Hydrostatic Pressure Calculator
Enter a fluid depth and choose a fluid to instantly calculate the hydrostatic (fluid column) pressure at that depth. Switch between gauge pressure and absolute pressure, pick metric or imperial units, and select from seven common fluids or enter a custom density. You can also reverse-solve: enter a target pressure to find the depth or fluid density that produces it. The results panel shows the full worked calculation, a pressure-vs-depth chart, and a reference table of common depth milestones.
Formula
Worked example
At 10 m depth in pure water: P_gauge = 998.2 kg/m³ × 9.80665 m/s² × 10 m = 97 887 Pa ≈ 97.9 kPa. Adding 1 atm (101.325 kPa) gives an absolute pressure of 199.2 kPa, roughly 2 atm.
What is hydrostatic pressure?
Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid column above a given point. It depends only on three things: the depth below the surface, the fluid density, and the local gravitational acceleration. Container shape, horizontal area, and the total volume of fluid are all irrelevant - this is known as the hydrostatic paradox or Pascal's paradox. Two connected vessels of completely different shapes reach the same pressure at the same depth as long as they contain the same fluid.
The hydrostatic pressure formula
Gauge pressure is calculated with P_gauge = rho * g * h, where rho is fluid density in kg/m³, g is gravitational acceleration in m/s², and h is depth in metres. The result is in Pascals. To get absolute pressure (what a closed pressure sensor actually measures), add the pressure at the surface, normally 1 atm = 101 325 Pa. For seawater (1025 kg/m³) at 10 m depth, gauge pressure = 1025 × 9.80665 × 10 = 100 518 Pa = 100.5 kPa, compared with 98.1 kPa for pure water. The difference grows with depth: at 1000 m, seawater pressure is about 0.27 MPa higher than freshwater pressure.
Gauge pressure vs. absolute pressure
Gauge pressure measures pressure relative to the surrounding atmosphere. An open tank at the surface reads 0 kPa gauge even though the atmosphere is pressing down with 101.325 kPa absolute. Most everyday pressure gauges (tire gauges, blood pressure cuffs, depth gauges) read gauge pressure because what matters for most applications is the pressure in excess of ambient. Absolute pressure is required for thermodynamic calculations, sealed systems, and instruments that measure from a true vacuum baseline. This calculator outputs both: switch the pressure type selector to "Absolute" to see both values in absolute terms.
Reverse-solving for depth or fluid density
Sometimes you know the pressure and need to work backwards. If you know the gauge pressure and the fluid, this calculator solves for the depth using h = P_gauge / (rho * g). If you measure a pressure at a known depth in an unknown fluid, it solves for density using rho = P_gauge / (g * h). This is useful in industrial pipework (inferring tank levels from pressure sensors), oceanography (identifying water mass properties), and dive medicine (setting safe ascent profiles). Select the appropriate mode from the "Solve for" dropdown to activate the reverse calculation.
Hydrostatic pressure at notable depths in freshwater
| Depth | Gauge pressure (kPa) | Gauge pressure (psi) | Context |
|---|---|---|---|
| 1 m (3.3 ft) | 9.8 | 1.42 | Shallow pool |
| 10 m (33 ft) | 98.1 | 14.2 | Open-water scuba limit |
| 18 m (59 ft) | 176 | 25.5 | Recreational scuba max |
| 40 m (131 ft) | 392 | 56.9 | Advanced scuba max |
| 100 m (328 ft) | 980 | 142 | Start of technical diving |
| 332 m (1089 ft) | 3253 | 472 | Deepest no-limits dive record |
| 1000 m (3281 ft) | 9809 | 1423 | Mesopelagic zone lower edge |
| 3800 m (12 467 ft) | 37 271 | 5405 | Average ocean depth |
| 10 924 m (35 843 ft) | 107 144 | 15 540 | Mariana Trench deepest point |
Gauge pressure at standard depths in pure water (998.2 kg/m³) under standard Earth gravity (9.80665 m/s²). Absolute pressure adds 1 atm (101.325 kPa).
Frequently asked questions
Does the shape of the container affect hydrostatic pressure?
No. Hydrostatic pressure at a given depth depends only on the fluid density and depth, not on the shape, horizontal area, or total volume of the container. Two tanks with the same fluid at the same depth - one narrow, one wide - have exactly the same pressure at the bottom. This counterintuitive fact is called the hydrostatic paradox.
Why does pressure increase with depth?
Pressure increases because each additional layer of fluid adds weight to the layers below it. At any point, the fluid must support the weight of all the fluid above. Since weight per unit area equals rho * g * h, pressure is proportional to depth. Double the depth and you double the gauge pressure.
How is gauge pressure different from absolute pressure?
Gauge pressure is measured relative to atmospheric pressure, so it reads zero at the fluid surface (in an open system). Absolute pressure includes the atmospheric pressure acting on the surface - at sea level, atmospheric pressure is 101.325 kPa, so a gauge pressure of 98.1 kPa corresponds to an absolute pressure of 199.4 kPa.
What units are commonly used for hydrostatic pressure?
Pascal (Pa) is the SI unit, but kilopascals (kPa), bar, atmospheres (atm), psi (pounds per square inch), and mmHg (millimetres of mercury) are all used in practice. Dive tables often use bar or atm (roughly 1 bar per 10 m of water depth for seawater), industrial systems often use psi, and medical devices often use mmHg.
Does the type of fluid change the pressure at a given depth?
Yes. Pressure is proportional to fluid density. Seawater (about 1025 kg/m³) is 2.7% denser than pure water (998.2 kg/m³), so it produces 2.7% more pressure at the same depth. Mercury is about 13.5 times denser than water, so just 1 m of mercury produces the same pressure as 13.5 m of water. This is why mercury was historically used in barometers - a manageable column length represents a full atmosphere of pressure.
How do I calculate pressure at depth on other planets?
Use the gravitational acceleration for the planet in question. Mars has g = 3.72 m/s², so water at 10 m depth produces only 998.2 × 3.72 × 10 = 37 133 Pa, compared with 97 887 Pa on Earth. The Moon has g = 1.62 m/s², giving even lower values. Enter the planetary g in the gravitational acceleration field to switch contexts.