The pressure on a swimmer 20 m below the water surface is about 3 atm in total, or about 3.0 ×1053.0\times 10^53.0×105 Pa. This is because water adds roughly 2 atm at 20 m depth, and the surface air pressure adds another 1 atm.

Quick scoop

Using P=P0+ρghP=P_0+\rho ghP=P0​+ρgh:

  • P0≈1 atmP_0\approx 1\text{ atm}P0​≈1 atm
  • ρ≈1000 kg/m3\rho \approx 1000\text{ kg/m}^3ρ≈1000 kg/m3
  • g≈10 m/s2g\approx 10\text{ m/s}^2g≈10 m/s2
  • h=20 mh=20\text{ m}h=20 m

So:

  • Water pressure from depth =1000×10×20=2×105 Pa=1000\times 10\times 20=2\times 10^5\text{ Pa}=1000×10×20=2×105 Pa
  • Total pressure =1.01×105+2×105≈3.01×105 Pa=1.01\times 10^5+2\times 10^5\approx 3.01\times 10^5\text{ Pa}=1.01×105+2×105≈3.01×105 Pa

That is approximately 3 atm.

In simple terms

  • Pressure due to the water alone: about 2 atm.
  • Pressure including air above the water: about 3 atm.

If you want, I can also show the same answer in bar or explain why water pressure rises so fast with depth.