Equivalent narcotic depth (END) is used in technical diving

Technical diving

Technical diving is a form of scuba diving that exceeds the scope of recreational diving...

 as a way of estimating the narcotic

Nitrogen narcosis

Narcosis while diving , is a reversible alteration in consciousness that occurs while scuba diving at depth. The Greek word ναρκωσις is derived from narke, "temporary decline or loss of senses and movement, numbness", a term used by Homer and Hippocrates...

 effect of a breathing gas

Breathing gas

Breathing gas is a mixture of gaseous chemical elements and compounds used for respiration.Air is the most common and only natural breathing gas...

 mixture, such as heliox

Heliox

Heliox is a breathing gas composed of a mixture of helium and oxygen .Heliox has been used medically since the 1930s, and although the medical community adopted it initially to alleviate symptoms of upper airway obstruction, its range of medical uses has since expanded greatly, mostly because of...

 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

Partial pressure

In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....

 of nitrogen

Nitrogen

Nitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...

 and oxygen

Oxygen

Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 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 (196.9 ft) has an END of 32 metres (105 ft).

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, the NOAA diving manual recommends treating oxygen and nitrogen as equally narcotic.
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.