Capsule Tank Volume Calculator: How to Find It

A capsule tank volume calculator works out the total capacity of a horizontally or vertically oriented capsule-shaped vessel—a cylinder with rounded ends—when you enter the tank’s diameter and overall length. It returns the volume in the unit you choose, such as liters, gallons, or cubic feet, so you can size a tank, plan a fill, or check a spec sheet.

Formula

The capsule is treated as a cylinder of length L minus one diameter (because the two hemispherical ends each take up half a diameter of the overall length) plus a sphere of diameter d. The volume is:

V = π × (d/2)² × (L − d) + (4/3) × π × (d/2)³

• V – total volume (cubic meters, liters, gallons, etc.)
• d – diameter of the cylinder and the hemispherical ends (same unit as L)
• L – overall length from one outer edge to the other (same unit as d)
• π – approximately 3.14159

If you measure in meters, the result is in cubic meters. Multiply by 1000 to get liters, or by 264.172 to get US gallons (1 cubic meter = 264.172 US gallons). For imperial gallons, multiply by 219.969.

Worked Example

Using the default values: diameter d = 1.2 m, overall length L = 3.0 m.

1. Cylinder radius = 1.2 / 2 = 0.6 m
2. Cylinder portion length = 3.0 − 1.2 = 1.8 m
3. Cylinder volume = π × (0.6)² × 1.8 = 3.14159 × 0.36 × 1.8 = 2.03575 m³
4. Sphere volume (two hemispheres) = (4/3) × π × (0.6)³ = 4.18879 × 0.216 = 0.90478 m³
5. Total volume = 2.03575 + 0.90478 = 2.94053 m³
6. In liters: 2.94053 × 1000 = 2940.5 L
7. In US gallons: 2.94053 × 264.172 = 776.8 gal

The calculator shows 2940.5 L, 2.941 m³, and 776.8 gal—matching the steps above.

When to Use a Capsule Tank Calculator

Capsule tanks appear in many real-world settings: fuel storage on trucks, hydraulic oil reservoirs, air receivers, chemical storage, and even some water tanks on boats or RVs. You might need the volume to:

• Estimate how much liquid a new tank will hold before buying.
• Check whether a tank meets a project’s capacity requirement.
• Calculate the weight of the contents (multiply volume by fluid density).
• Plan fill levels or mixing ratios.

The same formula works for horizontal or vertical orientation because orientation does not change total volume—only the fill-height calculation changes (which is more complex).

How to Measure a Capsule Tank Correctly

Getting accurate inputs is the most important step. Use these guidelines:

• Measure the outside diameter if you want the total volume including wall thickness. For the internal capacity, measure the inside diameter (or subtract twice the wall thickness).
• Measure the overall length from tip to tip, including the hemispherical ends. Do not measure just the cylindrical section.
• Use the same unit for both measurements—mixing meters and centimeters will throw off the result by a factor of 100 or more.
• For a tank that is not perfectly round (e.g., slightly oval), measure the widest and narrowest diameters and average them.

If you only have the cylindrical section length and the end cap radius, you can still calculate: overall length = cylinder length + diameter (because each hemisphere adds half a diameter).

Common Mistakes and How to Avoid Them

The most frequent errors come from unit confusion and misreading the shape.

• Using the wrong length: Some people enter the cylinder length instead of the overall length. That undercounts the volume by the two hemispherical ends.
• Mixing units: Entering diameter in inches and length in feet gives a wildly wrong result. Convert everything to one unit first.
• Forgetting the sphere volume: The capsule is not just a cylinder with flat ends; the rounded ends add significant capacity, especially on short, wide tanks.
• Confusing radius with diameter: The formula uses radius (d/2). If you enter the radius as the diameter, the volume becomes 8 times too small.
• Rounding too early: Rounding intermediate steps can shift the final result by several percent on large tanks. Keep full precision until the end.

Also note that the formula gives the total volume when the tank is completely full. Most tanks are not filled to the brim in practice—leave a safety margin for expansion or overflow.

Limits of the Formula

The capsule formula assumes perfectly hemispherical ends and a perfectly cylindrical middle. Real tanks may have slightly flattened ends, torispherical heads, or welded seams that reduce the internal volume. For most practical purposes the error is small (a few percent), but for critical applications—such as pressure vessels or precise chemical dosing—you should use the manufacturer’s certified capacity or a more detailed geometric model.

The formula also does not account for internal fittings (baffles, dip tubes, heating coils) that displace liquid. If those are present, subtract their volume for an accurate usable capacity.

Alternatives and Related Calculations

If your tank is a different shape, other formulas apply:

• Horizontal cylinder with flat ends: V = π × r² × L (full volume). For partial fill, use the segment area formula.
• Vertical cylinder: Same full-volume formula, but partial fill is simply a cylinder height fraction.
• Elliptical head tank: More complex, uses an ellipsoid volume for the heads.
• Rectangular tank: V = length × width × height.

For a capsule tank that is only partially filled, you need a different calculation that integrates the cross-sectional area of the cylinder and the spherical ends as a function of fill height—this is beyond the simple total-volume formula and usually requires a dedicated partial-fill calculator.

Frequently Asked Questions

How do I find the volume if I only know the cylinder length and the radius of the ends?
Add the diameter (2 × radius) to the cylinder length to get the overall length, then use the capsule formula. For example, a cylinder of 2 m with hemispherical ends of radius 0.5 m has an overall length of 2 + 1 = 3 m.

Does the orientation (horizontal vs vertical) change the volume?
No. The total volume is the same regardless of orientation. Orientation only affects how the liquid is distributed at a given fill height, which matters for partial-fill calculations.

What is the difference between a capsule and a cylinder with flat ends?
A flat-ended cylinder has volume π × r² × L, which is smaller than a capsule of the same overall length because the capsule adds the volume of two hemispheres (equivalent to one sphere). The capsule formula subtracts one diameter from the length to avoid double-counting the ends.

Can I use this for a tank that has torispherical heads?
Not accurately. Torispherical heads are flatter than hemispheres, so the actual volume is less than the capsule formula predicts. Use the manufacturer’s data or a specialized head-volume formula for precise results.

How do I convert the volume to weight?
Multiply the volume in liters by the density of the liquid in kg/L (water is approximately 1 kg/L). For example, 2940.5 L of water weighs about 2940.5 kg (6,483 lb). For other liquids, use their specific density.

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in d | Tank diameter | m | 1.2 | 0
in L | Overall length | m | 3.0 | 0
out volume | Total volume | L | (pi * (d/2)^2 * (L - d) + (4/3) * pi * (d/2)^3) * 1000 | 1
out volume_m3 | Volume in cubic meters | m³ | pi * (d/2)^2 * (L - d) + (4/3) * pi * (d/2)^3 | 3
out volume_gal | Volume in US gallons | gal | (pi * (d/2)^2 * (L - d) + (4/3) * pi * (d/2)^3) * 264.172 | 1