Pressure at Depth Calculator

Frequently Asked Questions

How is pressure at depth calculated?

Hydrostatic gauge pressure P = ρ·g·h (fluid density × gravity × depth). Absolute pressure adds atmospheric pressure (~101.3 kPa) on top.

How much does pressure increase underwater?

In seawater, about 1 atm (~10.1 kPa... ~1 bar) per 10 m of depth. At 30 m a diver feels ~4 atm absolute (3 from water + 1 atmosphere).

Does pressure depend on the container shape or water volume?

No - only on depth and fluid density (the hydrostatic paradox). A thin tube and a wide lake have the same pressure at the same depth.

How is this different from buoyancy?

This gives the pressure at a depth. Buoyancy is the net upward force from the pressure difference across a submerged object - a related but distinct calculation.

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How This Calculator Works

Pressure inside a still fluid rises with depth because every layer must support the weight of all the fluid above it. The hydrostatic relation is P = ρ × g × h, where ρ is fluid density (kg/m³), g is gravitational acceleration (≈ 9.80665 m/s²), and h is depth below the surface. That product is the gauge pressure - the pressure above the surrounding air. The absolute pressure adds the atmosphere pushing down on the surface: P᳏ᴰˢ = ρgh + P₀, with P₀ ≈ 101,325 Pa at sea level. This tool reports both, converted to pascals, kilopascals, atmospheres, and psi, and expresses the total as an equivalent number of "atmospheres of depth." Built-in densities: fresh water 1000, sea water 1025, light oil 870, and mercury 13,534 kg/m³. This is a static-pressure tool - it answers "how hard is the fluid squeezing," which is distinct from buoyancy (the net upward force on a submerged object).

Worked Example: A 10 m Sea Dive

A diver descends 10 m in sea water (ρ = 1025 kg/m³). Gauge pressure = 1025 × 9.80665 × 10 ≈ 100,518 Pa ≈ 0.992 atm. Adding the surface atmosphere gives an absolute pressure ≈ 201,843 Pa ≈ 1.99 atm. The familiar diving rule of thumb - pressure increases by about 1 atmosphere per 10 m of sea water - falls straight out of this. At 10 m a diver feels roughly double the surface pressure; at 20 m, triple. This is why scuba divers must equalise their ears on descent and ascend slowly to off-gas dissolved nitrogen and avoid decompression sickness.

Key Points About Hydrostatic Pressure

Shape does not matter: pressure depends only on depth and density, not the container's width or total volume - the hydrostatic paradox.

Acts in all directions: at a given depth pressure pushes equally up, down, and sideways (Pascal's principle).

Density matters hugely: mercury is ≈ 13.5× denser than water, so 760 mm of mercury equals about 10.3 m of water - both equal 1 atm.

Gauge vs. absolute: a tyre gauge reads gauge pressure; weather and physics often need absolute.

Where This Applies

Hydrostatic pressure governs dam design (walls are thicker at the base because pressure grows linearly with depth), submarine hull ratings, water-tower height for municipal supply, blood-pressure differences between your head and feet, and the crushing ≈ 1100 atm at the bottom of the Mariana Trench. It also explains why a straw works: you lower the pressure at the top so atmospheric pressure pushes liquid up. Barometers and manometers measure pressure directly as a fluid column height using this same ρgh relation in reverse.

Assumptions & Limits

The formula assumes an incompressible fluid of uniform density and a fluid at rest. Liquids are nearly incompressible, so it is very accurate for water down to great depths (sea water density rises only ≈ 5% at 11 km). It is not accurate for gases like air, whose density falls with altitude, making atmospheric pressure decay exponentially rather than linearly. It ignores fluid motion (moving fluids add dynamic pressure via Bernoulli's equation), temperature-driven density changes, and surface tension. Gravity is taken as constant; the default 9.80665 m/s² is standard sea-level gravity, adjustable for other locations or planets.

Pressure at Depth Calculator

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