Pressure CalculatorP = F ÷ A · P = ρgh
Pressure is force per unit area: P = F ÷ A. In a fluid, pressure rises with depth: P = ρgh. One pascal is one newton per square metre. Calculate pressure from a force on an area, find the water pressure at any depth (gauge and absolute), or size a hydraulic press using Pascal’s law. Results are shown in Pa, kPa, psi, bar and atm on a live gauge.
Formula verified against OpenStax — University Physics, Volume 1 · NIST Special Publication 811 — Guide for the Use of the SI
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Pressure inputs
Gauge pressure is measured above atmospheric. Absolute adds 101,325 Pa.
Step-by-step working
What is pressure?
Pressure is the force acting perpendicular to a surface, divided by the area of that surface. The same force concentrated on a smaller area produces a higher pressure.
In fluids, pressure acts in every direction and increases with depth. That is why dams are thicker at the bottom, why your ears hurt at the bottom of a pool, and why hydraulic machines can lift cars.
Quick answers
How do you calculate pressure from force and area?
Divide force by area: P = F ÷ A. A 70 kg person (687 N) standing on one foot of about 150 cm² exerts roughly 45.8 kPa (6.6 psi).
How do I calculate water pressure at a depth?
P = ρgh. For fresh water, gauge pressure rises by about 9.81 kPa (1.42 psi) per metre. At 30 m in seawater, absolute pressure is about 4 atm.
How does a hydraulic press multiply force?
Pascal’s law: pressure is the same throughout the fluid, so F₂ = F₁ × A₂ ÷ A₁. A piston with 5× the diameter has 25× the area and gives 25× the force. For the buoyant force in water, the same principle applies vertically.
How do I convert psi to bar or kPa?
1 psi = 6.895 kPa = 0.06895 bar. So 32 psi is 220.6 kPa or 2.21 bar. The tiles above convert automatically.
Pressure formulas
1 Pa = 1 N/m². 1 atm = 101,325 Pa = 14.696 psi = 1.01325 bar.
| Symbol | Meaning | SI unit |
|---|---|---|
| P | Pressure | Pa |
| F | Force perpendicular to the surface | N |
| A | Area | m² |
| ρ | Fluid density | kg/m³ |
| h | Depth below the surface | m |
| g | Gravitational acceleration | m/s² |
How to calculate pressure
- Find the force pressing perpendicular to the surface, in newtons.
- Find the contact area in m² (1 cm² = 0.0001 m²).
- Divide force by area for pressure in pascals.
- In liquids, multiply density × g × depth, and add atmospheric pressure for the absolute value.
Worked example: water pressure at 10 m
What is the pressure 10 m below the surface of a freshwater lake?
Pabs = 98,066.5 + 101,325 = 199,391.5 Pa ≈ 1.97 atm ≈ 28.9 psi
A hydraulic jack with a 2 cm and a 10 cm piston turns a 100 N push into 100 × (10 ÷ 2)² = 2,500 N of lift.
Pressure unit conversion
Equivalent values for one of each unit.
| Unit | Pa | psi | bar |
|---|---|---|---|
| 1 Pa | 1 | 0.000145 | 0.00001 |
| 1 kPa | 1,000 | 0.1450 | 0.01 |
| 1 psi | 6,894.76 | 1 | 0.06895 |
| 1 bar | 100,000 | 14.504 | 1 |
| 1 atm | 101,325 | 14.696 | 1.01325 |
| 1 mmHg | 133.32 | 0.01934 | 0.001333 |
Everyday pressures
For a sense of scale.
| Situation | Pressure |
|---|---|
| Blood pressure 120 mmHg (gauge) | 16 kPa · 2.3 psi |
| Car tyre (gauge) | 220–250 kPa · 32–36 psi |
| Bicycle road tyre | 550–700 kPa · 80–100 psi |
| Scuba tank (full) | 20 MPa · ≈ 3,000 psi |
| Mariana Trench floor | ≈ 110 MPa |
Common mistakes to avoid
- Leaving area in cm². 25 cm² is 0.0025 m², a factor of 10,000.
- Mixing gauge and absolute pressure. Tyre gauges read above atmospheric; physics equations such as the gas laws need absolute.
- Thinking container shape matters. Hydrostatic pressure depends only on depth and density (the hydrostatic paradox).
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who became a full-time tech geek, and I’ve spent 13+ years designing and coding web tools. Pressure is familiar ground from pharmacy, from manometer readings in physical pharmacy labs to blood pressure in mmHg at the counter, so I made sure this tool converts cleanly between all of them.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Pressure Calculator: frequently asked questions
P = F ÷ A, force divided by the area it acts on. In a fluid at rest, the pressure at depth h is P = ρgh above the surface pressure.
The pascal (Pa), equal to one newton per square metre. Because it is small, kPa and MPa are common, along with bar, psi and atm.
Absolute pressure is measured from a perfect vacuum. Gauge pressure is measured relative to atmospheric pressure: absolute = gauge + 101.325 kPa at sea level.
Because the fluid at a given depth supports the weight of all the fluid above it. More depth means more weight per unit area.
A pressure change applied to an enclosed fluid is transmitted undiminished to every part of the fluid. Hydraulic brakes, jacks and presses rely on it.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 14.1–14.3, Fluids, Density and Pressure; Pascal’s Principle
- NIST Special Publication 811 — Guide for the Use of the SI — pressure unit conversions
- NOAA — Ocean pressure — pressure increase with depth
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.