Pressure Calculator
Solve pressure from force and area, or the pressure of a liquid column from its density and depth, in any common unit.
🌡️ What is Pressure?
Pressure is the force acting perpendicular to a surface divided by the area of that surface, P = F / A. Its SI unit is the pascal (Pa), one newton per square metre. Because a pascal is tiny, everyday work uses kilopascals, megapascals, bar, atmospheres, psi and torr. This pressure calculator solves the relationship in either direction: leave pressure blank to find it from a force and an area, leave the force blank to find the load a pressure creates, or leave the area blank to find the contact area that keeps a load at a chosen pressure. A second mode applies the same idea to a fluid at rest, where the pressure at depth comes from the weight of the liquid above and is given by P = ρ g h.
Hydrostatic pressure is what divers, submarine designers, dam engineers and plumbers deal with. The pressure at a point in a still fluid depends on the fluid density ρ, the local gravity g and the vertical depth h, and acts equally in all directions. In fresh water it rises by about 9.8 kPa every metre, so it reaches one extra atmosphere at roughly 10.3 m. A tall thin tube and a wide tank filled to the same height produce the same pressure at the bottom. The hydrostatic pressure article explains the physics, and mercury, which is 13.6 times denser than water, is the reason a barometer needs only about 760 mm of liquid to balance the atmosphere.
The most common slip is mixing gauge and absolute pressure. The hydrostatic formula gives the extra pressure from the liquid, which is gauge pressure. The pressure a sensor in the water actually sees, measured from a vacuum, also includes the atmosphere pressing on the surface, so the calculator shows an absolute value that adds one standard atmosphere, 101325 Pa. Other usual traps are unit prefixes (kPa versus MPa), square centimetres versus square metres, and typing a pressure in bar while the selector still says kPa.
Use this page for general pressure problems and the pounds per square inch calculator when you work mainly in psi, with gauge and absolute conversions for tires and tanks. Pair it with the kg to newtons calculator to turn a mass into a force first, and see the Bernoulli equation calculator for pressure in moving fluids.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Pressure from a Force
A 500 N force pressing on a 0.01 m² plate
Example 2 — Force from a Pressure
A gas at 2.5 bar acting on a piston of area 40 cm²
Example 3 — Area from a Force and a Pressure
A 1500 N load that must not exceed 300 kPa
Example 4 — Pressure at 100 m in the Sea
Sea water of density 1025 kg/m³ at a depth of 100 m
Example 5 — Depth that Adds One Atmosphere
Fresh water of density 997 kg/m³, gauge pressure of 1 atm
Example 6 — Density from a Pressure Reading
A gauge reads 2 bar at a depth of 20 m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for pressure?
Pressure equals force divided by the area it acts on perpendicular to the surface: P = F / A. In SI units, newtons per square metre gives pascals. A 500 N force on 0.01 square metres is 50000 Pa, or 50 kPa.
How do you calculate hydrostatic pressure?
Use P = rho x g x h, with density in kg per cubic metre, g in m/s squared and depth in metres. Sea water of density 1025 kg/m3 at 100 m depth gives 1025 x 9.80665 x 100 = 1005182 Pa, about 1.005 MPa, of gauge pressure.
What is the difference between gauge and absolute pressure?
Gauge pressure is measured relative to the surrounding atmosphere and absolute pressure is measured from a perfect vacuum. Absolute = gauge + atmospheric pressure, and standard atmospheric pressure is 101325 Pa.
How many pascals are in a bar, an atmosphere and a psi?
One bar is 100000 Pa, one standard atmosphere is 101325 Pa, one psi is 6894.757 Pa and one torr is 101325 / 760 = 133.322 Pa.
How does pressure change with depth in water?
It increases linearly at about 9.8 kPa per metre for fresh water, so roughly one extra atmosphere every 10.3 m. At 10 m the gauge pressure is about 98 kPa and the absolute pressure about 199 kPa.
Does the shape of the container change the pressure at the bottom?
No. Hydrostatic pressure at a given depth depends only on the fluid density, g and the vertical depth, not on the container's width or shape. This is the hydrostatic paradox.
How do I find the force from a pressure?
Multiply pressure by area, F = P x A. With 2.5 bar acting on 40 cm squared the force is 250000 Pa x 0.004 m squared = 1000 N.
Why does a smaller area give a larger pressure?
Pressure is force per unit area, so the same force over less area means more force on each unit of surface. A sharp knife cuts because its edge has a tiny contact area.
What density should I use for sea water?
About 1025 kg per cubic metre is a typical value for ocean water, against roughly 997 for fresh water at 25 degrees C. The exact value depends on salinity, temperature and pressure.
What is torr and how does it relate to mmHg?
The torr is defined as 1/760 of a standard atmosphere, which is 133.322 Pa. It is very close to one millimetre of mercury, and the two units are interchangeable for most practical purposes.
Can the calculator find the depth for a given pressure?
Yes. In hydrostatic mode leave the depth blank and enter the gauge pressure, density and g. With 1 atm of gauge pressure in fresh water of 997 kg/m3 the depth is 10.36 m.