Computing safe O₂ / He / N₂ breathing gas blends for technical deep diving
Technical diving begins long before the water — with a target depth and a purpose. A wreck resting at 70 m, a cave system pushing past 90 m, or a deep pinnacle beyond recreational no-decompression limits all demand a breathing gas engineered specifically for that depth, not an off-the-shelf mix. Every subsequent gas decision (oxygen fraction, helium fraction, nitrogen residual) is a function of this one number.
In recreational diving, a single gas — air, or occasionally 32% or 36% nitrox — covers nearly every dive. Technical diving inverts that logic entirely: the dive plan starts with a target depth and required bottom time, and the breathing gas is engineered backward from those constraints to satisfy two independent physiological limits simultaneously.
Air becomes physiologically unsuitable well before 60 m for two separate reasons. First, its 21% oxygen fraction produces a dangerously high partial pressure of oxygen at depth, risking CNS oxygen toxicity (an underwater seizure is usually fatal). Second, its 79% nitrogen fraction produces severe nitrogen narcosis — the "martini effect" — that impairs judgment, motor coordination, and situational awareness at exactly the depths where mistakes are least survivable.
Trimix solves both problems at once by adding a third gas — helium — which is metabolically inert, essentially non-narcotic at depth, and allows the diver to independently dial down both the oxygen fraction (for toxicity) and the nitrogen fraction (for narcosis) while keeping the mix breathable.
Before any gas calculation begins, the dive is fully specified: maximum planned depth, expected bottom time, water temperature (helium's six-times-higher thermal conductivity versus nitrogen means deep cold-water divers lose body heat far faster and must plan for that), and the profile shape (square wreck penetration vs. multi-level cave traverse).
Bottom time interacts directly with decompression obligation: longer bottom times at depth load more inert gas (both nitrogen and helium) into body tissues, requiring longer staged decompression stops on the ascent. Technical divers typically plan bottom time conservatively and treat the ascent — often 60–90+ minutes of staged stops on multiple gases — as the true "dive," with the bottom phase being comparatively brief.
This is also the point where a diver selects their target working PO₂ (commonly 1.2–1.4 ATA for the bottom mix, kept conservative because exertion and cold both increase oxygen toxicity risk) and their personal narcosis tolerance, which becomes the END slider constraint used in Stage 3.
Helium-oxygen breathing gas was pioneered not by sport divers but by the offshore oil industry. Compagnie Maritime d'Expertises (Comex), a French commercial diving company, developed heliox and later trimix protocols through the 1960s–1980s to support saturation divers working on subsea pipelines and platforms at depths beyond 200 m, eventually setting experimental chamber dive records past 700 m.
Sport and technical trimix diving emerged in the 1990s, driven largely by cave explorers. The Woodville Karst Plain Project (WKPP), mapping Florida's flooded cave systems, pushed trimix protocols, gas-planning rules, and redundant-gas philosophy that became the backbone of modern technical training agencies (IANTD, TDI, GUE). Divers like Sheck Exley and later Jarrod Jablonski demonstrated that carefully planned trimix dives could push well past 90 m safely and repeatably — knowledge that filtered from cave exploration into wreck and open-water technical diving worldwide.
A useful rule of thumb some technical agencies still teach: keep the diver's Equivalent Narcotic Depth no deeper than what they would tolerate breathing air — commonly capped at 30 m (100 ft) equivalent narcosis, regardless of actual depth.
Oxygen is essential for life but becomes a neurotoxin at high partial pressure. The first gas decision in any trimix blend is choosing FO₂ (the fraction of oxygen in the mix) low enough that its partial pressure at the target depth stays under a safe ceiling — this defines the Maximum Operating Depth for that mix.
By Dalton's Law, the partial pressure of a gas in a mixture equals its fraction multiplied by the total ambient pressure: PO₂ = FO₂ × ATA, where ATA (atmospheres absolute) = (depth in meters ÷ 10) + 1.
Breathing oxygen above roughly 1.4–1.6 ATA risks acute CNS oxygen toxicity: symptoms include visual tunneling, tinnitus, nausea, twitching, and — without warning in many cases — a full tonic-clonic seizure. Underwater, a seizure reliably causes regulator loss and drowning. Because there is often no warning ("VENTID-C" symptoms are inconsistent), technical divers treat the PO₂ ceiling as a hard, non-negotiable limit rather than something to approach and back off from.
The standard working limit for a bottom (working) gas is PO₂ 1.4 ATA, with 1.6 ATA reserved as an absolute maximum typically only tolerated briefly on shallow decompression gases where exertion is minimal.
Maximum Operating Depth (MOD) is the deepest depth at which a given oxygen fraction stays at or below the chosen PO₂ ceiling. Rearranging Dalton's Law for depth:
MOD = (PO₂max ⁄ FO₂ − 1) × 10
For example, a bottom mix with FO₂ = 0.18 (18% oxygen) has: MOD (at PO₂ 1.4) = (1.4 / 0.18 − 1) × 10 = (7.78 − 1) × 10 ≈ 67.8 m MOD (at PO₂ 1.6, hard ceiling) = (1.6 / 0.18 − 1) × 10 ≈ 78.9 m
Conversely, working backward from a known target depth gives the maximum FO₂ that mix can safely contain: FO₂ = PO₂max / ATA. This is exactly the calculation this simulator performs live as the depth slider moves — deeper target depths force progressively "thinner" (more hypoxic) oxygen fractions.
Formula: MOD = (PO₂max / FO₂ − 1) × 10. At 90 m with PO₂max 1.4, the maximum allowable FO₂ is 1.4 / 10 = 0.14 → a 14% oxygen bottom mix.
Mixes with FO₂ below 18% ("hypoxic trimix") are unsafe to breathe at the surface — 12% or 10% oxygen at 1 ATA produces hypoxia and can cause blackout within seconds, with no warning sensation of breathlessness. This creates a critical procedural rule: hypoxic bottom mixes must never be breathed above their "minimum operating depth," and cylinders containing them must be clearly labeled and staged only at depth (e.g. clipped off at a shot line at 30 m, never carried from the surface as the diver's starting gas).
Divers instead breathe a separate travel gas (often nitrox or air) from the surface down to the depth where switching to the hypoxic bottom mix becomes both necessary (nitrogen narcosis mounting) and safe (PO₂ no longer dangerously low). This gas-switching choreography — travel gas, bottom mix, one or more decompression gases — is planned meticulously and rehearsed before every dive, with every cylinder analyzed and clearly marked with its MOD.
Nitrogen narcosis progressively impairs judgment and coordination with increasing depth, much like alcohol intoxication. Helium is added to displace nitrogen specifically because — for planning purposes — it is treated as producing no narcotic effect at typical technical diving depths, letting the diver dial narcosis back down to a chosen, tolerable equivalent.
Nitrogen narcosis (sometimes called "rapture of the deep") is caused by increased partial pressure of nitrogen dissolving into neural membranes, altering nerve signal transmission in a manner functionally similar to inert-gas anesthesia. Divers experience progressively impaired short-term memory, tunnel vision, slowed reaction time, poor judgment, and in severe cases euphoria or dread strong enough to cause fatal decision-making errors — at exactly the depths where task loading (navigation, gas switches, buoyancy in overhead environments) is highest.
Unlike oxygen toxicity, narcosis has no hard biological threshold — it is a continuum that worsens gradually with depth and varies significantly between individuals and even between dives for the same diver (cold, fatigue, and CO₂ retention all worsen it). Technical divers therefore plan not to a fixed biological limit but to a personally chosen, conservative comfort ceiling.
Equivalent Narcotic Depth (END) expresses the narcotic potency of a trimix blend in terms of the depth on ordinary air that would feel equally narcotic. Since helium is treated as non-narcotic, only the combined oxygen and nitrogen fractions contribute:
END = ((FN₂ + FO₂) × (depth + 10)) − 10
(Some conservative planning models also count oxygen as roughly as narcotic as nitrogen, which is exactly what this formula already does by combining FN₂ + FO₂ — a widely used and appropriately cautious convention.)
Rearranged to solve for the required narcotic gas fraction at a target depth and a chosen END limit: FN₂ + FO₂ (max) = (END + 10) / (depth + 10)
Subtracting the FO₂ already fixed by the MOD constraint in Stage 2 leaves the maximum allowable FN₂ — and whatever fraction remains after O₂ and that N₂ is filled with helium.
Formula: END = ((FN₂ + FO₂) × (depth + 10)) − 10. At 90 m breathing 14/50 trimix (14% O₂, 50% He, 36% N₂): END = (0.50 × 100) − 10 = 40 m — roughly the narcotic load of a 40 m air dive, not a 90 m one.
It is tempting to add as much helium as possible to minimize narcosis, but helium carries real costs beyond price: its high thermal conductivity accelerates convective heat loss through the lungs and skin, meaningfully increasing hypothermia risk on long, cold dives unless offset with heated undergarments or gas. Helium also produces a measurable "High Pressure Nervous Syndrome" (HPNS) — tremor, nausea, and reduced cognitive performance — at the very deep, fast-compression profiles used in saturation and record diving, though this is rarely a factor at typical 60–100 m sport-technical depths.
For these reasons, experienced trimix planners choose an END target that is "acceptable," not zero. A common working standard is an END no deeper than roughly the depth at which the diver would first notice mild narcosis on air (often 30 m), rather than driving END down to sea level, which would demand impractically large — and expensive — helium fractions.
Once FO₂ satisfies the MOD constraint and FHe satisfies the END constraint, the remaining fraction is nitrogen by definition — the three fractions must sum to 1.0 (100%). The finished mix is given a standard trimix name and, critically, is never trusted from calculation alone: it is cross-checked against printed dive tables or a dive computer before the dive.
Trimix blends are conventionally named "O₂/He" — two numbers giving the oxygen percentage first, then the helium percentage, with nitrogen left implicit as whatever remains. "Trimix 18/45" means 18% oxygen, 45% helium, and by subtraction 37% nitrogen (100 − 18 − 45). "Trimix 21/35" means 21% O₂, 35% He, 44% N₂.
Two related naming families exist for the boundary cases: "Heliox" describes a binary oxygen-helium mix with zero nitrogen (used at extreme depths or in saturation diving, where even helium's modest narcotic effect becomes relevant). "Nitrox" describes an oxygen-nitrogen mix with zero helium (used at shallower depths where narcosis is not yet a limiting factor and no helium is needed at all).
No experienced technical diver treats a hand or spreadsheet calculation as dive-ready without independent verification. Standard practice is threefold: (1) recompute MOD and END using printed reference tables or a second independent gas-planning tool, (2) enter the exact analyzed FO₂ and FHe into a multi-gas dive computer, which then computes real-time decompression obligation using that specific blend's inert gas loading, and (3) have a dive buddy or instructor independently verify the plan before kitting up.
This redundancy exists because a gas-planning error is not a minor inconvenience underwater — an unplanned hypoxic blackout, an unexpected oxygen seizure, or an incorrectly staged decompression gas can be unrecoverable at depth. The calculation shown in this simulator mirrors exactly what a real gas-blending worksheet or planning app performs, but is not a substitute for certified training.
The table below shows representative trimix blends used across common technical diving depth ranges, each satisfying a working PO₂ of 1.4 ATA and a target END of roughly 30 m or less. Notice how FO₂ falls and FHe rises steadily as target depth increases — both constraints tighten simultaneously with pressure.
| Product | Indication | Trial Design | Key Result |
|---|---|---|---|
| Trimix 21/35 | 45–55 m range | MOD ≈ 56.7 m at PO₂ 1.4; END ≈ 29 m at 50 m depth | Near-normoxic, safe to breathe at surface, modest He cost |
| Trimix 18/45 | 55–70 m range | MOD ≈ 67.8 m at PO₂ 1.4; END ≈ 28 m at 65 m depth | Workhorse wreck-diving blend, still normoxic |
| Trimix 12/60 | 80–95 m range | MOD ≈ 106.7 m at PO₂ 1.4; END ≈ 26 m at 90 m depth | Hypoxic — needs surface travel gas, strong narcosis control |
| Trimix 10/70 | 95–110 m range | MOD ≈ 130 m at PO₂ 1.4; END ≈ 24 m at 100 m depth | Deep hypoxic exploration mix, high He fraction, high cost |
A calculated recipe means nothing until it is physically realized in a cylinder and confirmed with instruments. Trimix is blended by one of two core methods, and every finished cylinder is analyzed for both oxygen and helium content before it touches the water — alongside a fully planned bailout strategy in case the primary gas plan fails underwater.
The classic method uses Dalton's Law directly: gases are added to a cylinder sequentially in order of increasing final partial pressure, most commonly helium first (cheapest to mismeasure early), then oxygen topped to the target partial pressure, then air or pure nitrogen to finish filling to the working pressure.
Because each gas's partial pressure is simply its fraction of the total fill pressure, a blender calculates target fill pressures at each stage: e.g., for a 200 bar final fill of Trimix 18/45, helium is added first to some intermediate pressure, then oxygen is added up to a calculated stopping pressure, then air tops off the rest — with the final analyzed FO₂ and FHe confirming the arithmetic worked. This method is inexpensive (no specialized equipment beyond a booster pump and gauges) but requires careful, patient technique, since overshooting the oxygen fill pressure even slightly can create a dangerously hyperoxic — or in the presence of oil/grease, combustion-risk — mixture.
Partial pressure blending relies entirely on Dalton's Law: total pressure = sum of each gas's partial pressure. Blend order matters — oxygen is always added with scrupulously clean, oxygen-compatible equipment to avoid adiabatic ignition.
Dive shops and technical fill stations increasingly use continuous blending systems: a computer-controlled panel meters streams of oxygen, helium, and compressed air (or nitrogen) simultaneously through mass-flow controllers into a booster compressor, monitoring the blend composition with inline analyzers in real time and adjusting flow rates to converge on the target FO₂/FHe automatically.
Continuous blending is faster, more repeatable, and reduces human error for high-volume operations (dive charter boats filling many hypoxic trimix cylinders daily), but requires significant capital investment in blending panels, membrane separators, and calibrated mass-flow equipment — one reason many technical divers still learn and use manual partial-pressure blending as a baseline skill.
Regardless of blending method, every finished cylinder is independently verified with a calibrated oxygen analyzer and helium analyzer immediately before the dive — never trusted from the blend recipe alone — and the measured FO₂/FHe (not the intended figures) are what get programmed into the dive computer and written on the cylinder label with a waterproof marker.
During the dive itself, divers track two oxygen exposure metrics: the CNS "oxygen clock" (a percentage-based model of acute CNS toxicity risk accumulated across the dive, with a single-exposure guideline around 300% before symptoms become statistically likely) and OTUs (Oxygen Tolerance Units, tracking cumulative pulmonary toxicity risk across repetitive diving days).
Finally, every trimix dive plan includes bailout gas: an independent, redundantly carried cylinder (often argon-inflated drysuit gas is kept fully separate from breathing gas for exactly this reason) sized and blended to get the diver safely to the surface — including through all staged decompression stops — if the primary gas supply is lost at the deepest point of the dive. Bailout gas selection follows the identical MOD/END logic taught in Stages 2–4, just planned for the worst-case failure point rather than the ideal profile.