Pressure in a still fluid increases with depth for one reason: everything above a given point has weight, and that weight presses down. The hydrostatic pressure calculator above turns that idea into a number, taking a fluid density, a depth and whatever pressure is acting on the surface, and returning both the gauge pressure — the increase caused by the fluid column alone — and the absolute pressure, which includes the atmosphere or whatever else sits on top. It also gives the result in pounds per square inch and in atmospheres, because those are the units real equipment is rated in.
Arb Digital builds free calculators that separate the quantities people routinely conflate, and gauge versus absolute pressure is the classic case. Most pressure gauges read zero at sea level while sitting in a full atmosphere, which means the number on the dial is already an absolute reading minus about 101 kilopascals. Mixing the two is the single most common error in fluid problems. This page computes pressure from physical conditions; if you already have a pressure and simply want it in different units, the pressure converter is the right tool and it performs no physics.
What This Hydrostatic Pressure Calculator Does
It applies P = ρ·g·h to find the pressure contributed by the fluid column, then adds whatever pressure you specify at the surface to give the absolute figure. The hero number is the absolute pressure, since that is what actually acts on a submerged surface, and the grid breaks out the gauge component separately along with two alternative unit expressions and the resulting force on one square metre of flat surface.
Density can be entered directly or picked from a short preset list. The presets exist because density is where most of the uncertainty in these calculations lives: fresh water is close to 1,000 kg/m³ near 4 °C but around 997 kg/m³ at room temperature, and seawater runs higher still because of dissolved salts. A three percent difference in density is a three percent difference in gauge pressure, which at depth is substantial.
Local gravity is exposed as an editable field rather than hard-coded. It defaults to the standard value of 9.806 65 m/s², but hydrostatic problems on other planetary bodies, or in contexts where a surveyed local gravity value is known, need to change it. Setting the surface pressure to zero gives the pressure in a sealed, evacuated vessel, which the second preset demonstrates.
How to Use It
- Set the fluid density. Use a preset for a quick answer or type a measured value. If your fluid is a mixture or a slurry, its bulk density is what matters, not the density of any one component.
- Enter the vertical depth. Straight down from the free surface. The horizontal distance from a wall, the width of the tank and the total volume are all irrelevant.
- Set the surface pressure. One standard atmosphere is the default for anything open to the air. Use zero for a sealed evacuated vessel, or the tank's own head pressure for a pressurised system.
- Adjust gravity only if you have a reason. The standard value is correct to within a fraction of a percent almost anywhere on Earth's surface.
- Read gauge and absolute separately. Equipment ratings, dive tables and structural calculations do not all use the same one, so check which your source means before comparing numbers.
The Formula: How Hydrostatic Pressure Is Calculated
The gauge pressure due to a column of still fluid is P = ρ·g·h, where ρ is the fluid density in kilograms per cubic metre, g is the acceleration due to gravity in metres per second squared, and h is the vertical depth in metres. The result comes out in pascals, which are newtons per square metre. Absolute pressure is that value plus the pressure acting on the free surface: Pabs = Psurface + ρ·g·h.
The derivation is a weight calculation. Take a column of fluid of cross-sectional area A extending from the surface to depth h. Its volume is A·h, its mass is ρ·A·h, and its weight is ρ·A·h·g. Pressure is force divided by area, so dividing by A gives ρ·g·h — and the area cancels completely, which is exactly why the shape and size of the container are irrelevant. The HyperPhysics static fluid pressure page at Georgia State University makes the same point: pressure depends on depth and density only, not on total mass or volume.
Work an example. Fresh water at 997 kg/m³, 10 metres deep, standard gravity. Gauge pressure is 997 × 9.806 65 × 10 = 97,772 Pa, or 97.77 kPa. Add one standard atmosphere — defined as exactly 101,325 Pa in the BIPM SI Brochure, which lists it among the non-SI units accepted for use with the SI — and the absolute pressure is 199,097 Pa, or 199.1 kPa. Divide by 6,894.757 to get 28.9 psi, and divide by 101,325 to get 1.965 atmospheres. Those are the numbers this page shows with its default inputs, and every step is reproducible by hand.
A useful mental shortcut falls out of that example: roughly every 10 metres of fresh water adds about one atmosphere of gauge pressure, and seawater does it in slightly less than 10 metres because it is denser. Divers use exactly this rule, and it is why pressure doubles between the surface and 10 metres — a proportionally larger change than between 10 and 20 metres, where it goes from two atmospheres to three.
Gauge Versus Absolute, and Why It Keeps Causing Errors
Absolute pressure is measured from a perfect vacuum. Gauge pressure is measured from the local ambient pressure, which at sea level is about 101.3 kPa. A tyre inflated to 32 psi on a gauge is at about 46.7 psi absolute, and a pressure gauge reading zero is not attached to a vacuum — it is simply matched to its surroundings.
The distinction decides which number is correct for which job. Structural calculations for a tank wall usually want the differential pressure across the wall, which is the gauge value, because the atmosphere pushes on both faces. Gas law calculations, boiling points and anything involving compressibility need the absolute value, because those laws are written in absolute terms. Dive planning uses absolute pressure for gas consumption and decompression because a diver's lungs experience the full pressure regardless of what reference a gauge uses.
Unit names sometimes carry the distinction and sometimes do not. In imperial practice psig and psia are explicit, and bar-g and bar-a serve the same purpose. Pascals and bars are frequently written with no qualifier at all, which is why this page shows both values side by side rather than making you infer which one it means.
Why the Shape of the Container Genuinely Does Not Matter
This result surprises people every time, and it is worth stating precisely. Take three vessels — a narrow vertical tube, a cone widening upward, and a cone narrowing upward — all filled with water to the same depth. The pressure at the bottom of all three is identical, even though the tube holds a litre and the wide cone holds a hundred. This is sometimes called the hydrostatic paradox, and it is not a paradox at all once you notice that the area cancelled out of the derivation.
What differs between the vessels is the total force on the base, which is pressure multiplied by base area. Same pressure, bigger base, bigger force. That is why the calculator reports force on one square metre as a separate item: multiply it by your actual submerged area to get the total load, and note that for a vertical wall you must integrate over depth rather than using the pressure at the bottom, since pressure varies from top to bottom.
The rule also explains why a very tall, thin standpipe can burst a large low tank connected to its base. The pressure at the connection depends on the height of the water column, not on how much water is in it. A few litres held ten metres up delivers the same pressure as a swimming pool at the same head.
Where the Simple Formula Stops Applying
P = ρgh assumes three things: the fluid is at rest, its density is constant, and gravity is uniform over the depth involved. All three hold well for liquids in ordinary tanks, pools and shallow water, and all three eventually fail.
Moving fluid is the first departure. As soon as the fluid flows, part of the pressure is converted to velocity and the static relationship no longer describes the total. That is the territory of Bernoulli's equation, which the Bernoulli equation calculator covers, and it is why a pressure reading in a flowing pipe differs from the static head of the same column.
Constant density fails for gases and for very deep water. Air density falls with altitude, so atmospheric pressure follows an exponential relationship rather than a linear one — the simple formula is only usable over small height changes. Water is nearly but not perfectly incompressible: at the bottom of the deepest ocean trenches, compression raises density by a few percent, so the linear formula slightly underestimates the true pressure. For anything above a few hundred metres of water the error is negligible.
What the Pressure Does: Force, Buoyancy and Heads
Pressure acts perpendicular to every surface it touches, in all directions equally at a given depth — that is Pascal's principle. Because pressure rises with depth, the upward push on the bottom of a submerged object exceeds the downward push on its top, and the difference is buoyancy. That is the whole of Archimedes' principle expressed through hydrostatic pressure, and the buoyancy calculator works it from the volume side.
Engineers frequently express pressure as a height of fluid rather than as force per area — metres of water, millimetres of mercury, inches of water gauge. That is simply this equation run backwards: divide the pressure by ρg to get the equivalent head. Mercury appears in the preset list because its density of about 13,534 kg/m³ makes it convenient for measuring pressures that would need an impractically tall water column.
If you are sizing a fluid system, the density converter handles density units, the pool volume calculator gives capacities for common pool shapes, and the water weight calculator converts a volume of water into a mass. The complete list of physics and engineering tools is on the free tools hub.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Comparing a gauge reading with an absolute value — they differ by about 101.3 kPa at sea level, which is a large error at shallow depths.
- Using slant distance instead of vertical depth — only the vertical component counts. A point ten metres along a sloping tank floor may be only four metres deep.
- Assuming a bigger tank means more pressure — volume is irrelevant. Only density, depth and gravity appear in the equation.
- Using the bottom pressure to size a vertical wall — pressure varies with depth along the wall, so the total force needs the average pressure over the wetted height, not the maximum.
- Ignoring temperature and salinity — a few percent of density error carries straight through to a few percent of pressure error at every depth.
Related Free Tools From Arb Digital
For moving fluid rather than still fluid, use the Bernoulli equation calculator, and for flotation the buoyancy calculator. Unit work belongs in the pressure converter or the density converter. For practical volumes and masses try the pool volume calculator and the water weight calculator, and for the force side of the physics the gravitational force calculator. Everything else is on the free online tools hub.
Frequently Asked Questions
Gauge pressure is the increase caused by the fluid column alone, ρgh. Absolute pressure adds whatever pressure acts on the free surface, normally one atmosphere of 101,325 pascals. Most dial gauges read the gauge value, while gas laws and dive planning need the absolute value.
No. The cross-sectional area cancels out of the derivation, so a narrow tube and a wide tank filled to the same depth have identical pressure at the bottom. What differs is the total force, which is pressure multiplied by the area it acts on.
Because hydrostatic pressure is proportional to local gravity. The default is the standard value of 9.806 65 m/s², but problems set on other planetary bodies, or in places with a surveyed local value, need a different figure.
Fresh water at about 997 kg per cubic metre adds roughly 97.8 kilopascals over ten metres, which is close to one standard atmosphere. Seawater is denser, so it reaches one atmosphere in slightly less than ten metres.
Only over small height changes. Gas density falls as pressure falls, so the relationship becomes exponential rather than linear over any significant altitude, and the constant-density assumption behind this formula breaks down.
Vertically, straight down from the free surface. Distance measured along a sloping floor or an inclined pipe must be converted to its vertical component before it is entered.
This page derives a pressure from physical conditions — density, depth, gravity and surface pressure. A pressure converter only rescales a pressure you already have between pascals, bar, psi and similar units.
This tool is provided for educational and study use. It applies an idealised static model and is not a substitute for engineering design, vessel certification, diving instruction or any safety-critical assessment.
