Calculation
p = F / A
Small contact areas create high pressure for the same force.
p = F/A
Pressure Calculator: Force per Area
Small contact areas create high pressure for the same force.
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Result
Select a target and calculate.
Understand the inputs
- Mean pressure p — The mean force per unit area, assumed uniformly distributed. For gases and liquids this usually means gauge pressure above atmospheric (a manometer reads gauge pressure), not absolute pressure – check the instrument or datasheet if unsure.
- Normal force F — The force pressing or pulling perpendicular to area A. Source: a force measurement, a known weight (F = m·g), or as the result of p·A.
- Effective area A — The area actually loaded by F – not the whole part's surface, only the contact or effective region. Source: calculate it from a drawing (e.g. circular area π·d²/4) or measure it directly.
Example
1,000 N over 100 cm² gives 1 bar.
Assumptions and limits
Uniformly distributed static normal load.
Understand Pressure Calculator: Force per Area
This calculator finds the missing quantity among pressure p, force F and area A from the other two. It shows why the same force can produce a vastly different pressure depending on the area it acts on, and explains the difference between gauge and absolute pressure.
What does this quantity describe?
Pressure is the force acting perpendicular to a surface, divided by the size of that surface: p = F/A. For the same force, a smaller area produces a higher pressure.
A person in stiletto heels and a person in flat, wide shoes can exert the same body weight, and therefore the same force, on the floor. Because a stiletto heel's contact area is far smaller than a flat sole, the pressure under the heel can be many times higher than under a wide shoe — in extreme cases even higher than under an elephant's foot.
Formula and variables
p = F / A
p = F / AF = p · AA = F / p
| Symbol / input | Meaning |
|---|---|
| Mean pressure p | The mean force per unit area, assumed uniformly distributed. For gases and liquids this usually means gauge pressure above atmospheric (a manometer reads gauge pressure), not absolute pressure – check the instrument or datasheet if unsure. |
| Normal force F | The force pressing or pulling perpendicular to area A. Source: a force measurement, a known weight (F = m·g), or as the result of p·A. |
| Effective area A | The area actually loaded by F – not the whole part's surface, only the contact or effective region. Source: calculate it from a drawing (e.g. circular area π·d²/4) or measure it directly. |
Choose the inputs correctly
Enter two of the three quantities. Pressure requires force and area, force requires pressure and area, area requires force and pressure. For fluids especially, clarify whether the pressure in question is gauge pressure (relative to the atmosphere) or absolute pressure.
How to use the calculator
Select the target quantity and enter the two known values with units. For technical data, check whether a force acts perpendicular to the area or whether a force component must be resolved first.
Worked example
Given F = 1,000 N and A = 100 cm² = 0.01 m², substitution gives p = 1,000 N / 0.01 m² = 100,000 Pa = 1 bar. If the same force acted on only 1 cm², the result would already be p = 100 bar.
Understand the result and units
A pressure of 1 bar (100,000 Pa) is roughly the average atmospheric pressure at sea level. The example shows that mechanical stress depends not on force alone but on the ratio of force to area — which is why wide foundations or skis spread a given force over a larger area to reduce pressure.
The SI unit is the pascal (Pa = N/m²). Engineering commonly uses bar, kPa, MPa and psi: 1 bar = 100,000 Pa = 100 kPa, and 1 MPa = 1 N/mm². One standard atmosphere (atm) equals 101,325 Pa.
What is the difference between gauge and absolute pressure?
Absolute pressure is measured relative to a vacuum (zero pressure). Gauge pressure is instead measured relative to the current atmospheric pressure and is what most technical pressure gauges display. Approximately, absolute pressure = gauge pressure + atmospheric pressure (about 1.013 bar at sea level). Calculations involving ideal gases or vacuum applications always require absolute pressure.
Typical applications
Pressure calculations are used to design foundations and bearing surfaces, hydraulic and pneumatic systems, tyre pressure specifications, and to estimate contact pressure in materials testing.
Assumptions, limits and common mistakes
The formula gives an area-averaged pressure for a uniformly distributed, perpendicular normal force. With uneven load distribution, notch effects or angled forces, the actual local contact pressure deviates from this average and requires a more detailed stress analysis.
Common mistake: Do not equate force and pressure: the same force can create very different pressures depending on area. For fluid pressures, do not confuse gauge and absolute pressure — most technical gauges display gauge pressure relative to the atmosphere, not absolute pressure.
Frequently asked questions
Why does a stiletto heel hurt more than a flat sole at the same body weight?
Because the force (body weight) is the same in both cases but spreads over a much smaller heel area. Following p = F/A, pressure rises as area falls.
Is 1 bar the same as 1 atm?
Nearly: 1 bar = 100,000 Pa, 1 atm = 101,325 Pa. For most engineering estimates the difference is negligible.
What is the difference between Pa and MPa?
1 MPa equals 1,000,000 Pa and is also equal to 1 N/mm², which is convenient for component calculations using millimetre dimensions.
Does a tyre pressure gauge show absolute pressure?
No, typical tyre gauges show gauge pressure relative to the atmosphere; the actual absolute pressure inside the tyre is higher by the atmospheric pressure.