Pressure & Gas Laws

Three gas laws govern almost everything that happens to your body underwater: Boyle, Dalton and Henry. Anyone who understands these three understands barotrauma, oxygen toxicity, nitrogen narcosis, nitrox and decompression as one coherent whole. This is the theoretical heart of diving — take your time with it. Everything about decompression, dive planning and emergencies leans on it.

As a diver you breathe gas, carry gas, and dissolve gas into your body. Gases behave under pressure according to fixed natural laws that have been known for centuries. Boyle describes what happens to the volume of a gas as pressure changes — why your ears hurt on descent, why you must never hold your breath, and why your BCD seems to fill on the way up. Dalton describes how a gas mixture (like air) is built from partial pressures — why oxygen becomes toxic deep, why nitrogen makes you feel "drunk", and why nitrox exists. Henry describes how much gas dissolves into a liquid (your blood and tissues) under pressure — the basis of all decompression theory.

Absolute pressure, always. All gas laws work with absolute pressure (including the 1 bar atmosphere), never with depth alone. Do not forget that +1 bar at the surface; it is the most common calculation error of beginning divemasters. At 10 m you calculate with 2 bar, not 1.

Key concepts

Term	Short definition	Belongs to
Boyle's Law	At constant temperature, pressure × volume is constant (P₁V₁ = P₂V₂)	Volume of cavities
Barotrauma	Injury from a pressure difference in an air space	Boyle
Dalton's Law	Total pressure is the sum of the partial pressures of all gases	Gas mixtures
Partial pressure (pp)	The share of one gas in the total pressure	Dalton
Oxygen toxicity	Poisoning from too high a ppO₂	Dalton
Nitrogen narcosis	Narcotic effect of nitrogen at high partial pressure	Dalton
Nitrox (EANx)	Breathing gas with more oxygen and less nitrogen than air	Dalton
Henry's Law	Amount of dissolved gas is proportional to the partial pressure	Dissolving gas
Decompression sickness (DCS)	Bubbles from too-fast off-gassing	Henry
MOD	Maximum Operating Depth for a gas mixture	Dalton

Understanding the gas laws

Boyle's Law: pressure and volume

At constant temperature, the product of pressure and volume is constant: P₁ × V₁ = P₂ × V₂. In plain terms: double the pressure and the volume halves; halve the pressure and the volume doubles. For the diver, the key point is that gas volumes change with depth, most strongly just below the surface.

Worked example. A 6-litre balloon at the surface (1 bar) taken to 30 m (4 bar): P₁V₁ = P₂V₂ → 1 × 6 = 4 × V₂ → V₂ = 1.5 litres. On 30 m the balloon is only a quarter of its original volume. Release it there, and it expands back to 6 litres on the way up.

Depth	Absolute pressure	Volume of 6 L gas	Relative size
0 m	1 bar	6.0 L	100%
10 m	2 bar	3.0 L	50%
20 m	3 bar	2.0 L	33%
30 m	4 bar	1.5 L	25%
40 m	5 bar	1.2 L	20%

Why this is vital. Your lungs are an air space. Breathe in at 10 m (2 bar) and hold your breath while rising to the surface (1 bar), and that air wants to double. Your lungs rupture (lung over-expansion injury). This is the physical basis of the golden rule: always keep breathing. Boyle also explains ear and sinus barotrauma on descent, mask squeeze, the BCD and drysuit "deflating" (compressing) at depth and re-expanding on the way up, and reverse block (air trapped in a sinus or ear that cannot escape on ascent).

A sealed crisp packet taken up a mountain bulges at the pass — lower pressure, larger volume. Underwater the opposite happens on descent, and the same as the packet on ascent: exactly Boyle.

Did you know? Because the biggest volume change is just below the surface, the last few metres of an ascent are the most dangerous for lung over-expansion. Never "sprint up the last few metres" with a held breath.

Dalton's Law: partial pressures

Air is not a pure gas but a mixture: about 21% oxygen (O₂) and 79% nitrogen (N₂), plus traces. Dalton states: the total pressure is the sum of the pressure each gas would exert on its own. The share of one gas is its partial pressure: partial pressure = fraction of that gas × absolute pressure. The fraction does not change with depth, but the partial pressure does, because the absolute pressure rises.

Depth	Absolute pressure	ppO₂ (air)	ppN₂ (air)
0 m	1 bar	0.21	0.79
10 m	2 bar	0.42	1.58
30 m	4 bar	0.84	3.16
40 m	5 bar	1.05	3.95

Oxygen toxicity. Oxygen is essential, but at too high a partial pressure it becomes toxic to the central nervous system (can cause convulsions, almost always fatal underwater). The widely accepted limit for recreational diving is ppO₂ 1.4 bar as a working limit, with 1.6 bar as an absolute emergency ceiling. Breathing air, you only reach ppO₂ 1.4 around 57 m, so for an air diver oxygen toxicity is rarely the first problem — but for a nitrox diver it is, because they breathe more oxygen.

MOD (Maximum Operating Depth). From the ppO₂ limit follows the maximum depth for a gas: MOD (m) = (ppO₂ limit / oxygen fraction − 1) × 10. For EAN32 at limit 1.4: MOD = (1.4 / 0.32 − 1) × 10 ≈ 33.8 m. For EAN36 at 1.4: ≈ 28.9 m. More oxygen means a shallower allowed depth. This is counter-intuitive for beginners: nitrox is not a "deep gas" but a gas with a lower maximum depth.

Nitrogen narcosis. Under high partial pressure, nitrogen acts as a narcotic, like a mild intoxication ("rapture of the deep"). It usually becomes noticeable from about 30 m and increases with depth. It is reversible in itself (it disappears as you go shallower), but it affects your judgement and reaction time, and that is what makes it dangerous.

So why nitrox? Nitrox contains less nitrogen, so you take up less nitrogen at the same depth and time (Henry). That means longer no-decompression times or more margin. The price is a shallower MOD due to the higher ppO₂. Nitrox = more bottom time or safety margin, not more depth.

Scenario. A diver in Egypt dives a wreck on EAN32, thinking "more oxygen, so safer, so I can go deeper". At 38 m they are already past the MOD of ~34 m and above ppO₂ 1.4. The error: confusing "more oxygen" with "more depth". Dalton says the opposite.

Henry's Law: gas that dissolves

Henry: the amount of gas that dissolves in a liquid is proportional to the partial pressure of that gas above the liquid. Your blood and tissues are the liquid; the nitrogen in your lungs is the gas. At depth the nitrogen is under higher partial pressure (Dalton), so more nitrogen dissolves into your body. The longer and deeper you dive, the more nitrogen you take up, until a tissue is "full" (saturated) for that depth. On ascent the partial pressure drops and the dissolved nitrogen wants to come back out: you off-gas.

Why ascend slowly? As long as off-gassing is gentle, the nitrogen is carried neatly via your blood to your lungs and exhaled. Ascend too fast, and the pressure drops faster than your body can shed the nitrogen, so the gas forms bubbles in your blood and tissues: that is decompression sickness (DCS). The safety stop and the slow ascent rate (max ~9-10 m/min) give your body time to off-gas in a controlled way.

Different tissues, different speeds. Not all your tissues load and unload at the same rate. Blood-rich "fast" tissues (blood, brain) saturate and off-gas quickly; fatty or poorly perfused "slow" tissues (joints, fat) take much longer. Dive computers and tables therefore model several theoretical tissue compartments at once. This is developed fully in the decompression topic; Henry is the law beneath it.

Did you know? Even after a safe dive, "residual nitrogen" remains in your tissues. That is why computers and tables account for repetitive dives, and why flying too soon after diving is risky: in the aircraft the cabin pressure drops, ppN₂ falls further, and residual gas can still form bubbles. Hence the wait times for flying after diving.

The three laws together

A single ascent touches all three at once: your lung volume expands (Boyle → keep breathing), the partial pressures fall (Dalton), and the dissolved nitrogen comes out (Henry → do it slowly). Good diving is nothing more than continuously respecting these three laws.

Real-world examples

The Netherlands (Vinkeveen / Zeeland). Shallow, cold dives. Boyle dominates: much pressure change per metre in the top layer makes equalising and buoyancy control crucial. Nitrogen uptake (Henry) usually stays limited by the shallow depth, but residual nitrogen adds up on repetitive dives.

Egypt (Red Sea, wreck and reef dives). Deep wrecks (SS Thistlegorm around 30 m) bring Dalton and Henry into play: narcosis can begin around 30 m, and the no-decompression limit becomes the limiting factor. Nitrox is popular here for more bottom time; mind the MOD.

Indonesia (Bali, depths at Tulamben). Deep sections on wrecks and walls; narcosis and NDL govern the dive. Nitrox extends bottom time on the reef plateaus.

Maldives. Warm, repeated dives (often 3 per day). Henry is the theme: residual nitrogen stacks over the day, so surface intervals and conservative computer settings matter.

Mozambique (Tofo and Vilanculos). At Tofo the famous sites (Manta Reef, Giant's Castle) often sit around 20-30 m; narcosis (Dalton) and nitrogen uptake (Henry) come into play, while the negative entry and current demand Boyle-wise fast buoyancy adjustments. At Vilanculos and the Bazaruto banks diving is usually shallower, so Boyle effects (equalising, buoyancy in changing tides) dominate and the nitrogen load stays limited.

Common mistakes

Mistake	Law	What goes wrong
Holding your breath while ascending	Boyle	Lung over-expansion injury
Calculating with depth instead of absolute pressure	All	Wrong ppO₂/MOD/volume calculation
Thinking "nitrox = deeper diving"	Dalton	Oxygen toxicity past the MOD
Ignoring the ppO₂ limit	Dalton	Risk of an oxygen seizure
Underestimating narcosis around 30 m	Dalton	Poor judgement, slower reactions
Ascending too fast	Henry	Decompression sickness
Forgetting residual nitrogen on a repeat dive	Henry	Exceeding the safe NDL
Flying too soon after diving	Henry	DCS from further pressure drop in the cabin

Pro tips

• Always calculate with absolute pressure: depth in metres ÷ 10, plus 1. At 25 m that is 3.5 bar. Never make an exception.
• Know your MOD before entering the water on nitrox, and label your tank. Always analyse your gas yourself with an O₂ analyser.
• Treat narcosis as insidious: if you feel "over-confident" or slow at depth, go shallower. The effect fades with depth.
• Ascend like a bubble, not a rocket. Follow your computer's ascent rate; the last 10 m extra slowly.
• Plan your surface intervals on multi-dive days; Henry does not forgive stacked nitrogen.

Frequently asked questions

A 4 L air bubble at the surface descends to 20 m. What is its volume? Boyle's Law. P₁V₁ = P₂V₂ → 1 × 4 = 3 × V₂ → V₂ ≈ 1.33 L (20 m = 3 bar absolute).

What is the ppO₂ of an air diver at 40 m? Absolute pressure 5 bar × 0.21 = 1.05 bar — still below the 1.4 working limit.

What is the MOD of EAN32 at a ppO₂ limit of 1.4? MOD = (1.4 / 0.32 − 1) × 10 ≈ 33.8 m.

Why does nitrox give longer no-decompression times than air? Nitrox contains less nitrogen, so at the same depth ppN₂ is lower (Dalton) and you take up less nitrogen (Henry). It therefore takes longer to reach the NDL.

Why must you ascend slowly, and which law is behind it? Henry's Law. As pressure drops, dissolved nitrogen comes out; ascending too fast causes over-saturation and bubbles (DCS). A slow ascent lets your body off-gas in a controlled way.

Summary

Three gas laws steer diving. Boyle (P₁V₁ = P₂V₂) describes how gas volumes change with pressure, strongest just below the surface; it explains barotrauma and the absolute rule never to hold your breath. Dalton describes that total pressure is the sum of partial pressures; from it follow oxygen toxicity above a ppO₂ of 1.4 bar (emergency ceiling 1.6), the MOD of a gas mixture, nitrogen narcosis from about 30 m, and the reason nitrox exists (less nitrogen, so more bottom time but a shallower maximum depth). Henry describes that the amount of dissolved gas is proportional to the partial pressure; it explains nitrogen uptake at depth, its release on ascent, and why you ascend slowly and make safety stops to avoid decompression sickness. Always calculate with absolute pressure. Every ascent involves all three laws at once: keep breathing (Boyle), mind your gas (Dalton), off-gas slowly (Henry).

The 10 things every diver should know by heart

1. Boyle: P₁V₁ = P₂V₂; gas volumes change with pressure, strongest just below the surface.
2. Never hold your breath; that is Boyle applied to your lungs.
3. Always calculate with absolute pressure (depth ÷ 10 + 1 bar).
4. Dalton: total pressure = sum of partial pressures; partial pressure = fraction × absolute pressure.
5. ppO₂ working limit 1.4 bar (emergency ceiling 1.6); above it, oxygen toxicity threatens.
6. MOD = (ppO₂ limit / O₂ fraction − 1) × 10; more oxygen means shallower.
7. Nitrox = more bottom time/margin, not more depth; mind the MOD.
8. Nitrogen narcosis begins around 30 m and worsens with depth; going shallower resolves it.
9. Henry: dissolved gas is proportional to the partial pressure; you load nitrogen at depth and off-gas on ascent.
10. Ascend slowly and make stops; off-gassing too fast causes decompression sickness.