Water Pressure at Depth Calculator

Background.

Water pressure at depth is the oldest calculation in plumbing and still the one that decides where a tank goes. A column of still water pushes down with a pressure that depends on exactly three things: how dense the water is, how strong gravity is, and how tall the column is. That is the whole of it — pressure equals density times gravity times height, written p = ρgh. Nothing else enters. Not the width of the container, not its shape, not how much water there is in total.

That last point surprises people often enough to have its own name, the hydrostatic paradox. A drinking straw full of water thirty feet tall produces exactly the same pressure at its base as a swimming pool thirty feet deep. A tank on a hill connected by a hose gives the pressure of the vertical rise, no matter how long or winding the hose is. And a sloping hundred-foot run that climbs only twelve feet gives you twelve feet of head, not a hundred. Depth here always means vertical depth below the free surface, measured straight down.

Working in US plumbing units, cold fresh water produces about 0.4335 psi for every foot of depth, and the reciprocal — 2.31 feet of head per psi — is the number most plumbers actually carry in their heads. Both come straight out of p = ρgh once the units are converted, and this calculator derives them rather than hard-coding them, which is why it can also give you the slightly different figures for warm water and for seawater. Fresh water is densest at 4 °C, at 999.972 kg/m³, and thins to 997.047 kg/m³ at 25 °C. That 0.3 percent spread is why this page offers the temperature as a choice: the textbook 0.433 constant is the cold-water case, and pretending it holds at every temperature would be quietly wrong.

The gauge-versus-absolute distinction matters more than it looks. Gauge pressure is measured relative to the atmosphere pressing on everything around you, and it is what a pressure gauge reads, what a plumbing system works against, and what this page reports as its headline number. Absolute pressure adds the atmosphere back on top. At the surface of a lake the gauge pressure is zero and the absolute pressure is one atmosphere, 14.6959487755 psi. Physics and thermodynamics want absolute; plumbing wants gauge; mixing them up is worth about fifteen psi of error, which is enough to matter.

The worked example is thirty feet of fresh water at 20 °C with a normal atmosphere on the surface. Thirty feet is 9.144 metres, and 998.207 × 9.80665 × 9.144 gives 89511.2256904 pascals — 89.5112256904 kPa, 0.8951122569 bar, or 12.9825056756 psi gauge. Adding the atmosphere gives 27.6784544511 psi absolute, which is 1.8834071127 atmospheres. The per-foot constant at this temperature is 0.4327501892 psi, and the reciprocal is 2.3108019938 feet per psi.

Two cross-checks confirm the arithmetic against sources that have nothing to do with the equation. Switch the fluid to fresh water at 4 °C and the calculator returns 0.4335153652 psi per foot and 2.3067233141 feet per psi, which round to the 0.4335 and 2.31 that every plumbing and pump reference prints. Switch to seawater at ten metres and it returns 100.5181625 kPa of gauge pressure against a 101.325 kPa atmosphere — the diving rule of thumb that every ten metres of seawater adds roughly one atmosphere, reproduced to within 0.8 percent.

A few honest limits. Standard gravity is fixed at 9.80665 m/s², which is exact by definition, but real local gravity ranges from about 9.780 at the equator to 9.832 at the poles, so there is a ±0.3 percent geographic variation this page does not model. Water is treated as incompressible and as having one density throughout, which is accurate to well under a percent at any depth this page is aimed at. Seawater at 1025 kg/m³ is a nominal representative value, not a physical constant — real seawater runs roughly 1020 to 1030 depending on salinity and temperature, and the custom option is there for anyone who has measured it.

Finally, the two things this page is not. It is not a dive planning tool: it gives ambient pressure at depth and says nothing about gas partial pressures, no-decompression limits, ascent rates or breathing gas, all of which need certified tables or a dive computer and proper training. And it is not a pressure-rating check: whether a pipe, tank, liner or fitting can withstand a computed pressure is a materials and code question governed by the plumbing and building codes your jurisdiction has adopted, adopted editions and local amendments vary, and a licensed plumber or engineer has to sign off.

What is water pressure at depth calculator?

Hydrostatic pressure is the pressure exerted by a fluid at rest because of the weight of the fluid above it. It increases linearly with depth, and at any given depth it acts equally in every direction. The governing relation is p = ρgh, where ρ is the fluid density, g is the acceleration of gravity and h is the vertical depth below the free surface.

Gauge pressure is measured relative to the surrounding atmosphere; absolute pressure is measured relative to a perfect vacuum, so absolute equals gauge plus the atmospheric pressure acting on the surface. Plumbing, pumps and pressure vessels are almost always specified in gauge; thermodynamics and gas laws need absolute.

Static head is the plumbing term for the vertical height of a water column, expressed either in feet of water or converted to psi. Because it converts at a fixed rate for a given fluid — about 0.4335 psi per foot for cold fresh water, or 2.31 feet per psi — head and pressure are used almost interchangeably in pump and system design.

This calculator handles still fluid of a single, uniform density. It does not model moving water, where friction and velocity head change the picture, and it does not account for compressibility, stratification, or the small geographic variation in gravity.

How to use this calculator.

1. 01Enter the vertical depth below the free surface and choose feet or metres. Measure straight down — the length of a sloping pipe or hose is not the depth.
2. 02Choose the fluid. Fresh water at 20 °C is the general default; pick 4 °C if you want the classic 0.4335 psi per foot constant, or seawater for marine work.
3. 03For anything else — brine, glycol, a measured salinity — choose Custom and enter the density in kilograms per cubic metre.
4. 04Set the surface pressure. Leave it at 101.325 kPa for anything open to the air at sea level, reduce it at altitude, or set it to zero for a sealed vessel under vacuum. It changes the absolute pressure only.
5. 05Read the gauge pressure as the headline figure. That is what a gauge would show and what your plumbing works against.
6. 06Use the psi-per-foot and feet-per-psi outputs to scale the answer to any other depth of the same fluid without re-running the calculator.

The formula.

Hydrostatic pressure is p = ρgh: density times gravity times vertical depth. The calculator works entirely in SI internally and converts at the boundary. For the worked example, 30 feet is 30 × 0.3048 = 9.144 metres exactly, fresh water at 20 °C has a density of 998.207 kilograms per cubic metre, and standard gravity is 9.80665 metres per second squared — a value fixed exactly by the 3rd General Conference on Weights and Measures in 1901. Multiplying gives 998.207 × 9.80665 × 9.144 = 89511.2256904 pascals of gauge pressure. Converting: divide by 1000 for 89.5112256904 kilopascals, by 100,000 for 0.8951122569 bar, and by 6894.757293168361 — the exact number of pascals in one psi — for 12.9825056756 psi. Absolute pressure adds the surface pressure: 89511.2256904 + 101325 = 190836.2256904 pascals, which is 27.6784544511 psi absolute or 1.8834071127 standard atmospheres. The psi-per-foot output is computed from the density directly rather than by dividing the pressure by the depth, as ρ × g × 0.3048 ÷ 6894.757293168361 = 0.4327501892 psi per foot, and its reciprocal is 2.3108019938 feet per psi. Deriving it that way keeps it defined at a depth of exactly zero, where dividing pressure by depth would be zero over zero, and a test covers that case. Every unit constant used is exact by definition: one foot is exactly 0.3048 metres, one bar is exactly 100,000 pascals, one standard atmosphere is exactly 101,325 pascals, and one psi is exactly 6894.757293168361 pascals because a pound-force is exactly 4.4482216152605 newtons and a square inch is exactly 0.00064516 square metres. Arithmetic is carried at twenty significant digits and rounded only at the final result.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST Special Publication 811 (2008), Guide for the Use of the International System of Units (SI) — standard acceleration of gravity 9.806 65 m/s², standard atmosphere 101 325 Pa, pound-force per square inch 6894.757 293 168 361 Pa, and bar 100 000 Pa, all exact.
2. [2]Bureau International des Poids et Mesures — CGPM resolutions: the 3rd CGPM (1901) fixing standard gravity at 9.806 65 m/s², and the 10th CGPM (1954) fixing the standard atmosphere at 101 325 Pa.
3. [3]IAPWS — Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance (IAPWS-95), the reference formulation behind the liquid water densities of 999.972, 998.207 and 997.047 kg/m³ at 4, 20 and 25 °C.
4. [4]Intergovernmental Oceanographic Commission — TEOS-10, the Thermodynamic Equation of Seawater 2010. Cited to support the statement that 1025 kg/m³ is a nominal representative surface seawater density rather than a constant; real values run roughly 1020–1030 kg/m³ with salinity and temperature.
5. [5]US Geological Survey — Water Science School, water properties and the behaviour of water density with temperature, supporting the temperature options offered on this page.