END: equivalent narcotic depth
At what air depth does your mix "feel" like? Pick your gas and depth: END, gas density and the ideal mix show up instantly.
Your mix
Air, nitrox, trimix or heliox: tap a shortcut or set O₂ and helium.
Depth
Planned actual depth, in sea water.
Is oxygen narcotic?
Agencies disagree. It makes no difference for air, but it matters as soon as there is more than 21 % O₂ or any helium.
Oxygen counts as much as nitrogen, helium does not count. Used by GUE, PADI, CMAS and the NOAA manual: the most conservative choice.
How it is calculated
The idea
Narcosis comes from the pressure of the narcotic gases you breathe. END is the depth at which air would give the same narcotic gas pressure as your mix at your actual depth. The lower the END, the clearer your head.
P = depth ÷ 10 + 1 (bar, sea water)
Who counts what?
- O₂ narcotic: GUE, PADI, CMAS, PSAI, NOAA manual. SSI calls it narcotic "but much less than nitrogen".
- O₂ not narcotic: TDI, IANTD, BSAC, NAUI, ANDI. A 2022 EEG study (Vrijdag et al.) points that way, without consensus.
- Everyone agrees helium is (almost) non-narcotic.
When in doubt, the tool starts from the most conservative convention (O₂ + N₂).
1. O₂ + N₂ narcotic
Oxygen is considered as narcotic as nitrogen, and helium as non-narcotic. More conservative with oxygen-rich mixes.
END = [ P × (1 − fHe) − 1 ] × 10
2. N₂ only
Only nitrogen counts, compared with air's 79 % nitrogen. This is the historical formula; with nitrox it gives the same value as EAD.
END = [ P × fN₂ ÷ 0.79 − 1 ] × 10
3. All gases
Each gas is weighted by its narcotic potency, estimated from its lipid solubility (Meyer-Overton rule), nitrogen = 1: O₂ ≈ 1, He ≈ 0.23. Air is the reference (index 1).
Index = P × (fN₂ + fO₂ + fHe × 0.23); END = (Index − 1) × 10
This model gives a slightly deeper END than convention 1. It remains theoretical, best used to compare mixes.
Max depth and minimum helium
Max depth = [ (max END ÷ 10 + 1) ÷ (fO₂ + fN₂) − 1 ] × 10
min fHe = 1 − (max END ÷ 10 + 1) ÷ P
(Convention 1 formulas; the tool applies the version of the convention you chose.)
Ideal mix
The richest O₂ that stays under a PpO₂ of 1.4 bar at depth (rounded down to the %, capped at 40 %), then the least helium that keeps you under your END limit (rounded up to the %).
Gas density
A gas that is too dense is hard to breathe: CO₂ builds up and narcosis gets worse. Anthony and Mitchell (2016): ideally 5.2 g/L at most, never more than 6.2 g/L. Air passes 5.2 g/L around 33 m and 6.2 g/L around 41 m (gases at 20 °C).
Density ≈ P × (fO₂ × 1.331 + fN₂ × 1.165 + fHe × 0.166) g/L
Rounding
- END rounded up to the metre, max depth down to the metre, minimum helium up to the %: always on the safe side.
- Sea water, 10 m = 1 bar. In fresh water or at altitude the real pressure is slightly lower: the END shown stays conservative.
A learning aid: it replaces neither trimix training nor your dive planning. Sensitivity to narcosis varies from day to day and diver to diver (cold, fatigue, CO₂, stress).
END · O₂ + N₂
29m
At 60 m, this mix feels like air at 29 m.
Close to your limit (END 30 m)
gas density · above 5.2: limit exertion
Your limits
The maximum END you allow yourself. From it we derive the max depth of this mix and the ideal mix for your depth.
Partial pressures
At 60 m, absolute pressure 7.0 bar.
| Gas | Fraction | Pressure (bar) | Narc. weight |
|---|---|---|---|
| Oxygen | 18 % | 1.26 | × 1.00 |
| Nitrogen | 37 % | 2.59 | × 1.00 |
| Helium | 45 % | 3.15 | × 0.23 |
| Narcotic index | 4.57 | air = 1 |
Understanding END
What is END in diving?
END (Equivalent Narcotic Depth) is the depth at which air would produce the same narcosis as your mix at your actual depth. With helium, the END is shallower than the actual depth: that is the whole point of trimix. For the effect of nitrogen on nitrox decompression, the term is EAD: see the EAD tool.
Is oxygen narcotic?
Agencies disagree. GUE, PADI and CMAS count oxygen as narcotic; TDI, IANTD and BSAC count only nitrogen. It makes no difference for air, but matters as soon as the mix has more than 21 % oxygen or any helium. By default, the tool uses the most conservative convention.
Gas density: the other limit
The deeper you go, the denser the gas you breathe: breathing takes more effort, CO₂ builds up and worsens narcosis. The most quoted guidelines are 5.2 g/L ideally and 6.2 g/L at most. To pick the right bottom trimix directly, use the trimix blend tool; for the oxygen limit, the MOD tool.
Frequently asked questions
How do you calculate the END of a trimix?
Counting oxygen as narcotic: END = [P × (1 − fHe) − 1] × 10, with P = depth ÷ 10 + 1. Example: trimix 21/35 at 60 m, P = 7 bar, END = (7 × 0.65 − 1) × 10 = 35.5 m, i.e. 36 m rounded up.
What is the maximum END in diving?
30 m is the most common limit for mixed-gas dives. Some agencies go down to 24 m in demanding conditions (cold, poor visibility, exertion); 36 to 40 m are high limits.
Is the END of a nitrox shallower than the depth?
Only if you count nitrogen alone (it then equals the EAD). Counting oxygen as narcotic, a nitrox is as narcotic as air at the same depth: its advantage is decompression, not narcosis.
What gas density should you not exceed?
Ideally 5.2 g/L, and never more than 6.2 g/L (Anthony and Mitchell, 2016). With gases at 20 °C, air reaches 5.2 g/L around 33 m and 6.2 g/L around 41 m.