Formulas used
- P = F / A
- F = P × A
- A = F / P
- 1 Pa = 1 N/m²
Meaning of the variables
- P
- Pressure, defined as the normal force acting over a given area.
- F
- Force. The equation uses the component acting perpendicular to the surface.
- A
- Area of contact or action. The same force produces higher average pressure on a smaller area.
Unit reference tables
Pressure units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Nanopascal | nPa | 1.0000000000e-9 Pa | Extremely small differential pressures and experimental measurements |
| Micropascal | µPa | 0.000001 Pa | Acoustics and precision sensor applications |
| Millipascal | mPa | 0.001 Pa | Very small pressure differences and laboratory instruments |
| Pascal | Pa | 1 Pa | Base SI pressure unit and scientific calculations |
| Hectopascal | hPa | 100 Pa | Meteorology and atmospheric pressure reporting |
| Kilopascal | kPa | 1,000 Pa | Building, HVAC and general engineering measurements |
| Megapascal | MPa | 1,000,000 Pa | Material strength and higher-pressure systems |
| Gigapascal | GPa | 1,000,000,000 Pa | Elastic modulus and advanced materials engineering |
| Terapascal | TPa | 1.0000000000e+12 Pa | Theoretical material models and extreme stiffness calculations |
| Millibar | mbar | 100 Pa | Legacy meteorology and process gauges |
| Bar | bar | 100,000 Pa | Compressors, hydraulics, pneumatics and industry |
| Standard atmosphere | atm | 101,325 Pa | Reference atmospheric pressure and laboratory work |
| Technical atmosphere | at | 98,066.5 Pa | Legacy technical documents and some mechanical tables |
| Kilogram-force per square centimeter | kgf/cm² | 98,066.5 Pa | Legacy pump, boiler and analog gauge usage |
| Torr | Torr | 133.322368421 Pa | Vacuum technology and laboratory pressures |
| Millimeter of mercury | mmHg | 133.322387415 Pa | Medical measurements and manometer readings |
| Millimeter of water column | mmH₂O | 9.80665 Pa | Low differential pressure and ventilation systems |
| Centimeter of water column | cmH₂O | 98.0665 Pa | Respiratory devices and low-pressure applications |
| Pound-force per square inch | psi | 6,894.75729317 Pa | Tires, hydraulics and Anglo-American equipment |
| Kilopound-force per square inch | ksi | 6,894,757.29317 Pa | Material strength and structural engineering |
| Pound-force per square foot | psf | 47.8802589803 Pa | Building loads and HVAC differential pressures |
| Inch of mercury | inHg | 3,386.389 Pa | Barometers, aviation and engine vacuum |
| Inch of water column | inH₂O | 249.08891 Pa | Gas lines and low-pressure air systems |
Force units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Nanonewton | nN | 1.0000000000e-9 N | Nanoscale forces and surface interactions |
| Micronewton | µN | 0.000001 N | Micromechanics and precision sensor work |
| Millinewton | mN | 0.001 N | Laboratory instruments and small actuators |
| Newton | N | 1 N | Base SI force unit and general engineering |
| Kilonewton | kN | 1,000 N | Structural members, presses and load-bearing systems |
| Meganewton | MN | 1,000,000 N | Large hydraulic presses and heavy infrastructure loads |
| Giganewton | GN | 1,000,000,000 N | Very large structural loads and theoretical comparisons |
| Dyne | dyn | 0.00001 N | CGS system and legacy scientific references |
| Gram-force | gf | 0.00980665 N | Small mechanical measurements and older catalogs |
| Kilogram-force | kgf | 9.80665 N | Press loads and legacy mechanical charts |
| Ounce-force | ozf | 0.278013850954 N | Small springs and light load measurements |
| Pound-force | lbf | 4.44822161526 N | Machine parts, tension tests and Imperial systems |
| Kip | kip | 4,448.22161526 N | Steel structures and US structural engineering |
| Short ton-force | tonf US | 8,896.44323052 N | Heavy equipment and US industrial loads |
Area units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Square micrometer | µm² | 1.0000000000e-12 m² | Microsurfaces and thin-film applications |
| Square millimeter | mm² | 0.000001 m² | Cross-sections, bolts and cable calculations |
| Square centimeter | cm² | 0.0001 m² | Small contact areas and laboratory samples |
| Square decimeter | dm² | 0.01 m² | Surface coverage and area calculations |
| Square meter | m² | 1 m² | Base SI area unit and general calculations |
| Hectare | ha | 10,000 m² | Land, agriculture and large open areas |
| Square kilometer | km² | 1,000,000 m² | Geographic regions and large surfaces |
| Square inch | in² | 0.00064516 m² | Small machine parts and psi-based calculations |
| Square foot | ft² | 0.09290304 m² | Architectural floor areas and light construction |
| Square yard | yd² | 0.83612736 m² | Textiles and outdoor coverage measurements |
| Acre | ac | 4,046.8564224 m² | Land and real-estate measurements |
Scientific notes
- kgf, gf and technical-atmosphere calculations use the standard acceleration of gravity g₀ = 9.80665 m/s².
- Liquid-column units such as mmHg, mmH₂O, cmH₂O, inHg and inH₂O can vary with the defining temperature and convention; this calculator uses the stated conventional conversion factors.
- Mass and force are not the same quantity, so kg is not presented as a force unit; only kgf is included.
Worked examples
1000 N / 0.01 m² = 100000 Pa
A force of 1000 N distributed over 0.01 m² produces a pressure of 100000 Pa, which is also 100 kPa.
1 kgf / 1 cm² = 98066.5 Pa
Under standard gravity, 1 kgf equals 9.80665 N. Since 1 cm² equals 0.0001 m², the pressure becomes 9.80665 / 0.0001 = 98066.5 Pa.
1 kN / 100 cm² = 100 kPa
1 kN becomes 1000 N and 100 cm² becomes 0.01 m². Dividing 1000 by 0.01 gives 100000 Pa, or 100 kPa.
1 bar × 10 cm² = 100 N
1 bar equals 100000 Pa and 10 cm² equals 0.001 m². Using F = P × A gives 100000 × 0.001 = 100 N.
1 MPa × 1 mm² = 1 N
1 MPa equals 1000000 Pa. Since 1 mm² equals 0.000001 m², multiplying them gives exactly 1 N.
1 lbf / 1 in² ≈ 1 psi
With 1 lbf ≈ 4.4482216152605 N and 1 in² = 0.00064516 m², the result is about 6894.757 Pa, which is approximately 1 psi.
Typical applications
- Contact pressure estimates
- Pressing, clamping and tooling calculations
- Preliminary hydraulic and pneumatic sizing
- Comparisons of tire, seal and surface loads
Limitations and measurement accuracy
- The result represents an average and uniformly distributed pressure.
- It is not sufficient on its own for stress concentrations, inclined forces, dynamic loading or material deformation.
- Pressure and mechanical stress share the same unit, but they are not always used in the same engineering context.