth – for a 2:1 head, the depth is D/4, but many people measure the total head height including the straight flange (the short cylindrical lip), which adds extra volume.

Also, be careful with units. If you measure in inches, the volume will be in cubic inches; convert to gallons (1 gallon = 231 in³) or liters (1 L = 61.02 in³) as needed. The calculator above works in meters, but you can use any consistent unit – just be consistent.

Limitations of the Formula

The formula assumes perfectly elliptical heads. Real heads may have manufacturing tolerances, and the exact shape might be torispherical (with a knuckle radius) or hemispherical. For torispherical heads, the volume is slightly different, but the elliptical formula is a good approximation for most purposes. Also, the formula gives the internal volume of an empty tank – if the tank has internal components (baffles, coils, agitators), subtract their volume for a net capacity.

For partially filled tanks, the volume of the liquid depends on the fill level and the orientation (horizontal or vertical). That calculation is more complex and not covered by this simple formula.

Frequently Asked Questions

What is a 2:1 elliptical head?

A 2:1 elliptical head has a dish depth equal to one-quarter of the diameter (h = D/4). This shape is widely used in pressure vessels because it offers a good balance of strength and material usage. The volume formula given above is exact for this shape.

How do I convert the volume to gallons?

If you measure in meters, multiply the cubic meters by 264.172 to get US gallons, or by 1000 to get liters. For imperial gallons, multiply by 219.969. If you measure in inches, divide cubic inches by 231 for US gallons.

Can I use this for a horizontal tank?

Yes, the total volume is the same regardless of orientation. However, if you need the volume of liquid at a certain level, you need a different calculation that accounts for the fill height and the shape of the heads.

What if my head is not elliptical?

For torispherical heads (like ASME F&D), the volume is slightly less than an elliptical head of the same depth. For hemispherical heads, the depth equals the radius (h = D/2), and the volume is simply the sphere volume. In practice, the elliptical formula is often used as a good approximation for torispherical heads.

Why does my tank hold less than the calculated volume?

This can happen if the tank has internal fittings, if the heads are not perfectly elliptical, or if the cylinder length was measured incorrectly (including the head’s straight flange). Also, the nominal diameter might be the outside diameter, not the inside. Always use internal dimensions.

Do I need to include the thickness of the tank wall?

Only if you are calculating the volume of the contents – then you must use the internal dimensions. If you are calculating the volume of the metal (for weight), you would use the outside dimensions and subtract the inside volume. The calculator here gives the internal volume.

Related

• Octagonal Prism Volume Calculator & Formula
• Prism Volume Calculator: Formula & Steps
• Rectangular Prism Volume Formula Calculator

in d | Tank diameter | m | 1.0 | 0
in l | Cylinder length (tan-to-tan) | m | 2.0 | 0
in h | Dish depth | m | 0.15 | 0
out v | Total volume | m³ | (pi * d^2 / 4) * l + 2 * (pi * h * (3 * (d/2)^2 + h^2) / 6) | 3
out v_l | Volume in liters | L | v * 1000 | 0