Are pressure and density directly proportional underwater?

Yes. Gas density and absolute pressure are directly proportional — when pressure doubles, density doubles. At 10m the absolute pressure is 2 ata, so air is twice as dense as at the surface. At 30m the absolute pressure is 4 ata, so air is four times as dense. This relationship holds at every depth.

How do you answer a density question in the PADI physics exam?

Density questions always use division. Find the absolute pressure at both depths. Divide the pressure at the denser depth by the pressure at the less dense depth to get the ratio. For example, air at 50m (6 ata) compared to the surface (1 ata): 6 ÷ 1 = 6 times as dense. For depth-to-depth density questions, divide the higher pressure by the lower pressure.

What is the density of air at 10m, 20m and 30m?

In salt water: at 10m (2 ata) air is twice as dense as at the surface. At 20m (3 ata) it is three times as dense. At 30m (4 ata) it is four times as dense. Density increases in direct proportion to absolute pressure, so the surface density is always the baseline and the depth pressure is always the multiplier.

Can a PADI physics exam question disguise a pressure question as a density question?

Yes. Some questions give a starting density value and ask what happens to density when depth changes — this looks like a density question but is fundamentally asking about the pressure ratio. The answer method is identical: find both absolute pressures and divide to get the relationship. The key is recognising that density and pressure change by exactly the same factor at any depth.

Density

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Pressure Depth Calcs Density Partial Pressure Buoyancy Lift Bags Fresh Water General Knowledge

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Density — concept introduction

Will Welbourn introduces the core concept behind density questions in the PADI physics exam, using the shopping bag analogy to show why you always divide.

Density questions are one of the most reliably straightforward question types in the PADI physics exam — once you understand the one rule that makes them different from every other calculation question on the paper. Unlike Boyle's Law questions, where you have to stop and decide whether to multiply or divide, density questions have no decision to make. You always divide. Every time, without exception.

Core principle The density of a gas is directly proportional to the pressure it is under. Double the pressure, double the density. Halve the pressure, halve the density. As a diver goes deeper, pressure increases — so each breath contains more gas molecules packed into the same lung volume. That gas is denser.

Why you always divide

The shopping bag analogy makes this intuitive. Imagine two identical shopping bags. One contains six apples, the other contains three. Same size bag — which bag has the greater density of apples? The one with six. And without thinking about it, you already knew to divide: 6 ÷ 3 = twice as dense.

That instinct is exactly what density questions are testing. You are comparing the number of gas molecules in a breath at one depth to the number of molecules in a breath at another depth. More pressure = more molecules = denser gas. The comparison is always a division.

How density differs from Boyle's Law In Boyle's Law (volume and air consumption) questions, you decide: deeper means more pressure, so multiply for consumption and divide for volume. With density questions there is no decision. Density always goes up as you go deeper, and you always divide the two pressures to find the proportional change. Never multiply.

The 3-step method

Density questions — 3 steps Step 1 — Identify the depth the diver is at in the question. Write down the pressure at that depth in ata.
Step 2 — It is a density question. Always divide. Write the division symbol.
Step 3 — Identify the comparison depth. Write down the pressure at that depth. If the comparison is the surface, write 1.

The number you get is your answer. If the result is a whole number, match it to the answer option that says "X times as dense." If the result is a fraction (e.g. 0.25), look for the fraction answer option (e.g. "1/4 of the density") — the fraction you wrote down in your working will often be written on the answer sheet already.

Pressure at key depths — quick reference

Depth	Pressure (ata)	Density relative to surface
Surface	1.0	1× (baseline)
10m	2.0	2× as dense
20m	3.0	3× as dense
30m	4.0	4× as dense
40m	5.0	5× as dense
50m	6.0	6× as dense

Seawater density Seawater has a density of approximately 1.03 kg/l (compared to 1.0 kg/l for fresh water). This figure appears in PADI theory exams and refers to the water the diver is moving through — not the gas being breathed. It is a fixed property of seawater, unaffected by depth. Do not confuse this with the density of the breathing gas, which changes with pressure.

Density — example question 1

Will Welbourn works through density example question 1 — comparing the density of air at 50m to the surface using the 3-step method.

Example question 1 What is the difference in the density of the air a diver breathes at 50m compared to the surface?

Depth the diver is at: 50m → pressure = 6 ata
It is a density question → always divide: 6 ÷ ...
Comparison depth: the surface → pressure = 1 ata
6 ÷ 1 = 6

Answer: 6 times as dense — the air at 50m contains six times as many molecules per breath as at the surface.

Exam trap — ratio, not difference If you answered 5 times as dense, here is what happened: you subtracted the pressures (6 − 1 = 5) instead of dividing them. The question asks how many times denser the air is at 50m — that is a ratio between two values, not the gap between them. Divide the two pressures to find how many times one fits into the other: 6 ÷ 1 = 6.

Why the answer is a whole number here Whenever the comparison depth is the surface (1 ata), dividing by 1 leaves the pressure figure unchanged. The depth pressure is the answer. At 50m the pressure is 6 ata, so the air is 6 times as dense. This shortcut holds for any question comparing a depth to the surface.

Density — example question 2

Will Welbourn works through density example question 2 — comparing the density of air at 10m to the surface.

Example question 2 At a depth of 10m approximately how much denser is the air a diver breathes compared to the surface?

Depth the diver is at: 10m → pressure = 2 ata
It is a density question → always divide: 2 ÷ ...
Comparison depth: the surface → pressure = 1 ata
2 ÷ 1 = 2

Answer: twice as dense — every breath at 10m delivers twice as many gas molecules as the same breath taken at the surface.

What "twice as dense" means for the diver At 10m a diver is breathing air at 2 ata. The regulator delivers air at ambient pressure, so each breath contains twice as many molecules as a breath at the surface — even though the lung volume is the same. This is why air consumption doubles at 10m compared to the surface, and why understanding density is directly linked to understanding why divers use more gas at depth.

Density — example question 3

Will Welbourn works through density example question 3 — the first question where the diver starts at the surface, producing a fractional answer.

Example question 3 What is the difference in the density of the air a diver breathes at the surface compared to a depth of 30m?

Depth the diver is at: the surface → pressure = 1 ata
It is a density question → always divide: 1 ÷ ...
Comparison depth: 30m → pressure = 4 ata
1 ÷ 4 = 1/4

Answer: 1/4 of the density — the air at the surface is one quarter as dense as the air at 30m.

Exam trap — which depth comes first? This question names the surface first and 30m second. Step 1 always uses the depth the diver is at in the question — here that is the surface. Read the question carefully: "the density of the air a diver breathes at the surface compared to a depth of 30m." The surface is Step 1, 30m is Step 3. Reversing them gives 4 ÷ 1 = 4, which is wrong.

Fractional answers — no calculator needed 1 ÷ 4 = 0.25, but you will rarely need to reach for a calculator. The PADI exam consistently offers the fraction itself as an answer option — here "1/4 of the density." What you write down at Step 1 and Step 3 (1 and 4) is the answer written as a fraction. If the numbers do not divide to a clean whole number, look for the fraction form on the answer sheet before doing the long division.

Density — example question 4

Will Welbourn works through density example question 4 — comparing the density of air at 40m to the surface.

Example question 4 How much denser is the air a diver breathes at 40m compared to the surface?

Depth the diver is at: 40m → pressure = 5 ata
It is a density question → always divide: 5 ÷ ...
Comparison depth: the surface → pressure = 1 ata
5 ÷ 1 = 5

Answer: 5 times as dense — at 40m the diver is breathing air at 5 ata, so each breath contains five times as many molecules as at the surface.

Sanity check — does the answer make sense? The diver is deeper than the comparison depth, so the air must be more dense, not less. A whole number greater than 1 is the right shape of answer. If your calculation produces a fraction (e.g. 1/5), you have the depths the wrong way around — swap Steps 1 and 3 and recalculate.

Density — example question 5

Will Welbourn works through density example question 5 — the first question comparing two depths neither of which is the surface.

Example question 5 How does the density of the air a diver breathes at a depth of 20m compare to the density of the air they breathe at a depth of 5m?

Depth the diver is at: 20m → pressure = 3 ata
It is a density question → always divide: 3 ÷ ...
Comparison depth: 5m → pressure = 1.5 ata
3 ÷ 1.5 = 2

Answer: twice as dense — the air at 20m contains twice as many molecules per breath as the air at 5m.

Exam trap — the comparison depth is not always the surface Questions 1 to 4 all compared a depth to the surface, so Step 3 was always 1. This question compares two depths, neither of which is the surface. Step 3 is 5m — pressure 1.5 ata, not 1. Writing 1 in Step 3 gives 3 ÷ 1 = 3, which is wrong. Always look at what the question is actually comparing to, and look up the correct pressure for that depth.

Pressure at 5m 5m sits halfway between the surface (1 ata) and 10m (2 ata), so the pressure is 1.5 ata. The pattern holds for any shallow intermediate depth: every 10m adds 1 ata, so every 5m adds 0.5 ata. 3 ÷ 1.5 divides cleanly to give 2 — no calculator needed.

Density — example question 6

Will Welbourn works through density example question 6 — the first question where the answer options are given in pressure terms rather than density terms.

Example question 6 What is the difference in the density of the air a diver breathes at the surface compared to a depth of 20m?

Depth the diver is at: the surface → pressure = 1 ata
It is a density question → always divide: 1 ÷ ...
Comparison depth: 20m → pressure = 3 ata
1 ÷ 3 = 1/3

Answer: 1/3 of the density — the air at the surface is one third as dense as the air at 20m.

Exam trap — the answer options use pressure language The calculation is identical to the density questions above. What changes here is the answer sheet: instead of "1/3 of the density," the options may be worded using pressure terms such as "1/3 of the pressure" or "1/3 as much pressure." The number you calculated is still 1/3 — just match it to whichever answer option expresses that ratio, regardless of whether the word used is density or pressure. Because density is directly proportional to pressure, the ratio is the same either way.

Density — example question 7

Will Welbourn works through density example question 7 — one of the most frequently missed questions in the PADI physics exam.

Read this before looking at the working This is the question that catches the most candidates in the PADI physics exam. It does not ask about density at all — it asks about pressure. If you apply the density method without reading the question carefully, you will get the right number but choose the wrong answer option. Read what the question is actually asking before you calculate anything.

Example question 7 How does the pressure at 10m compare to the pressure at 30m?

Depth named first: 10m → pressure = 2 ata
Always divide: 2 ÷ ...
Comparison depth: 30m → pressure = 4 ata
2 ÷ 4 = 1/2

Answer: 1/2 as much pressure — the pressure at 10m is half the pressure at 30m.

Exam trap — density answer on a pressure question The calculation gives 1/2. On the answer sheet you will see options including both "1/2 of the density" and "1/2 as much pressure." The number is the same — the word is not. This question asks about pressure, so the correct answer is "1/2 as much pressure." Candidates who have been working through density questions on autopilot select the density option and lose a mark. Slow down, re-read the question stem, and match your answer to what was actually asked.

Density — example question 8

Will Welbourn works through density example question 8 — two non-surface depths with a decimal pressure value at Step 3.

Example question 8 How does the density of the air a diver breathes at 40m compare to the density at 15m?

Depth the diver is at: 40m → pressure = 5 ata
It is a density question → always divide: 5 ÷ ...
Comparison depth: 15m → pressure = 2.5 ata
5 ÷ 2.5 = 2

Answer: twice as dense — the air at 40m contains twice as many molecules per breath as the air at 15m.

Pressure at 15m 15m sits halfway between 10m (2 ata) and 20m (3 ata), so the pressure is 2.5 ata. The same halfway rule applies here as it did for 5m in question 5: every 5m adds 0.5 ata. 5 ÷ 2.5 = 2 — a clean whole number answer despite the decimal at Step 3.

You have now seen every question type Across the eight examples on this page you have worked through: depths compared to the surface, the surface compared to a depth, two non-surface depths, fractional answers, decimal pressures at Step 3, pressure-language answer options, and a pressure question placed inside the density section. The 3-step method — identify the depth, always divide, identify the comparison — handles every variation without modification. Use the practice quiz below to confirm you can apply it under exam conditions.

Physics Practice — Density Question 1 of 5

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Physics — Topics

Pressure Depth Calcs Density Partial Pressure Buoyancy Lift Bags Fresh Water General Knowledge

Practice Questions ← Physics Hub ← Theory Hub