Before Nitrox-capable dive computers became standard, EAD solved a practical planning problem. Most decompression tables were built for air. Instead of requiring a separate table for every possible Nitrox mixture, a diver could translate a Nitrox dive into a shallower equivalent depth on air and use the existing air table.
Modern dive computers have largely eliminated that job. Analyze your gas, enter the actual oxygen percentage into the computer, and dive the real depth. For recreational divers today, EAD is mostly a historical and theoretical concept.
It remains useful because it provides a good way to understand what Nitrox actually changes.
A Practical Way to Think About Partial Pressure
Partial pressure sounds much more complicated than the idea behind it.
As you descend, the pressure around you increases. The breathing gas in your regulator is delivered at that surrounding pressure. Every gas in the mixture represents some fraction of the total.
Think of the total pressure as being divided among the gases according to how much of each gas is present.
At 80 feet of seawater, the absolute pressure is:
\[ P_{ambient}=\frac{80+33}{33} \]
\[ P_{ambient}=\frac{113}{33} \]
\[ P_{ambient}=3.4242\ ATA \]
Air is approximately 79 percent nitrogen for purposes of the EAD calculation, so the nitrogen partial pressure while breathing air at 80 feet is:
\[ P_{N_2}=3.4242\times0.79 \]
\[ P_{N_2}=2.7051\ ATA \]
EAN32 contains 32 percent oxygen, leaving 68 percent nitrogen:
\[ P_{N_2}=3.4242\times0.68 \]
\[ P_{N_2}=2.3285\ ATA \]
Both divers are physically at 80 feet. Both are under exactly the same ambient pressure. The diver breathing EAN32 simply has less nitrogen making up that pressure.
For an intuitive mental model, you can think of nitrogen partial pressure as the intensity of your nitrogen exposure at that moment. That is not technically the same thing as the amount of nitrogen already absorbed by your body. Nitrogen uptake also depends on time and how different tissues absorb and release gas. But lower nitrogen partial pressure means there is less pressure driving nitrogen into those tissues.
EAN32 at 80 feet therefore produces less nitrogen pressure than air at 80 feet.
Equivalent Air Depth expresses that difference as a depth.
What Equivalent Air Depth Means
Equivalent Air Depth asks what depth you would have to reach on air to produce the same nitrogen partial pressure as the Nitrox mixture produces at the actual depth.
EAN32 at 80 feet produces approximately the same nitrogen partial pressure as air at 64 feet.
So:
\[ \text{80 ft on EAN32}\approx\text{64 ft EAD} \]
For normal conversation, saying that EAN32 at 80 feet gives roughly the same nitrogen exposure as air at 64 feet is a useful shorthand. More precisely, it produces the same nitrogen partial pressure.
Nothing else about the 80-foot dive has become a 64-foot dive.
The Equivalent Air Depth Formula
For depth measured in feet of seawater:
\[ \boxed{ EAD=((Depth+33)\times\frac{F_{N_2}}{0.79})-33 } \]
Depth is the actual depth of the dive.
\(F_{N_2}\) is the fraction of nitrogen in the Nitrox mixture.
0.79 is the nitrogen fraction used for air in the calculation.
For a Nitrox mixture containing only oxygen and nitrogen:
\[ F_{N_2}=1-F_{O_2} \]
EAN32 contains 32 percent oxygen:
\[ F_{N_2}=1-0.32 \]
\[ F_{N_2}=0.68 \]
The formula can also be used in meters of seawater by replacing 33 with 10:
\[ \boxed{ EAD=((Depth+10)\times\frac{F_{N_2}}{0.79})-10 } \]
Why 33 Feet Appears in the Formula
Depth and absolute pressure are not the same thing.
At the surface, you are already under approximately one atmosphere of pressure from the atmosphere above you. Descending approximately 33 feet in seawater adds another atmosphere.
A diver at 33 feet is therefore at approximately:
\[ 2\ ATA \]
A diver at 66 feet is at approximately:
\[ 3\ ATA \]
Adding 33 feet to the actual depth incorporates the atmosphere that already exists at the surface:
\[ Depth+33 \]
The nitrogen fraction of the Nitrox mixture is then compared with the nitrogen fraction of air:
\[ \frac{F_{N_2}}{0.79} \]
For EAN32:
\[ \frac{0.68}{0.79}=0.86076 \]
EAN32 therefore contains about 86 percent as much nitrogen as air.
The formula applies that relationship to absolute pressure and subtracts 33 feet at the end to convert the result back into an underwater depth.
Example: EAN32 at 80 Feet
Start with:
\[ EAD=((Depth+33)\times\frac{F_{N_2}}{0.79})-33 \]
EAN32 contains 68 percent nitrogen:
\[ F_{N_2}=0.68 \]
Insert the actual depth:
\[ EAD=((80+33)\times\frac{0.68}{0.79})-33 \]
Add the surface atmosphere:
\[ 80+33=113 \]
Calculate the relationship between the nitrogen fractions:
\[ \frac{0.68}{0.79}=0.860759 \]
Multiply:
\[ 113\times0.860759=97.2658 \]
Subtract the surface atmosphere:
\[ 97.2658-33=64.2658 \]
Rounded normally:
\[ \boxed{EAD\approx64.3\ ft} \]
The nitrogen partial pressure calculation confirms the result.
At 80 feet:
\[ P_{ambient}=\frac{80+33}{33}=3.4242\ ATA \]
Breathing EAN32:
\[ P_{N_2}=3.4242\times0.68=2.3285\ ATA \]
At an air depth of 64.2658 feet:
\[ P_{ambient}=\frac{64.2658+33}{33}=2.9474\ ATA \]
Nitrogen partial pressure while breathing air:
\[ P_{N_2}=2.9474\times0.79=2.3285\ ATA \]
The nitrogen partial pressures are the same.
See EAD in the Nitrox Calculator
The DiveOtter Nitrox Calculator shows oxygen partial pressure, Maximum Operating Depth, and Equivalent Air Depth together.
Change the oxygen percentage and you can see the relationship directly. As oxygen increases, nitrogen decreases, and the Equivalent Air Depth becomes shallower.
The calculator rounds EAD upward to five-foot increments for its table. The EAN32-at-80-feet calculation above produces a raw EAD of 64.27 feet, so the calculator displays it as 65 feet.
You do not need the calculator to plan an ordinary recreational dive around EAD. It is useful for seeing the concept in action without repeatedly working the formula by hand.
Why Divers Used EAD
Air decompression tables already provided depth and time limits based on breathing air. Nitrox changed the nitrogen fraction, which meant the nitrogen pressure at a given depth no longer matched the value represented by that same depth on an air table.
EAD converted the Nitrox dive into a depth the air table could use.
If EAN32 at 80 feet produced the same nitrogen partial pressure as air at approximately 64 feet, the diver could use the appropriate air-table depth for the nitrogen portion of the dive planning.
The same method could be applied to other Nitrox mixtures without producing a separate decompression table for every possible oxygen percentage.
Dive computers now perform decompression calculations using the breathing-gas mixture entered into the computer. The conversion to an equivalent air depth is no longer necessary for normal recreational computer diving.
What EAD Does Not Change
An 80-foot dive on EAN32 remains an 80-foot dive.
Ambient pressure is based on 80 feet. Gas consumption is affected by the pressure at 80 feet. Your BCD and exposure protection respond to the pressure at 80 feet. Your actual depth is still 80 feet.
Oxygen partial pressure is also calculated using the actual depth:
\[ P_{O_2}=P_{ambient}\times F_{O_2} \]
For EAN32 at 80 feet:
\[ P_{O_2}=3.4242\times0.32 \]
\[ P_{O_2}=1.0957\ ATA \]
The 64-foot EAD has no role in that calculation.
Equivalent Air Depth is specifically a way to express the nitrogen component of the dive as an equivalent depth on air.
EAD and MOD Answer Different Questions
Equivalent Air Depth describes the nitrogen side of Nitrox. Maximum Operating Depth describes the oxygen side.
Increasing the oxygen percentage decreases the nitrogen fraction. At the same actual depth, nitrogen partial pressure decreases and the EAD becomes shallower.
The higher oxygen fraction simultaneously increases oxygen partial pressure. As depth increases, oxygen partial pressure eventually reaches the limit selected for the dive, establishing the Maximum Operating Depth.
A richer Nitrox mixture therefore provides less nitrogen exposure at a given depth while also imposing a shallower oxygen depth limit.
For a recreational diver using a modern computer, understanding and respecting MOD has direct operational importance. EAD is primarily the conceptual explanation for what happened to the nitrogen.