Education

Equivalent Narcotic Depth (END)

END tells you the narcotic effect of a trimix at depth, expressed as an equivalent air depth. Essential for technical divers using helium.

When you add helium to your breathing mix, you reduce narcosis — but by how much? Equivalent Narcotic Depth gives you that answer, translating the narcotic load of any gas mix at any depth into an equivalent depth on air.

What it is

Nitrogen is narcotic under pressure. So is oxygen (this is debated but widely assumed in technical diving for conservative planning). Helium, however, is not. END calculates the combined narcotic effect of the nitrogen and oxygen fractions in your mix and tells you what depth on air would produce the same narcotic impairment.

A trimix dive to 60 meters might have an END of only 24 meters — meaning you feel as clear-headed as you would on air at 24 meters.

The formula

END = (((fN2 + fO2) × P) / 0.79 - 1) × 10
VariableMeaning
ENDEquivalent Narcotic Depth in meters of seawater
fN2Fraction of nitrogen in the mix
fO2Fraction of oxygen in the mix
PAbsolute pressure at depth in bar: (depth / 10) + 1
0.79Fraction of narcotic gas in air (N2 + O2 = 0.79 + 0.21)

Note on oxygen narcosis: This formula assumes oxygen is narcotic, which is the conservative assumption used by most technical diving agencies (TDI, IANTD, GUE). Some older references treat only nitrogen as narcotic. Dalton uses the conservative (oxygen-inclusive) model.

Worked example

What is the END for a dive to 60 meters on Trimix 18/45 (18% O2, 45% He)?

Step by step

fO2 = 0.18, fHe = 0.45, fN2 = 1 - 0.18 - 0.45 = 0.37
P = (60 / 10) + 1 = 7.0 bar
Narcotic fraction = fN2 + fO2 = 0.37 + 0.18 = 0.55
END = ((0.55 × 7.0) / 0.79 - 1) × 10
END = (3.85 / 0.79 - 1) × 10
END = (4.873 - 1) × 10
END = 38.73 msw

At 60 meters on Trimix 18/45, your narcotic load is equivalent to being on air at 38.7 meters. Without helium, you would experience full air narcosis at 60 meters — the equivalent of nearly 6 bar of narcotic gas.

Why it matters

Narcosis impairs judgment, slows reaction time, and can cause euphoria or anxiety. At depth, impaired judgment can be fatal. Technical divers use helium specifically to keep their END manageable:

  • Recreational threshold: Most divers notice narcosis starting around 30 meters on air
  • Technical planning: Many tech divers plan for a maximum END of 30 meters, regardless of actual depth
  • Deep diving: At 60+ meters, narcosis on air is severe. Trimix makes these depths workable

Safety considerations

  • END is not the same as EAD: EAD measures nitrogen loading for decompression purposes. END measures narcotic load. They use different gas fractions
  • Individual variation: Narcosis susceptibility varies between divers and even between dives for the same diver. Fatigue, cold, stress, and CO2 loading all increase narcotic effects
  • Conservative planning: If your END exceeds 30 meters, consider adding more helium to your mix
  • Oxygen narcosis debate: Some agencies do not count oxygen as narcotic. If you use the nitrogen-only model, your calculated END will be lower (less conservative)

Sources