How to use the buoyancy and hydrostatic pressure calculator
- Enter the volume of the object in liters and its mass in kilograms. Count the whole volume, including any air inside it.
- Enter the fluid density. Example values are about 1000 kg/m3 for fresh water and 1025 kg/m3 for seawater.
- Read whether the object floats or sinks, the buoyant force if it were fully under, and either the share of it under the surface or the lift needed to hold it.
- Add a depth to get the gauge and absolute pressure at that depth in kilopascals and psi.
Formula
buoyant force F = fluid density x volume x g
weight W = mass x g
floats when the object density (mass / volume) is less than the fluid density
submerged share of a floating object = object density / fluid density
gauge pressure at depth h = fluid density x g x h
g is 9.80665 m/s2. Absolute pressure adds the pressure of the air above the fluid, shown in the advanced options as an example value near sea level.
A wooden block and a steel bar
A block of 12 liters (0.012 m3) with a mass of 8 kg has an average density of 666.7 kg/m3. In fresh water at 1000 kg/m3, the buoyant force if it were fully under is 117.68 N against a weight of 78.45 N, so it floats with 66.7 percent of it under the surface. Adding 4 kg would make it just sink. At a depth of 3 m the gauge pressure is 29.42 kPa (4.27 psi) and the absolute pressure is 130.74 kPa.
A steel bar of 5 liters and 39.3 kg has a density of 7860 kg/m3. In seawater at 1025 kg/m3 it feels a buoyant force of 50.26 N against a weight of 385.4 N. It takes a lift equal to the weight of 34.175 kg to hold it up. At 10 m deep the seawater pressure is 100.52 kPa above the surface pressure, about 14.6 psi.
Why shape matters even when density does not
A steel ship floats because its hull encloses a great deal of air, so its average density, mass divided by the volume of the whole hull below the waterline, is less than water. When you enter the volume of the whole enclosed shape and the mass of the whole object, this tool handles that case correctly. If you enter only the volume of the metal, you get the answer for a solid lump.
What the pressure figure means
Gauge pressure is the extra pressure from the weight of the fluid above you. It grows in a straight line with depth, by about 9.8 kPa for each meter of fresh water. Absolute pressure adds the air pressure at the surface. This tool does not account for the fluid being squeezed at great depth, so it is best for depths of a few hundred meters or less.
More motion and materials tools
For other forces and material effects, try the Spring Oscillation Calculator, Thermal Expansion Calculator and Pulley Belt Length Calculator.
Assumptions and limits
- The fluid is at rest and has the same density at every depth.
- The object is at rest. Waves, currents and motion are not modeled.
- The volume you enter is the full volume of the object, including any enclosed air.
- The pressure uses a fixed acceleration of gravity of 9.80665 m/s2.
- The densities, the surface pressure and the sample object are examples. Use the figures for your own fluid and object.
Frequently asked questions
Why does a heavy ship float?
Because the hull is mostly air, the mass of the ship divided by the volume it displaces is less than the density of water. The object floats when the buoyant force on the volume below the waterline equals its weight.
What does the net force mean when an object sinks?
It is the weight minus the buoyant force. That is the downward force you would have to cancel with a rope, a float or a person to hold the object at rest under the surface.
Is this the right tool for planning a dive or a boat load?
No. It teaches the physics and gives estimates. Load limits, stability and dive planning involve many other factors and must follow the rules and guidance for the activity.
Why is the pressure shown in two units?
Kilopascals are the standard metric unit and psi is common in the United States. Both describe the same pressure, so use whichever you read more easily.