Hydrostatic Pressure Calculator
Calculate hydrostatic pressure at a depth using fluid density, gravity, and optional external pressure. Includes presets for common fluids.
Hydrostatic Pressure Calculator
Result will appear here...
What the hydrostatic pressure calculator does
The deeper you go into a fluid, the greater the pressure, because more fluid is stacked above pressing down. This calculator finds that hydrostatic pressure at a given depth from the fluid's density, the depth, the strength of gravity, and the pressure pushing down on the surface. It includes presets for common fluids, from water to oils and acids.
Below is why pressure builds with depth, the equation behind it, why only the depth matters and not the shape of the container, and a worked example.
How to use it
- Choose a fluid, which fills in its density, or pick Custom Density to enter your own.
- Enter the depth, the external pressure on the surface, and the gravitational acceleration. The external pressure defaults to one atmosphere and gravity to Earth's value.
- Press Calculate for the hydrostatic pressure, or Reset to clear it.
Why pressure grows with depth
Pressure in a fluid comes from the weight of the fluid above. At any depth, everything stacked overhead, the whole column of fluid up to the surface, presses down, and the deeper you are, the taller that column and the more it weighs. So the pressure rises steadily the farther down you go. Divers feel this in their ears within the first few metres, and it is why deep-sea vessels must be built to withstand crushing loads.
On top of the fluid's own contribution, there is whatever pressure already pushes on the surface, usually the atmosphere. That surface pressure is felt undiminished at every depth, with the fluid's weight added on below it. The total of the two is the hydrostatic pressure, the actual pressure the fluid exerts at that depth.
The equation it uses
The hydrostatic pressure P at depth h is the surface pressure plus the weight of the fluid column per unit area. With external pressure Pext, fluid density ρ, gravity g, and depth h:
P = Pext + ρ g h
The term ρgh is the pressure due to the fluid alone, growing with density, gravity, and depth together. The external pressure Pext is what acts on the surface, usually atmospheric pressure. The fluid term on its own is called the gauge pressure, the amount above the surrounding pressure; adding the surface pressure gives the absolute pressure.
Depth, not shape, sets the pressure
A surprising feature of the formula is what it leaves out: the shape of the container and the total amount of fluid do not appear. The pressure depends only on the depth below the surface, the fluid's density, and gravity. A narrow tube and a vast lake filled to the same depth have exactly the same pressure at the bottom, even though the lake holds millions of times more water.
This sometimes feels wrong, but it follows from pressure being a force per area: what matters is the height of fluid directly above each patch, not how wide the body of fluid is. It is the principle behind water towers, which create pressure throughout a town simply by holding water high, and behind the way a tall, thin standpipe can generate the same pressure as a reservoir. Height is what counts.
Units, fluids, and precision
The calculator works in SI units: density in kilograms per cubic metre, depth in metres, pressure in pascals, and gravity in metres per second squared. The fluid presets carry typical densities, such as 1000 for water and about 1022 for sea water, and you can enter any value with the custom option. The external pressure defaults to one atmosphere, 101,325 pascals, and gravity to Earth's surface value. Results are shown to two decimal places.
A worked example
Take a depth of 10 metres in fresh water, density 1000 kg/m³, with the atmosphere pressing on the surface.
The fluid's own contribution is ρgh = 1000 × 9.81 × 10 = 98,100 Pa, about 98 kilopascals. Adding the atmospheric 101,325 Pa gives a hydrostatic pressure of about 199,425 Pa, close to two atmospheres. This is the well-known rule of thumb that every 10 metres of water adds roughly one atmosphere of pressure, which is why a diver at 10 metres feels about twice the surface pressure.
Questions people ask
What is the formula for hydrostatic pressure?
It is P = Pext + ρgh, the surface pressure plus the fluid density times gravity times depth. The ρgh term is the pressure from the fluid's own weight.
Why does pressure increase with depth?
Because more fluid is stacked above, and its weight presses down. The deeper you go, the taller and heavier that column, so the pressure rises steadily.
Does the shape of the container matter?
No. The pressure depends only on depth, density, and gravity, not on the container's shape or how much fluid it holds. A thin tube and a wide lake at the same depth have the same pressure.
What is the difference between gauge and absolute pressure?
Gauge pressure is the fluid's contribution alone, ρgh, the amount above the surrounding pressure. Absolute pressure adds the surface pressure on top, which this calculator includes as the external pressure.
References
A quick note on where the physics comes from. Hydrostatic pressure as Pext + ρgh, and the fact that it depends only on depth, are standard fluid mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The pascal and the value of standard gravity follow the US National Institute of Standards and Technology.
- OpenStax, University Physics Volume 1, Section 14.1, Fluids, Density, and Pressure (variation of pressure with depth). https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure
- HyperPhysics, Georgia State University, Pressure in a Fluid. http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.