Calculating SCUBA Cylinder Capacities

Why Cylinder Capacity Names Can Be Misleading

Descriptions of the amount of air in SCUBA cylinders (aka diving tanks), and conversions between cylinders sold in imperial and metric markets, are often problematic because manufacturers, distributors, and divers do not always calculate or describe capacity the same way. This article will show a practical way to determine how much breathing gas is actually contained in an imperial or metric SCUBA cylinder, but first a few housekeeping details...

In the US, SCUBA cylinders are regulated by standards of the Department of Transportation, Hazardous Materials Division (aka the DOT), and in commerce are typically described by their free air capacity in cubic feet at a stated service pressure in pounds per square inch. Internationally, most SCUBA cylinders are regulated by European (EN) or International Organization for Standardization (ISO) standards and are described by their water volume in liters and working pressure in bar.

This article makes a careful distinction between gas capacity and water volume, although technically both are volumes expressed in different units {ft³ | L}. Because gases are highly compressible compared to liquids, a gas volume such as air must always be understood in relation to pressure, usually expressed as pounds per square inch or bar { psi | bar }. Here, capacity means the gas volume at one Standard Atmosphere of pressure {14.696 psi | 1.01325 bar}, also called free capacity.

How True Cylinder Capacity Is Calculated

The ideal capacity is determined using a Boyle's law ideal gas equation. At room temperature and below about {2030 psi | 140 bar}, air behaves closely enough to the ideal gas laws for many practical purposes. At higher pressures, however, the calculated ideal capacity increasingly departs from observed real capacity. That is because an ideal gas is perfectly compressible, while real gases are not; their compressibility is limited by the atomic forces of their specific composition. Temperature matters too. True capacity can be significantly less, depending on breathing gas, working pressure, and cylinder temperature: about 5% to 10% less for air or sport Nitrox, and about 10% to 20% less for Trimix.

Here is the practical part: To calculate ideal capacity, multiply the cylinder water volume by the cylinder pressure and divide by atmospheric pressure. (Divers using metric cylinders usually get that last part wrong.) The easiest method to estimate true capacity is to use the Compressibility Factor (Z). To calculate true capacity, divide the ideal capacity by the Z Factor for the specific gas at the same pressure. Values for Z can be looked up in a Z Factor reference table or can be computed from experimental data for real properties of a specific gas. The Z Factors used in this article were computed using the NIST REFPROP database and software.

Ideal_Capacity(ft³) = Water_Volume(ft³) × Service_Pressure(psi) ÷ Atmospheric_Pressure(14.696 psi)

Ideal_Capacity(L) = Water_Volume(L) × Working_Pressure(bar) ÷ Atmospheric_Pressure(1.01325 bar)

True_Capacity ≈ Ideal_Capacity ÷ Z_Factor _{(gas & pressure@temperature)}

Some Real-World Examples

SCUBA cylinder manufacturers and distributors publish the basic information you need to make these simple calculations. From their specifications you need only find the water volume and pressure for your SCUBA tank. International divers have it easy, because those two values are usually stamped on the crown of the cylinder as WC and WP. You also need the temperature in order to determine the Z Factor, and these calculations assume the temperature is the same for both ideal and true capacity. If temperature is not stated in the specifications, the US standard is 70°F and most international standards are 15°C. (FYI, they are not equivalent, 15°C is only 59°F.)

XS Scuba Steel X7-100 (Faber DOT) US Specifications

1. Water Volume = 12.9 L (28.32 L = 1 ft³)
2. Service Pressure @ 70°F = 3442 psi
3. Ideal capacity (12.9÷28.32) ×3442 ÷14.696 = 106.7 ft³
4. Z Factor = 1.0532
5. True capacity 106.7 ÷1.0532 ≈ 101.3 ft³

Aluminum "S80" (Luxfer DOT) US Specifications

1. Water Volume = 678 in ³ (1728 in ³ = 1 ft³)
2. Service Pressure @ 70°F = 3000 psi
3. Ideal capacity (678÷1728) ×3000 ÷14.696 = 80.1 ft³
4. Z Factor = 1.0320
5. True capacity 80.1 ÷1.0320 ≈ 77.6 ft³

The 77.6 ft³ true air capacity calculated here varies slightly from a historically published Luxfer figure of 77.4 ft³. Luxfer engineers may have determined compressibility using a different method, may have performed calculations with different precision, or may have used different conversion assumptions between imperial and metric standards. For sport diving, small differences in accuracy and precision are usually not operationally significant. Those small differences can compound to become genuinely significant for pre-dive gas planning in technical diving and, in other fields, can be critical.

Authoritative sources for the cylinder water volumes and pressures mentioned in this article included published Luxfer technical specifications for imperial models, private engineering data from Faber, and direct communications with XS Scuba (aka Sea Pearls) regarding Metal Impact cylinders. The Luxfer values reflect historically published specifications and may not match current public Luxfer specifications.

Why Metric and Imperial Capacities Do Not Match

For DOT cylinders, the water volume specification is usually given in cubic inches or liters, so start by converting the water volume into cubic feet. However, conversions between metric and imperial cylinder free capacities are more complex than simple units conversions. The international "Ali 80" cylinder and the US "S80" are physically the same Luxfer cylinder. So why is the true air capacity of the international cylinder, simply converted to imperial units 2210÷28.32 = 78.0 ft³, not the same as the domestic cylinder at 77.6 ft³? The reason is small differences in temperature and pressure between the EN/ISO and DOT standards. This is why simple units conversion of free capacity between imperial and metric cylinders is improper, becoming more significant as the water volume or pressure increases particularly for manifolded cylinders (aka "doubles" or "twinsets".)

Aluminum "Ali 80" (Luxfer EN/ISO) International Specifications

1. Water Volume = 11.1 L
2. Working Pressure @ 15°C = 207 bar
3. Ideal capacity 11.1 ×207 ÷1.01325 = 2268 L
4. Z Factor = 1.0263
5. True capacity 2268 ÷1.0263 ≈ 2210 L

Why 3442 psi Exists

Did you ever wonder how the unusual service pressure value of 3442 psi came to be established? The first US manufactured high pressure steel SCUBA cylinder (designed by Pressed Steel Tank Company circa 1987) had a 3500 psi service pressure that could only be used with 300 bar DIN valves and regulators; a considerable annoyance to sport divers in North America who overwhelmingly use yoke fitting regulators. In 2004, PST introduced a new design that could be used with yoke (aka A-clamp) regulators. The international standard at the time for a yoke connection maximum cylinder working pressure was 230 bar at 15°C. However, DOT specifications are in pounds per square inch at a different temperature, so some conversions had to be done...

The Gay-Lussac's law of pressure–temperature says that the pressure of the ideal gas will vary in direct proportion to its temperature (for a constant volume.) Divers commonly see the effect of this gas law when a "hot fill" cools and pressure drops, but the inverse is also true. Instead of using ideal calculations, PST used software to model the properties of dry Air as a mixture of pure nitrogen, argon and oxygen. The engineers determined that for a cylinder filled to a gas density of ≈9.24 moles per liter at 230 bar and 15°C, the pressure would have to be {3442.7 psi | 237.4 bar} at 70°F to maintain the same density. Thus the 230 bar @15°C metric standard corresponds to the 3442 psi @70°F imperial standard used in the US. The earlier 230 bar limit was later superseded by ISO 12209:2013 with a 232 bar limit for this connection standard, so the DOT maximum cylinder service pressure could hypothetically be about 3472 psi if it were established today using the same method. Here is a screenshot of my independently reproduced results using different software.

Capacity calculations also ignore the practical limits of breathing residual gas in a SCUBA tank below about {150 psi | 10 bar} due to regulator flow restrictions, and pressure gauges can also be significantly inaccurate, so best practice is to always plan your dive with a generous reserve.

☆ Heliair 10/50 is not a particularly good breathing gas for open-circuit divers, with questionable suitability as an inflation gas. Heliair always is less than optimal for either PO₂ or narcosis, depending on your TOD. However, Heliair is easy to make so it is widely used and the reason it appears in this table.

† Many years ago the first US importer of Faber low pressure 2400+10% = 2640 psi steel cylinders did some specious math for the marketing descriptions of their capacities. The 13 ×(2640÷14.5) ÷28 = 85 ft³ (?) description has followed this 13 liter water capacity cylinder through the years and it is still referred to in the US as the "LP85" because the name has become synonymous with its excellent buoyancy characteristics and in-water trim, even though 85 ft³ is nowhere near its true capacity. The cylinders were notorious for being overfilled by technical divers because of how they were marketed by the importer, who claimed their service life was 10,000 hydrostatic tests at 4000 psi. North Florida cave country divers called their 4000 psi overfill a "dry hydro", but at that pressure real-gas effects become even more significant and the overfill benefit is diminished by about 10 ft³. Regardless, the practice became so widespread that Faber eventually started stamping the US import version "DO NOT OVER PRESSURIZE".

† A 10 L cylinder at 232 bar does not contain 2320 free liters of air! Divers using metric cylinders are fond of saying they don't have to deal with this stuff, just multiply the water volume in liters by the working pressure in bar, but that's not entirely correct. Many divers think that atmospheric pressure is defined as 1 bar. A bar is actually defined as exactly 100,000 Pa, not 1 atmosphere. Ten meters of sea water is only a practical diving approximation. The metric calculation typically used by divers omits the division by atmospheric pressure, which is 1.01325 bar. That makes the ideal capacity overstated by 1.3% plus the difference between ideal and true capacity for a total variance of ≈6% at 232 bar and ≈11% at 300 bar. Notice that the "Ali 80" actually has a larger true capacity than the "10 Liter" even though the "10 Liter" has a larger ideal capacity; that is the effect of compressibility at the two different working pressures.

For similar water volumes, the 232 bar cylinders are similar in true capacity to the 3442 psi cylinders. Comparing the ISO "15 Liter" with the DOT "HP117", they look identical with the same diameter and the ISO version longer by just 5 mm. They do differ in weight and buoyancy, with the ISO version being 0.5 kg heavier. They are both made by Faber, so could it be that to yield the same water volume the ISO cylinder is slightly taller because it has a thicker cylinder wall than the DOT cylinder? Divers are sometimes heard to say that cylinders in the US are the same as cylinders elsewhere; this is an example of why that may not be true even for cylinders that are very close in size and pressure.

Z Factors for SCUBA

Because ideal capacity does not reliably reflect true free capacity, the Z Factors table below provides a practical way to estimate actual gas capacity more consistently for common gases and pressures. To calculate true capacity, divide the ideal capacity by the Z Factor obtained from the table below. This table is arranged so that interpolation is possible for most pressures and mixtures. Keep in mind, just because this table lists Z Factors at higher pressures does not mean you can or should fill tanks to that pressure, especially with pure oxygen.

† This Z Factors table was prepared using the NIST REFPROP database and software , version 10. For calculation purposes, the gases were defined to be pseudo-pure air (dry), Nitrox mixtures (O₂, balance N₂) and Trimix (O₂, Helium, balance N₂) mixtures composed of the stated percentages on a molar basis and all without the trace gases or contaminants typically found in the breathing gases used for SCUBA. That means these perfect gas Z Factors would be a little different for the stuff in your tank, but not enough to be significant.