Pressure and Density Calculator
Choose pressure from a force, density from mass and volume, pressure at depth in water, or a float or sink check. Fill in what you know.
Fill in all but one box for the first three. For reference: water about 1,000 kg/m³, sea water 1,025, steel 7,850, aluminium 2,700, copper 8,960, air 1.2.
Worked examples
Pressure
500 N on 0.02 square metres
25 kPa
F / A.
Under water
10 m of fresh water
98.07 kPa above the air pressure
1000 x 9.80665 x 10.
About Pressure and Density Calculator
Pressure is force spread over an area. The same force on a small area gives a high pressure, which is why a knife cuts and snow shoes stop you sinking. Density is how much mass is packed into a volume. The two come together underwater: the pressure at a depth is the fluid density times gravity times the depth, which is why pressure rises by about one atmosphere for every ten metres of water. This calculator handles all of these in one place.
It also checks whether something floats. An object floats if its average density is lower than that of the fluid, and the fluid pushes up on the part below the surface with a force equal to the weight of fluid displaced, which is Archimedes' principle. Enter the mass and volume of the object and the fluid density and you get the upthrust, the share below the surface and the extra mass it could carry before it sinks. Results for pressure are also shown in bar, psi and atmospheres.
How to use Pressure and Density Calculator
- Choose pressure, density, pressure at depth or the float check.
- Fill in all boxes but one for the first three, or the object and fluid details for the float check.
- Choose units for each box, such as litres, kilopascals or pounds per cubic foot.
- Read the answer and the extra figures.
Common uses
- Finding the pressure under a foot, a table leg or a machine base
- Working out the mass of a steel plate from its size
- Calculating the pressure on a diver or a submarine hatch
- Checking if a boat, buoy or piece of wood will float
Frequently asked questions
What is the pressure formula?
Pressure equals force divided by area. In SI units that is newtons per square metre, called pascals. A force of 500 newtons on 0.02 square metres gives 25,000 pascals.
How does pressure increase with depth?
By the density of the fluid times g times the depth. In fresh water that is about 9.8 kilopascals for each metre, so ten metres adds nearly one atmosphere.
How do I find density?
Divide the mass by the volume. A kilogram of material filling one litre has a density of 1,000 kilograms per cubic metre, the same as water.
Why do steel ships float?
A ship's hull is hollow, so its average density, including the air inside, is lower than water. It displaces enough water to equal its weight before it sinks.