Cylindrical Tank Volume Calculator: Formula & Examples

This calculator works out the volume of a vertical or horizontal cylindrical tank from the diameter (or radius) and length, giving the result in cubic meters, liters, and US gallons. You enter the tank’s dimensions and it returns the total capacity, which is the first number shown; the other outputs give you the same volume in different units so you can use whichever fits your project.

Formula

The volume \(V\) of a cylindrical tank is the area of the circular end times the length:

\(V = \pi \times r^2 \times L\)

where:

• \(r\) = radius of the tank (half the diameter), in meters (m)
• \(L\) = length of the tank, in meters (m)
• \(\pi\) ≈ 3.14159

If you only have the diameter \(d\), use \(r = d/2\). The result is in cubic meters (m³). To convert: 1 m³ = 1000 liters = 264.172 US gallons.

Worked Example

Using the default values from the calculator: diameter = 2 m, length = 4 m.

1. Radius: \(r = 2 / 2 = 1\) m
2. End area: \(A = \pi \times 1^2 = 3.14159\) m²
3. Volume: \(V = 3.14159 \times 4 = 12.566\) m³
4. In liters: \(12.566 \times 1000 = 12566\) L
5. In US gallons: \(12.566 \times 264.172 = 3319.6\) gal

The calculator rounds the first output to two decimals, giving 12.57 m³.

When to Use This Calculator

You need this whenever you are sizing a storage tank, planning a water reserve, estimating fuel capacity, or checking how much liquid a cylindrical vessel can hold. It works for both vertical and horizontal tanks as long as the tank is a full cylinder – that is, the ends are flat and the sides are straight. The formula is identical; orientation does not change the total volume.

Common real-world uses:

• Choosing a rainwater collection tank for a house
• Calculating the capacity of a propane or diesel storage cylinder
• Determining the volume of a cylindrical aquarium or septic tank
• Estimating how much liquid a tanker truck or rail car can carry

How to Read the Result

The first output, volume in cubic meters, is the raw geometric capacity. The liters and gallon outputs are the same volume expressed in units you might actually order or fill with. Note that these are nominal capacities – they assume the tank is filled to the very top. In practice, most tanks are filled to 90–95% of capacity to leave room for expansion, especially for liquids that change volume with temperature (like fuel) or that need a vapor space.

If you need the volume of liquid partially filling a horizontal tank, this simple formula will not give it – the partially filled horizontal cylinder requires a more complex calculation involving the segment area of a circle. For a vertical tank, partial volume is simply the full formula with the filled height in place of the length.

Common Mistakes and How to Avoid Them

• Unit mix-ups: The formula works in any consistent unit set, but if you mix meters and centimeters, you will be off by a factor of 100 in area and 1,000,000 in volume. Always convert all dimensions to the same unit first.
• Using diameter instead of radius: Forgetting to halve the diameter is the most frequent error. A 2 m diameter tank has a 1 m radius – using 2 m as the radius would give 4× the actual volume.
• Rounding too early: If you round π to 3.14, you lose about 0.05% accuracy. For most purposes that is fine, but for large tanks the error can add up to tens of liters.
• Confusing liters and gallons: A US gallon is 3.785 liters, while an imperial gallon is 4.546 liters. This calculator uses US gallons. If you need imperial gallons, multiply the liters by 0.22.

Limits of the Formula

This formula assumes a perfect cylinder: straight sides, flat ends, and uniform diameter. Real tanks often have dished (curved) ends, which add a small amount of volume – typically 5–10% for pressure vessels. The formula also ignores the thickness of the tank walls; the internal volume is slightly less than the external dimensions suggest. For thin-walled tanks (most plastic and steel tanks), the difference is negligible, but for thick-walled pressure vessels, measure the inside diameter instead of the outside.

Additionally, the formula gives the geometric volume. The actual usable volume may be less due to internal fittings, baffles, or a dip tube that prevents complete emptying.

Alternatives and Related Calculations

If your tank is not a full cylinder, you have other options:

• Partially filled horizontal tank: Use a dedicated partial-volume calculator that accounts for the liquid height.
• Rectangular tank: Volume = length × width × height.
• Spherical tank: Volume = (4/3) × π × r³.
• Conical or tapered tank: Volume = (1/3) × π × h × (r₁² + r₁r₂ + r₂²) for a frustum.

For most cylindrical tanks, the simple formula above is all you need. Just be careful with units and remember to halve the diameter.

Frequently Asked Questions

Does the calculator work for horizontal tanks?

Yes, the total volume of a horizontal cylinder is exactly the same as a vertical one – the formula only uses the cross-section area and the length. Orientation does not matter for total capacity. However, if you need the volume of liquid at a certain fill height in a horizontal tank, that requires a different calculation.

How do I convert the result to imperial gallons?

Multiply the liters by 0.21997 to get imperial gallons. For example, 1000 liters ≈ 220 imperial gallons. The calculator gives US gallons (1 US gal = 3.785 L); imperial gallons are about 20% larger.

What if my tank has rounded ends?

The formula assumes flat ends. For dished or elliptical ends, add the volume of the end caps. A common approximation is to treat each end as a hemisphere, adding (2/3) × π × r³ per end. For a more accurate figure, consult the tank manufacturer’s data sheet.

Why does my tank hold less than the calculated volume?

Real tanks have wall thickness, internal fittings, and are rarely filled to the absolute brim. Also, if the tank is not perfectly cylindrical (e.g., it has a slight bulge or taper), the actual volume will differ. For safety and expansion, most tanks are filled to 90–95% of the geometric capacity.

Can I use this for a tank that is partly buried?

Yes, the volume calculation is independent of where the tank is installed. The formula gives the total internal volume, which is what you need to know for capacity regardless of burial depth. Just make sure you measure the internal dimensions, not the external ones if the walls are thick.

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in d | Tank diameter | m | 2 | 0
in l | Tank length | m | 4 | 0
out v_m3 | Volume (m³) | m³ | pi * (d/2)^2 * l | 2
out v_l | Volume (liters) | L | v_m3 * 1000 | 0
out v_gal | Volume (US gallons) | gal | v_m3 * 264.172 | 1