Pressure Calculator
Calculate pressure from force and area (P = F/A) with results in Pa, kPa, atm, psi, bar, mmHg, and more. Supports multiple input units. See also our Hydraulic Pressure Calculator and Hydrostatic Pressure Calculator.
How to Calculate Pressure
Pressure is defined as force per unit area: P = F/A. It measures how concentrated a force is over a surface. The same force spread over a larger area creates less pressure (snowshoes distribute weight to prevent sinking), while concentrating force on a small area creates high pressure (a knife edge cuts because force is concentrated on a tiny area). Pressure is a scalar quantity — at any point in a fluid, it acts equally in all directions.
The SI unit of pressure is the pascal (Pa), equal to one newton per square meter (N/m²). Since one pascal is very small (atmospheric pressure is 101,325 Pa), kilopascals (kPa), bars, and atmospheres are commonly used. In the US and UK, pounds per square inch (psi) remains common for tire pressure, hydraulics, and industrial applications. Medical applications often use mmHg (millimeters of mercury) for blood pressure.
To calculate pressure, simply divide the total force by the area over which it acts. If a 70 kg person stands on both feet (total area ≈ 0.05 m²), the pressure on the floor is P = (70×9.81)/0.05 = 13,734 Pa ≈ 0.14 atm. Standing on one foot doubles the pressure. Wearing stiletto heels (area ≈ 1 cm² per heel) creates pressures exceeding 5 MPa — enough to damage soft flooring.
Pressure Formula
Basic Pressure:
P = F / A
Hydrostatic Pressure:
P = ρgh (gauge) or P = P₀ + ρgh (absolute)
Unit Conversions:
1 atm = 101,325 Pa = 101.325 kPa
1 atm = 1.01325 bar = 14.696 psi
1 atm = 760 mmHg = 29.92 inHg
1 bar = 100,000 Pa = 100 kPa
1 psi = 6,894.76 Pa = 6.895 kPa
1 MPa = 10 bar = 145.04 psi
Pressure in Fluids:
Pressure acts equally in all directions (Pascal's principle)
Pressure increases with depth: ΔP = ρgΔh
Example Calculation
A 1000 N force is applied to a surface area of 0.1 m². Calculate the pressure:
Given: F = 1000 N, A = 0.1 m²
P = F/A = 1000/0.1 = 10,000 Pa
Converting to other units:
= 10 kPa
= 0.1 bar
= 0.0987 atm
= 1.450 psi
= 75.01 mmHg
Context: This is about 10% of atmospheric pressure.
Equivalent to the pressure at ~1 meter water depth.
Pressure Reference Table
| Scenario | Pa | kPa | atm | psi |
|---|---|---|---|---|
| Atmospheric pressure (sea level) | 101,325 | 101.325 | 1.000 | 14.696 |
| Car tire | 220,000 | 220 | 2.17 | 32 |
| Bicycle tire (road) | 690,000 | 690 | 6.81 | 100 |
| Scuba tank | 20,000,000 | 20,000 | 197 | 2900 |
| Water at 10m depth | 199,425 | 199.4 | 1.97 | 28.9 |
| Blood pressure (systolic) | 16,000 | 16 | 0.158 | 2.32 |
| Vacuum cleaner suction | 20,000 | 20 | 0.197 | 2.9 |
| Hydraulic press | 70,000,000 | 70,000 | 691 | 10,153 |
| Diamond anvil cell | 100,000,000,000 | 100,000,000 | 987,167 | 14.5M |
Frequently Asked Questions
What is pressure?
Pressure is the force exerted per unit area, measured in pascals (Pa = N/m²). It describes how concentrated a force is on a surface. In fluids (liquids and gases), pressure acts equally in all directions at any given point. Pressure can be caused by gravity (atmospheric and hydrostatic pressure), mechanical force (hydraulic systems), molecular collisions (gas pressure), or electromagnetic forces. It is one of the most fundamental quantities in physics and engineering.
What is the difference between absolute and gauge pressure?
Absolute pressure is measured relative to a perfect vacuum (zero pressure). Gauge pressure is measured relative to atmospheric pressure. The relationship is: P_absolute = P_gauge + P_atmospheric. A tire gauge reading 32 psi means the tire pressure is 32 psi above atmospheric — the absolute pressure is 32 + 14.7 = 46.7 psi. Vacuum is expressed as negative gauge pressure. Most everyday pressure measurements are gauge pressure.
Why do we have so many pressure units?
Different fields developed their own units historically: meteorology uses mbar/hPa, medicine uses mmHg, engineering uses psi or bar, physics uses Pa, and diving uses atm. The pascal (SI unit) is very small (atmospheric pressure = 101,325 Pa), making it inconvenient for everyday use. The bar (100,000 Pa ≈ 1 atm) is a practical compromise. PSI remains common in the US. mmHg persists in medicine because mercury manometers were the original blood pressure instruments.
How does atmospheric pressure work?
Atmospheric pressure is caused by the weight of the air column above you. At sea level, this column weighs about 101,325 N per square meter (14.7 psi). That means about 10 tons of air press on every square meter of surface — we do not feel it because the pressure acts equally from all sides and our bodies have internal pressure that balances it. Atmospheric pressure decreases with altitude (roughly halving every 5.5 km) because there is less air above.
Why does a sharp knife cut better?
A sharp knife concentrates the applied force on an extremely small area (the edge), creating very high pressure. If you push with 20 N on a knife edge that is 0.1 mm × 100 mm = 10⁻⁵ m², the pressure is 20/10⁻⁵ = 2,000,000 Pa = 2 MPa. This exceeds the yield strength of many materials, causing them to separate. A dull knife has a larger contact area, so the same force creates less pressure — not enough to cut. This is why pressure (not just force) determines cutting ability.
What is a pascal and why is it so small?
One pascal equals one newton per square meter (1 Pa = 1 N/m²). It is named after Blaise Pascal who studied fluid pressure in the 1600s. It seems small because a square meter is large — spreading 1 N (about the weight of an apple) over an entire square meter gives very little pressure. Atmospheric pressure is 101,325 Pa because the entire weight of the atmosphere above each square meter is enormous (about 10,330 kg). For practical use, kPa, MPa, or bar are more convenient.
Pressure in Engineering and Science
Pressure calculations are essential in structural engineering (wind loads, soil bearing capacity), mechanical engineering (hydraulic systems, pneumatics, pressure vessels), chemical engineering (reactor design, distillation), aerospace (cabin pressurization, aerodynamic loads), civil engineering (water supply systems, dam design), and biomedical engineering (blood pressure, respiratory mechanics). Understanding pressure helps engineers design safe structures, efficient systems, and reliable equipment across all disciplines.