Pressure, Water Pressure & Buoyancy Calculator
Calculate pressure p = F ÷ S, water pressure p = ρgh and buoyancy F = ρVg (Archimedes’ principle) with unit conversion for N, g, kg, cm², m², Pa, hPa, kPa, g/cm³, kg/m³, cm³, m³ and L. Shows the working, total pressure including the atmosphere, and whether an object floats or sinks.
Try an example
Enter the values and press Calculate.
How to use
- 1
Choose the calculation
Select pressure (force and area), water pressure (depth and density) or buoyancy (Archimedes).
- 2
Enter values and units
Enter force or mass, area, depth, density and volume. Mass is converted with F = mg.
- 3
Check the result and working
See the substitution, unit conversions, total pressure and the floating/sinking verdict.
Features
- Pressure p = F ÷ S from force, mass, area or pressure
- Liquid pressure p = ρgh with optional total pressure including the atmosphere
- Buoyancy F = ρVg with reverse calculation of volume or density
- Mass-to-force conversion with g = 9.8, 10 or 9.80665 m/s²
- Liquid presets (water, seawater, oil, ethanol, mercury) and a floating/sinking verdict
- Runs entirely in your browser; no sign-up and nothing uploaded
Use cases
School physics homework
Check pressure, water pressure and buoyancy problems with the working shown.
Physics revision
Practise choosing between p = F/S, p = ρgh and F = ρVg.
Depth and floating estimates
Estimate pressure at depth and whether an object floats or sinks.
Details
Pressure is the perpendicular force divided by the area it acts on (p = F ÷ S). The unit is the pascal, with 1 Pa = 1 N/m². Convert the area to m² first (1 m² = 10,000 cm²). When starting from mass, use F = mg and choose g = 9.8 m/s² (standard) or g = 10 m/s² (the introductory approximation that 100 g weighs 1 N).
The pressure from a liquid is p = ρgh, proportional to depth h, where ρ is the liquid density in kg/m³ and h is the depth below the surface in metres. In water the pressure rises by about 100 kPa (roughly one atmosphere) for every 10 m of depth. The total pressure on a submerged object adds atmospheric pressure (about 101.3 kPa). At the same depth the pressure is the same regardless of container shape or the amount of liquid, and it acts perpendicular to every surface.
By Archimedes’ principle the buoyant force is F = ρVg, the weight of the displaced liquid. Once fully submerged, the force does not depend on depth. If the object density (mass ÷ volume) is less than the liquid’s, it floats; greater, it sinks; equal, it is neutral. A floating object experiences a buoyant force equal to its weight.
The tool converts force units (N, and g or kg through F = mg), area (cm², m²), pressure (Pa, hPa, kPa, N/cm²), density (g/cm³, kg/m³) and volume (cm³, m³, L), and shows exactly which values went into which formula. It also reports the total pressure including the atmosphere and compares weight with buoyancy to judge floating or sinking.
FAQ
What is the difference between force and pressure?
Force is the push itself in newtons; pressure is force per unit area in pascals. The same force over a smaller area gives a larger pressure. Use p = F ÷ S with the area in m².
How large is 1 Pa?
It is the pressure of 1 N acting perpendicularly on 1 m², so 1 Pa = 1 N/m². When an area is given in cm², remember 1 m² = 10,000 cm².
Does 100 g weigh 1 N?
Introductory courses often use the approximation 100 g = 1 N (g = 10 m/s²). In physics, g = 9.8 m/s², so 100 g weighs about 0.98 N. The tool lets you switch g.
What determines water pressure?
The liquid density ρ, the depth h and gravity, as p = ρgh. At the same depth in the same liquid the pressure is identical regardless of container shape. It increases by about 100 kPa (roughly one atmosphere) per 10 m of water.
Does buoyancy increase with depth?
Once the object is fully submerged, the buoyant force is constant regardless of depth. It equals the weight of the displaced liquid, determined by the object volume and the liquid density.
How do I judge whether an object floats or sinks?
Compare the object density (mass ÷ volume) with the liquid density. Lower density floats, higher sinks. A floating object has a buoyant force equal to its weight.
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Verified: Known values (2.5 N over 50 cm² giving 500 Pa, 50 kg × g 10 over 2000 cm² giving 2,500 Pa, 500 g × g 9.8 over 0.2 m² giving 24.5 Pa, 10 m of water at ρ 1000 and g 9.8 giving 98,000 Pa = 980 hPa, 1 m plus the atmosphere giving 1.111×10⁵ Pa, 50 m of seawater giving 5.047×10⁵ Pa, 100 cm³ in water giving 0.98 N, a 150 g object sinking, and 0.98 N giving 100 cm³) plus invalid and depth errors are covered by browser tests
Did you know?
Water pressure rises by about 100 kPa (roughly one atmosphere) for every 10 m of depth, so 10 m down the total pressure is about two atmospheres. Once fully submerged, buoyancy is constant with depth and equals the weight of the displaced liquid.