Calculator
END calculator — Equivalent narcotic depth
Equivalent narcotic depth (END) estimates how narcotic a gas mix feels at depth, expressed as the depth on air that would produce a similar narcosis level. END is what drives the helium content of a trimix — the deeper the dive, the more helium you add to keep END inside an acceptable range.
How END is calculated
Both nitrogen and oxygen are considered narcotic in the technical-diving convention used here. Helium is treated as non-narcotic. END is the depth at which the sum of N₂ + O₂ partial pressures matches what air would produce.
END (m) = (FO₂ + FN₂) × (D + 10) − 10 FO₂ oxygen fraction FN₂ nitrogen fraction (1 − FO₂ − FHe) D actual depth (m)
Worked example: Trimix 18/45 at 60 m. FO₂ + FN₂ = 0.55. END = 0.55 × (60 + 10) − 10 ≈ 28 m. Adding more helium would lower END further, at the cost of cylinder fill complexity and cost.
Why O₂ is included
Most modern texts and the engine on this site treat oxygen as equally narcotic to nitrogen. Some older sources only count nitrogen, giving a slightly lower END — both conventions exist and either is defensible for personal limits, but the FO₂ + FN₂ approach is the standard for technical dive planning.
Frequently asked questions
- What's a typical END limit?
- Most technical agencies cap END at 30 m for normoxic trimix dives and tighter (24 m or less) for hypoxic mixes where workload and gas-density concerns also tighten.
- What's the END of Trimix 18/45 at 60 m?
- About 28 m using the standard FO₂ + FN₂ convention. Same mix at 50 m drops to ~22 m END, which is why 18/45 is a common 50–60 m gas.
- Should I worry about O₂ narcosis specifically?
- There's still active debate, but lab and field evidence is strong that oxygen contributes to narcosis at elevated partial pressures. Treating O₂ as narcotic gives a slightly more conservative END — useful margin for mixed-gas planning.
- Can I use END for Nitrox?
- Yes — for Nitrox, FHe = 0, so END essentially equals actual depth (since you replaced N₂ with O₂, which we treat as narcotic). For nitrogen-only narcosis modeling, EAD is the standard tool.