Pressure Calculator
Calculate pressure from force and area using P = F/A, with results in pascals, kilopascals and bar. Includes a worked example and unit pitfalls.
Results
Pressure
- kPa
- 0.20
- bar
- 0.002
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Educational estimates · not financial advice · free, no signup
Formula / how it works
P = F ÷ A, with force in newtons and area in square metres giving pascals (1 Pa = 1 N/m²). 1 kPa = 1,000 Pa and 1 bar = 100,000 Pa.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Pressure measures how concentrated a force is: the same push spread over a large area feels gentle, while the same push on a tiny area can cut. Physics defines it as force divided by the area it acts on. In SI units, one newton spread over one square metre is one pascal, a very small unit, so engineers often quote kilopascals or bar. This calculator takes a force in newtons and an area in square metres and returns the pressure in pascals, kilopascals and bar. Students use it for physics homework, and makers use it to compare the load on a pad, a tyre contact patch or a hydraulic piston. It assumes force acts uniformly and perpendicular to the surface.
When to use / who it helps
- You need the pressure a known force produces on a given area.
- You are checking a physics problem on pressure, stress or hydraulics.
- You are comparing how footprint size changes ground pressure for a machine or person.
- You want pascals converted into kilopascals or bar for a spec sheet.
- You are sizing a piston or contact area for a target pressure.
How to use
Steps
- Enter the force in newtons. To use weight, multiply mass in kilograms by 9.80665.
- Enter the area in square metres. Convert cm² by dividing by 10,000.
- Read the pressure in pascals first.
- Read the kilopascal and bar equivalents for more convenient scales.
- To find force for a target pressure, multiply pressure by area instead.
- Compare with atmospheric pressure, about 101,325 Pa, for context.
How to interpret results
- Pressure rises when force increases or area shrinks; halving the area doubles the pressure.
- Pascals are small, so everyday pressures are often in kilopascals; tyre pressures are around a few hundred kPa.
- One bar equals 100,000 Pa, close to ordinary atmospheric pressure.
- The result is the average pressure; real contact pressures may be uneven.
- Gauge pressure and absolute pressure differ by atmospheric pressure, which this simple formula does not add.
Common mistakes & gotchas
- Entering mass in kilograms as force. Multiply by 9.80665 m/s² to convert weight to newtons.
- Entering area in cm² or in² without converting to m².
- Using total area when only part of it is in contact.
- Confusing gauge and absolute pressure in engineering contexts.
- Mixing pounds-force and newtons.
Worked example
Worked example — 70 kg person on two shoes of 0.04 m² total area
- Weight force: 70 × 9.80665 ≈ 686.5 N.
- Divide by area: 686.5 ÷ 0.04 ≈ 17,162 Pa.
- Convert: 17,162 Pa ≈ 17.2 kPa ≈ 0.17 bar.
- Compare: on a stiletto heel of 1 cm² (0.0001 m²) carrying the same force, the pressure would be 686.5 ÷ 0.0001 ≈ 6.9 MPa, about 400 times higher.
Result: About 17.2 kPa on flat shoes; reducing the contact area increases pressure in proportion.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
P = F ÷ A, with force in newtons and area in square metres giving pascals (1 Pa = 1 N/m²). 1 kPa = 1,000 Pa and 1 bar = 100,000 Pa.
Frequently asked questions
What is the formula for pressure?
Pressure equals force divided by area, P = F/A.
What unit is pressure measured in?
The SI unit is the pascal, one newton per square metre. Kilopascals, bar, psi and atmospheres are also common.
How do I convert weight to force?
Multiply mass in kilograms by 9.80665 m/s² to get weight in newtons.
Why do sharp objects cut?
The same force on a smaller area produces a much higher pressure, which can exceed what the material can withstand.
Is atmospheric pressure the same everywhere?
No. It averages about 101,325 Pa at sea level and falls with altitude and changes with weather.
Does this include fluid pressure?
No. Fluid pressure at depth is ρ·g·h and needs the fluid density and depth.
Textbook formulas under ideal assumptions. For safety-critical, structural, or regulated work, verify with a qualified engineer and the governing standards. Full disclaimer