What is the MOD of EAN32?

33.8 metres, or 111 feet, at a 1.4 bar oxygen partial pressure limit in sea water. At the 1.6 bar contingency limit it is exactly 40 metres, or 131 feet, which is why 32% became the standard mix for recreational diving to the 40 m limit. Most divers round the working figure down and mark the cylinder MOD 33 m.

Should I plan to 1.4 or 1.6 bar?

Plan the working part of the dive to 1.4 bar and treat 1.6 as a contingency ceiling or a decompression-stop figure. The difference matters because the factors that trigger an oxygen seizure - exertion, carbon dioxide retention, cold and immersion - are all present while you are swimming and largely absent while you hang on a stop. For long, cold or hard-working dives, 1.2 or 1.3 bar is a reasonable further step down.

How do I work out the best mix for a planned depth?

Divide your partial pressure limit by the ambient pressure at that depth. Ambient pressure in bar is depth in metres divided by 10, plus 1. For 30 m that is 4.0 bar, so at a 1.4 limit the best mix is 1.4 ÷ 4.0 = 0.35, or EAN35. Fill stations usually blend standard mixes, so you take the nearest one below the ideal figure and accept slightly less benefit.

Does fresh water change the maximum operating depth?

Yes, by about 3%. Fresh water is less dense, so it takes 10.3 metres of it to produce one bar rather than 10 metres of sea water. EAN32 at a 1.4 bar limit gives 33.75 m in the sea and 34.76 m in a lake. The difference is small, but using sea water figures in fresh water is the conservative direction and using fresh water figures at sea is not.

What is equivalent air depth and why does it matter?

It is the depth on air that would give you the same nitrogen partial pressure as your nitrox mix at your actual depth, and it is the number you use for decompression planning with air tables. EAN32 at 30 m has an equivalent air depth of 24.4 m, so you plan as a 24 m dive. That reduction in nitrogen loading is the entire reason for diving enriched air.

What happens if I exceed the maximum operating depth?

You raise the risk of a central nervous system oxygen seizure, which can happen without warning and is very often fatal underwater. It is not a gradual effect you notice and correct, and there is no reliable set of early symptoms to rely on. Exceeding the MOD briefly does not guarantee harm - the risk is probabilistic - but the consequence when it occurs is severe enough that the limit is treated as absolute.

How is the CNS percentage calculated?

It is the planned bottom time divided by the NOAA single-exposure limit for the oxygen partial pressure you are breathing, expressed as a percentage. This calculator interpolates between the published table values, so 1.28 bar gives roughly 186 minutes and a 25-minute dive uses about 13%. It covers one exposure only: repetitive dives accumulate, and the clock decays with roughly a 90-minute half-time on the surface rather than resetting.

Why is the MOD in feet not exactly the metric figure converted?

It is on this page, because the calculation is done in metres at 10 m per bar and then converted at 0.3048 m per foot. Published imperial tables often use 33 feet per atmosphere instead, which is 10.06 m, so their figures run about half a percent deeper. Both conventions round to the same operational limit, but if you compare a printed table with a calculated value expect a foot or so of difference.

Can I use this for trimix?

The oxygen side of the calculation is identical, since the maximum operating depth depends only on the oxygen fraction and the limit. Enter the oxygen percentage of your trimix and the MOD is correct. What this page does not give you is the equivalent narcotic depth, which accounts for helium, or the minimum operating depth that hypoxic mixes have because the oxygen fraction is too low to breathe at the surface.

Nitrox MOD Calculator: Max Operating Depth & Best Mix

Inputs this calculator takes, with typical values
Input	What to enter	Example
Oxygen fraction of the mix	The figure you measured with an analyser on the cylinder you are going to dive, not the mix that was ordered.	32 % O2
Oxygen partial pressure limit	The ceiling you are planning to; 1.4 bar is the working limit taught by every recreational agency.	1.4 bar - standard working limit
Planned maximum depth	The deepest point of the dive, used for the best mix, the partial pressure you will breathe and the equivalent air depth.	30 m
Water type	Sets how much depth adds one bar of pressure; fresh water is less dense so it takes more of it.	Sea water - 10 m per bar
Planned bottom time	Time at the planned depth, used only for the CNS oxygen clock; a real dive spends part of its time shallower and accumulates less.	25 min

Why enriched air has a depth limit at all

Nitrox trades one risk for another. Replacing some of the nitrogen in your breathing gas with oxygen slows nitrogen loading, which buys longer no-decompression limits at recreational depths. It also means every breath contains more oxygen, and oxygen becomes toxic to the central nervous system when its partial pressure gets high enough. The depth at which that happens is the maximum operating depth, and unlike a no-decompression limit it is a hard ceiling rather than a planning target.

What matters is partial pressure, not percentage. Dalton's law says each gas in a mixture exerts the pressure it would exert alone, so the oxygen partial pressure is the oxygen fraction multiplied by the ambient pressure. At the surface, EAN32 gives 0.32 bar of oxygen — harmless. At 30 m, where the ambient pressure is 4 bar, the same mix gives 1.28 bar, and at 40 m it gives 1.6 bar. The gas has not changed; the pressure has.

The consequence of exceeding the limit is what makes this calculation different in character from most dive planning. Central nervous system oxygen toxicity can present as a convulsion with no useful warning, and a convulsion underwater with a regulator in your mouth is very often fatal. There is no gradual degradation to notice and correct, which is why the discipline is to analyse every cylinder, mark it with its mix and its MOD, and treat that depth as a wall.

The formula, and what each piece does

Start from the definition. Oxygen partial pressure is PO₂ = FO₂ × P_ambient, so the ambient pressure at which a given mix reaches your limit is P = PO_2max ÷ FO₂. That gives a pressure in bar, and depth is what you actually need.

Converting takes two steps. One bar of the total is atmospheric pressure, present before you enter the water, so subtract it. The remainder is water column, and in sea water it takes 10 metres to produce one bar. Hence MOD = (PO_2max ÷ FO₂ − 1) × 10. Fresh water is less dense, so it takes 10.3 m to make a bar and every depth is correspondingly greater. In imperial units the convention is 33 feet of sea water per atmosphere, which is where the familiar (PO_2max ÷ FO₂ − 1) × 33 comes from.

Best mix inverts the same relation. If you already know the depth you intend to reach, the ambient pressure there is d ÷ 10 + 1, and the richest mix that stays at your limit is FO₂ = PO_2max ÷ P. For 30 m at 1.4 bar that is 1.4 ÷ 4 = 0.35, so EAN35. Richer than that exceeds the limit at depth; leaner wastes some of the decompression benefit.

Equivalent air depth answers the other half of the question: how much nitrogen are you taking on? Match the nitrogen partial pressure of your mix to the depth on air that would produce the same figure, and you get EAD = (FN₂ ÷ 0.79) × (d + 10) − 10. EAN32 at 30 m gives an EAD of 24.4 m, so you plan the decompression as if you had been at 24.4 m. That is the entire benefit of nitrox, expressed as a number, and the equivalent air depth calculator covers it in detail.

Note that air itself is a nitrox mix in this arithmetic. Put 21% into the EAD formula and it returns the actual depth, exactly as it should, which is a useful check that the equation has been entered correctly.

Worked example: planning a 30 metre dive on EAN32

You have a cylinder that analyses at 32% oxygen and you plan a dive to 30 metres in sea water, with 25 minutes at depth, working to a 1.4 bar limit.

Pressure at which the mix hits the limit. 1.4 ÷ 0.32 = 4.375 bar.
Remove the atmosphere. 4.375 − 1 = 3.375 bar of water column.
Convert to depth. 3.375 × 10 = 33.75 m, which is 110.7 ft. In practice you would mark the cylinder MOD 33 m, rounding down.
Check the planned depth. Ambient pressure at 30 m is 30 ÷ 10 + 1 = 4.0 bar, so the oxygen partial pressure you breathe is 0.32 × 4.0 = 1.28 bar. That is inside the 1.4 limit with 3.75 m of depth to spare.
Best mix for 30 m. 1.4 ÷ 4.0 = 0.35, so EAN35 would use the limit exactly. Your 32% is slightly conservative, which is normal because fill stations blend to standard mixes.
Equivalent air depth. The nitrogen fraction is 1 − 0.32 = 0.68, so EAD = (0.68 ÷ 0.79) × (30 + 10) − 10 = 0.8608 × 40 − 10 = 34.43 − 10 = 24.43 m. Plan the decompression as a 24 m dive rather than a 30 m dive.
CNS clock. The NOAA single-exposure limit at 1.2 bar is 210 minutes and at 1.3 bar it is 180 minutes, so at 1.28 bar it is about 186 minutes. Twenty-five minutes is 25 ÷ 186 = 13.4% of the clock, leaving ample room for a second dive.

Now test the boundary. If the same cylinder were taken to 40 m, the ambient pressure would be 5.0 bar and the oxygen partial pressure 0.32 × 5.0 = 1.6 bar — the contingency ceiling, not a working depth, and 6.25 m past the calculated MOD of 33.75 m. That six metres is the entire margin between a routine dive and a partial pressure most agencies will not let you work at.

Choosing a limit and reading the numbers

1.4 bar is the working limit taught by every recreational agency, and it is the number to plan the deepest part of a dive against. 1.6 bar is a contingency ceiling — it appears in decompression planning, where the diver is stationary, warm-ish and unstressed at a shallow stop, and as the absolute figure beyond which a mix is simply wrong for that depth. Working at 1.6 is not a slightly bolder version of working at 1.4; the factors that trigger a seizure are exertion, carbon dioxide retention, cold and immersion, and all of them are present in the working phase of a dive and largely absent at a deco stop. Dropping to 1.2 or 1.3 bar is reasonable for long dives, repetitive days, cold water or hard work.

Round the MOD down, never up. A calculated 33.75 m becomes 33 m on the cylinder label. The half metre you give away is worth nothing; the half metre you take is spent in exactly the regime the limit exists to avoid.

Read the CNS percentage as a budget across the day, not a per-dive score. The NOAA figures are single-exposure limits, and repetitive dives accumulate. The clock also decays with a half-time of about 90 minutes on the surface, which this calculator does not model — it reports the single dive only. Treat anything above 80% on one dive as a plan that leaves you no second dive.

Equivalent air depth is the payoff figure. An EAD several metres shallower than the actual depth is why you are diving nitrox at all, and it is what to feed into a table or a planning tool. If your computer is set to the correct mix it is already doing this internally — but if you dive nitrox with the computer set to air, you get the decompression conservatism of air with the oxygen exposure of nitrox, which is the worst of both and a surprisingly common error.

NOAA single-exposure oxygen limits

Maximum time at a given oxygen partial pressure for a single exposure, from the NOAA Diving Manual.
Oxygen partial pressure (bar)	Single exposure limit (min)	Depth on EAN32 (m, sea water)
0.6	720	8.8
0.8	450	15.0
1.0	300	21.3
1.2	210	27.5
1.3	180	30.6
1.4	150	33.8
1.5	120	36.9
1.6	45	40.0

Depths are the depth at which EAN32 produces that partial pressure, computed as (PO2 ÷ 0.32 − 1) × 10. The drop from 120 minutes at 1.5 bar to 45 minutes at 1.6 bar is a real discontinuity in the published table, so linear interpolation across that last interval is crude and conservative planning should not rely on it.

Maximum operating depth for standard mixes in sea water

MOD in metres and feet at the two limits in common use.
Mix	1.4 bar (m)	1.4 bar (ft)	1.6 bar (m)	1.6 bar (ft)
Air (21%)	56.7	186	66.2	217
EAN28	40.0	131	47.1	155
EAN30	36.7	120	43.3	142
EAN32	33.8	111	40.0	131
EAN34	31.2	102	37.1	122
EAN36	28.9	95	34.4	113
EAN40	25.0	82	30.0	98
EAN50	18.0	59	22.0	72
EAN80	7.5	25	10.0	33
Oxygen (100%)	4.0	13	6.0	20

All values are the MOD formula evaluated at 10 m per bar, then converted at 0.3048 m per foot. Note that EAN28 at 1.4 bar and EAN32 at 1.6 bar both give exactly 40 m. EAN32 is the default recreational mix because it gives 33.8 m at the 1.4 bar working limit - clear of the common 30 m dive with 3.8 m in hand - while its 1.6 bar contingency depth falls exactly on the 40 m recreational limit.

Mistakes and assumptions worth knowing about

Diving the label instead of the analysis. A cylinder marked EAN32 that analyses at 35% has a MOD of 30.0 m against 33.75 m — nearly 4 m shallower. Analyse every cylinder yourself, record the reading, and mark the MOD on the tank.
Setting the computer to air while breathing nitrox. You keep the decompression conservatism of air and lose all track of oxygen exposure. Set the computer to the analysed mix before the dive.
Treating 1.6 bar as a working limit. It is a contingency and decompression figure. Exertion, cold and carbon dioxide retention all lower the threshold at which a seizure occurs, and all of them belong to the working phase of a dive.
Forgetting fresh water. A quarry or a lake needs 10.3 m per bar, so every MOD is about 3% deeper than the sea water figure. The difference is small but it is in the unhelpful direction if you use fresh-water figures at sea.
Ignoring the depth overshoot. A MOD is a limit for the deepest point reached, including the moment you drop below the intended depth chasing something. Plan with a margin rather than to the exact number.
Assuming the CNS clock resets between dives. It decays with roughly a 90-minute half-time on the surface and does not clear instantly. This calculator reports a single exposure and does not track a surface interval or a series of dives.
Confusing CNS toxicity with pulmonary toxicity. The CNS clock is about seizures over minutes to hours; pulmonary oxygen toxicity is a separate, slower injury measured in oxygen tolerance units and matters on long or repetitive technical exposures.

This is a planning aid, not a substitute for training

Diving enriched air requires formal training and a certification most fill stations will ask to see. The arithmetic on this page is the easy part of that training; the judgement about limits, analysis discipline, cylinder marking, blending safety and what to do when a plan changes underwater is the rest of it, and it is not something a web page can supply. Nothing here overrides your training agency's standards, your instructor, the analysis on the cylinder in front of you, or a dive computer set to the correct mix. If you have not been trained to use nitrox, the answer to any question this calculator raises is a course, not a deeper dive.

Where MOD sits among the other gas calculations

Maximum operating depth is one of four numbers that define a nitrox dive, and they are worth computing together. MOD is the depth ceiling set by oxygen. Equivalent air depth is the decompression benefit set by nitrogen. Gas consumption is set by your surface air consumption rate multiplied by the ambient pressure, which is why a 30 m dive drains a cylinder four times as fast as the same swimming at the surface. And the ambient pressure itself, the quantity all three depend on, comes from the depth to pressure relationship.

If you blend your own gas, the same partial pressure arithmetic runs in the other direction: how much oxygen to put in a cylinder before topping with air to reach a target mix at a target pressure. That is the partial pressure blending calculation, and it uses Dalton's law exactly as this page does, applied to cylinder pressure rather than to depth.

Beyond recreational nitrox, the same limit governs technical diving with a different emphasis. Trimix adds helium to reduce both narcosis and oxygen fraction, so deep mixes are hypoxic at the surface and have a minimum operating depth as well as a maximum. Decompression gases are chosen so that the switch depth puts the partial pressure near 1.6 — EAN50 at 21 m and oxygen at 6 m are the standard pair, and both fall straight out of the formula on this page.

Key terms

Nitrox / EANx: Enriched air nitrox: a breathing mix of oxygen and nitrogen with more than 21% oxygen. EAN32 means 32% oxygen, the rest nitrogen.
Partial pressure: The pressure a single gas in a mixture would exert on its own, equal to its fraction multiplied by the total pressure. Physiological effects depend on partial pressure, not percentage.
Maximum operating depth (MOD): The deepest point at which a given mix keeps oxygen partial pressure at or below the chosen limit. A hard ceiling, not a target.
Best mix: The richest mix whose oxygen partial pressure reaches the chosen limit exactly at the planned depth, giving the most decompression benefit the limit allows.
Equivalent air depth (EAD): The depth on air that produces the same nitrogen partial pressure as your mix at the actual depth. Used for decompression planning with air tables.
CNS oxygen clock: Accumulated central nervous system oxygen exposure, expressed as a percentage of the published single-exposure limit for the partial pressure being breathed.

References

NOAA Diving Manual: Diving for Science and Technology, 6th ed. — U.S. National Oceanic and Atmospheric Administration
U.S. Navy Diving Manual, Revision 7 — Naval Sea Systems Command
Bennett and Elliott's Physiology and Medicine of Diving, 5th ed. — Saunders

Nitrox Maximum Operating Depth Calculator

Calculator

It returns

The formula