What this calculator does
Pressure is force divided by the area it acts over, which is why a drawing pin pushes into wood under the same hand force that a flat palm cannot. Nothing about the force changed; the area did.
The second half of this calculator covers hydrostatic pressure, the pressure produced by the weight of water above a given depth. It rises by very nearly one atmosphere for every ten metres of depth, which is a useful figure to carry around.
The formula
Divide force by area for the applied pressure, then convert into the common units. Hydrostatic pressure is water density times gravity times depth, which gives the gauge pressure, and adding atmospheric pressure gives the absolute figure.
| Term | Meaning |
|---|---|
| Pascal (Pa) | One newton spread over one square metre. It is a small unit, so kilopascals and bar are more common in practice. |
| Gauge pressure | Pressure above atmospheric. A tyre gauge reads gauge pressure, which is why a flat tyre reads zero rather than one atmosphere. |
| Absolute pressure | Gauge pressure plus atmospheric pressure: the true total pressure. |
The inputs explained
| Field | What to enter |
|---|---|
| Force (N) | The force applied, in newtons. For a weight, multiply mass in kilograms by 9.81. |
| Area (m²) | The area the force is spread over, in square metres. Small areas produce large pressures. |
| Water depth (m) | Water depth in metres, used only for the hydrostatic rows. |
When to use it
Checking a load on a surface
Whether a floor, a soil or a bearing can take a load depends on pressure rather than weight, so the contact area matters as much as the mass.
Diving and pressure at depth
Pressure roughly doubles between the surface and ten metres, which is why depth has such a strong effect on air consumption.
Converting between pressure units
Equipment is specified variously in kPa, bar and psi, and comparing two specifications means putting them in the same unit first.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does water pressure build with depth?
Hydrostatic pressure at a range of water depths.
| Depth | Water pressure (gauge) | Absolute pressure |
|---|---|---|
| 5 m | 49.0 kPa gauge | 150.4 kPa |
| 10 m | 98.1 kPa gauge | 199.4 kPa |
| 20 m | 196.1 kPa gauge | 297.5 kPa |
| 50 m | 490.3 kPa gauge | 591.7 kPa |
Questions
Why does a sharp point exert so much pressure?
Because pressure is force divided by area, and a point concentrates the same force into a tiny area. Halving the contact area doubles the pressure without any change in how hard you push.
Does the shape of a container change water pressure?
No. Hydrostatic pressure depends only on depth, not on the volume or shape above. A narrow pipe ten metres tall produces the same pressure at its base as a wide tank of the same depth.
What is the difference between gauge and absolute pressure?
Gauge pressure is measured relative to the surrounding atmosphere, absolute pressure relative to a vacuum. They differ by about 101 kPa at sea level, and mixing them up is a common source of error in gas calculations.
Why one atmosphere per ten metres of water?
It falls out of the numbers: water is about 1,000 kg per cubic metre, gravity is about 9.81, and ten metres of it gives roughly 98,000 Pa, which is very close to standard atmospheric pressure of 101,325 Pa.
For the density figure behind hydrostatic pressure, see the density calculator. For stress in a material under load, which is the same arithmetic with a different name, see the mechanical stress calculator.