# Equivalent narcotic depth

Equivalent narcotic depth (END) is used in technical diving as a way of estimating the narcotic effect of a breathing gas mixture, such as heliox and trimix. The method is, for a given mix and depth, to calculate the depth which would produce the same narcotic effect when breathing air.

The equivalent narcotic depth of a breathing gas mix at a particular depth is calculated by finding the depth of a dive when breathing air that would have the same total partial pressure of nitrogen and oxygen as the breathing gas in question. For example, a trimix containing 20% oxygen, 40% helium, 40% nitrogen (trimix 20/40) being used at 60 metres (200 ft) has an END of 32 metres (105 ft).

## Calculations

### Metres

The equivalent narcotic depth can be calculated for depths in metres as follows:

END = (Depth + 10) × (1 − Fraction of helium) − 10

Working the earlier example, for a gas mix containing 40% helium being used at 60 metres, the END is:

END = (60 + 10) × (1 − 0.4) − 10
END = 70 × 0.6 − 10
END = 42 − 10
END = 32 metres

So at 60 metres on this mix, the diver would feel the same narcotic effect as a dive on air to 32 metres.

### Feet

The equivalent narcotic depth can be calculated for depths in feet as follows:

END = (Depth + 33) × (1 − Fraction of helium) − 33

Working the earlier example, for a gas mix containing 40% helium being used at 200 feet, the END is:

END = (200 + 33) × (1 − 0.4) − 33
END = 233 × 0.6 − 33
END = 140 − 33
END = 107 feet

So at 200 feet on this mix, the diver would feel the same narcotic effect as a dive on air to 107 feet.

## Oxygen Narcosis

Since there is evidence that oxygen plays a part in the narcotic effects of a gas mixture,[1] the NOAA diving manual recommends treating oxygen and nitrogen as equally narcotic.[2] This is now preferred to the previous method of considering only nitrogen as narcotic, since it is more conservative. In this analysis, it is assumed that the narcotic potentials of nitrogen and oxygen are similar. Although oxygen has greater lipid solubility than nitrogen and therefore should be more narcotic (Meyer-Overton correlation), it is likely that some of the oxygen is metabolised, thus reducing its effect to a level similar to that of nitrogen.

## References

1. ^ Hesser CM, Fagraeus L, Adolfson J (December 1978). "Roles of nitrogen, oxygen, and carbon dioxide in compressed-air narcosis". Undersea Biomed Res 5 (4): 391–400. PMID 734806. Retrieved 2008-05-01.
2. ^ "Mixed-Gas & Oxygen". NOAA Diving Manual, Diving for Science and Technology. 4th. National Oceanic and Atmospheric Administration. 2002. [16.3.1.2.4] ... since oxygen has some narcotic properties, it is appropriate to include the oxygen in the END calculation when using trimixes (Lambersten et al. 1977,1978). The non-helium portion (i.e., the sum of the oxygen and the nitrogen) is to be regarded as having the same narcotic potency as an equivalent partial pressure of nitrogen in air, regardless of the proportions of oxygen and nitrogen.