This former Blogger draft was fully rewritten, fact-checked and updated in July 2026.
Diving mathematics is not about performing complicated algebra underwater. It is about understanding a few relationships well enough to recognise whether a plan makes sense.
The examples below are simplified metric calculations for education. Real planning must follow training standards, the actual cylinder specification, analysed gas and an agreed reserve.
Ambient pressure
In seawater, pressure increases by approximately 1 bar every 10 metres. A useful approximation is:Ambient pressure (bar) = depth (m) ÷ 10 + 1At 20 metres the ambient pressure is about 3 bar absolute.
Boyle’s law and expanding gas
For a fixed amount of gas at constant temperature, pressure and volume vary inversely:P₁ × V₁ = P₂ × V₂A 1-litre gas space at 20 metres (3 bar) would expand toward 3 litres at the surface. This is why a scuba diver must breathe normally and continuously during ascent and never hold the breath.
Dalton’s law and maximum operating depth
The partial pressure of a gas equals its fraction multiplied by ambient pressure. For nitrox, maximum operating depth can be estimated with:MOD = (ppO₂ ÷ FO₂ − 1) × 10For EAN32 at a working ppO₂ of 1.4 bar, MOD is about 34 metres.
Cylinder gas
A nominal 12-litre cylinder at 200 bar contains approximately 2,400 litres of gas measured at surface pressure. If the planned reserve is 50 bar, about 600 litres are reserved, leaving roughly 1,800 litres for the working portion of the dive. Real cylinder markings and compressibility effects should be considered in formal planning.
SAC and RMV
Surface air consumption expressed as pressure per minute depends on cylinder size. Respiratory minute volume expresses litres per minute at the surface:RMV = pressure used × cylinder water volume ÷ time ÷ average ambient pressureIf a diver’s RMV is 15 L/min, the approximate demand at 20 metres is 45 L/min because the ambient pressure is 3 bar.
Why the numbers matter
Mathematics does not replace judgment. A practical example of why these relationships matter is the apparent simplicity of mini scuba tanks and tiny compressed-gas systems: a small cylinder does not change the pressure physics. Current, stress, cold and workload can increase consumption rapidly. Calculate with a realistic rate, preserve the reserve and compare the answer with what the team can actually execute.
