Equivalent Narcotic Depth Notes

The 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.


There are three different ways you can calculate the END of a mix:

1. Only Nitrogen is narcotic
2. Nitrogen and Oxygen are narcotic - This is the accepted BSAC standard
3. Nitrogen and helium are narcotic
4. Nitrogen, oxygen and helium are narcotic

Q1. What is the Equivalent Narcotic Depth of an 18/35 mix at 60 meters?

This answer assumes that only nitrogen is narcotic

First we need to work out the total narcotic fraction of the mix:

1 - (0.18 + 0.35) = 0.47

Then we need to work out the absolute pressure at 60 meters and adjust it by the relative difference of the narcotic constituents of the mix compared to air.

((60 / 10) + 1) * (0.47 / 0.79) = 4.164 bar

Then we need to convert this pressure back into a depth:

(4.164 -1) * 10 = 31.64 meters

These steps can be expressed in a single formula as:


We can further simplify the calculation by

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

Q2. You are planning a closed circuit trimix dive. You intend to dive to 75m for 25 minutes using a 15/55 bottom mix using twin 7lt stage cylinders for bailout. One stage cylinder contains 18/55 and the other contains 60% nitrox. What is the equivalent narcotic depth at 75m?

This answer assumes that only nitrogen and oxygen are narcotic

The back gas and bailout both contain 55% helium so the END would be:

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

END = (75 + 10) × (1 − 0.55) − 10

28 = (75 + 10) × (1 − 0.55) − 10

The Nitrox 60% has MOD of about 15 meters so its not breathable at 75 meters but for the sake of completeness the END would be:

33 = (75 + 10) * (0.4 / 0.79) - 10