What is the formula for pressure at depth?

The standard hydrostatic equation is P = P₀ + ρgh, where P₀ is the pressure at the surface, ρ (rho) is the fluid density in kg/m³, g is gravitational acceleration in m/s², and h is the depth in metres. The term ρgh gives the gauge pressure — the extra pressure the fluid column adds. Adding P₀ gives the absolute pressure referenced to a perfect vacuum.

How much does pressure increase per metre in seawater?

Seawater has a density of approximately 1 025 kg/m³. At standard gravity (9.806 65 m/s²), each metre of seawater adds ρg ≈ 1 025 × 9.807 ≈ 10 052 Pa ≈ 10.05 kPa ≈ 0.1 bar ≈ 1.46 psi of gauge pressure. A common rule of thumb is "roughly 1 atm (≈ 10 m seawater)", which is only approximate — 10 m seawater ≈ 0.993 atm gauge.

What is the difference between gauge pressure and absolute pressure?

Gauge pressure is measured relative to the ambient surface pressure (the zero point is atmospheric pressure). Absolute pressure is measured relative to a perfect vacuum, so it equals gauge pressure plus the surface pressure. A diver at 10 m in seawater experiences roughly 2 atm absolute (1 atm surface + 1 atm from the water column) but only 1 atm gauge.

Does salinity or temperature affect underwater pressure?

Yes. Seawater density ranges from about 1 020 to 1 030 kg/m³ depending on salinity and temperature. Colder, saltier water is denser and creates slightly higher pressure at the same depth. The calculator uses 1 025 kg/m³ as the ISO/NOAA representative value; for precise oceanographic work you can enter a custom density based on in-situ CTD measurements and the UNESCO EOS-80 equation of state.

How deep is the Mariana Trench and what is the pressure there?

Challenger Deep in the Mariana Trench reaches approximately 10 935 m. At that depth in seawater (ρ = 1 025 kg/m³), gauge pressure is about 109 900 kPa ≈ 1 086 atm ≈ 15 950 psi. Absolute pressure (adding 1 atm surface) is approximately 1 087 atm — roughly 1 000 times the pressure felt at sea level. The reference table in the calculator shows this and other famous depths.

Can I use this calculator for non-water fluids like mercury or oil?

Yes. The hydrostatic formula P = ρgh applies to any static fluid. Mercury (ρ ≈ 13 546 kg/m³) produces about 13 times the pressure of water at the same depth — a 760 mm column of mercury equals exactly 1 atm (the origin of mmHg as a pressure unit). Engine oil at ≈ 870 kg/m³ produces slightly less pressure than fresh water. Select the appropriate fluid or enter a custom density for any liquid.

Pressure at Depth Calculator

The pressure at depth calculator applies the fundamental hydrostatic equation to give you gauge pressure and absolute pressure at any depth in any fluid — in seconds, entirely in your browser.

Whether you are a scuba diver checking tank ratings, a mechanical engineer sizing a submersible hull, a physics student verifying homework, or simply curious about conditions at the Mariana Trench, this tool handles the arithmetic instantly and shows the full working so you understand where every number comes from.

How it works

The governing equation is the hydrostatic pressure formula, derived directly from Newton’s second law applied to a column of static fluid:

P = P₀ + ρ g h

Symbol	Meaning	Default value
P₀	Surface pressure	101 325 Pa (1 atm)
ρ	Fluid density	1 025 kg/m³ (seawater)
g	Gravitational acceleration	9.806 65 m/s² (standard)
h	Depth (positive downward)	user input

The term ρgh is called the gauge pressure — the pressure added by the fluid column alone, above whatever pressure already exists at the surface. Adding P₀ to it gives the absolute pressure, referenced to a perfect vacuum.

The calculator also works in reverse: given a target absolute pressure, it solves h = (P_target − P₀) / (ρg) to tell you exactly how deep you must go to reach that pressure in the chosen fluid.

Worked example: scuba recreational limit

A diver descends to 40 m in seawater (ρ = 1 025 kg/m³, g = 9.806 65 m/s², P₀ = 101 325 Pa):

Gauge    = 1 025 × 9.80665 × 40 = 401 873 Pa ≈ 402 kPa ≈ 3.97 atm
Absolute = 101 325 + 401 873    = 503 198 Pa ≈ 503 kPa ≈ 4.97 atm

At this depth the diver is exposed to nearly 5 atmospheres absolute, which is why equipment such as regulators, cylinders and drysuits must be rated to exceed that figure with a safety margin.

Depth (m)	Gauge (kPa)	Absolute (kPa)	Absolute (atm)
10	100.5	201.8	1.99
40	402.1	503.4	4.97
200	2 010.4	2 111.7	20.8
3 800	38 197	38 298	378
10 935	109 899	110 001	1 086

(All figures computed at seawater 1 025 kg/m³, standard g, 1 atm surface.)

Formula note

The hydrostatic equation assumes a static, incompressible fluid of uniform density. Real seawater is slightly compressible, and its density increases with depth by about 4–5 % between the surface and the deepest trenches. For most engineering and recreational purposes the incompressible approximation is entirely adequate. For high-accuracy deep-ocean work, use the UNESCO EOS-80 equation of state and integrate the pressure in layers of varying density.

The tool lets you adjust both surface pressure (useful for pressurised vessels or altitude diving) and gravitational acceleration (useful for polar vs. equatorial locations, or other planets and moons).