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Pressure Calculator

Computes pressure as force divided by the area it acts on, and reports it in pascals, kilopascals, bar, pounds per square inch and standard atmospheres.

When to use

You know a force (or a weight in newtons) and the contact area and need the pressure: a load on a footing, a hydraulic piston, a heel on a floor.

Do not use when: You need fluid pressure at depth (P = ρ·g·h is not implemented), gas pressure from temperature and amount (use ideal-gas-law), or the force from a mass first (use force).

Formula

pressure_pa = force_n / area_m2; kPa = Pa / 1000; bar = Pa / 100000; psi = Pa / 6894.757293; atm = Pa / 101325

Inputs

Parameter	Type	Unit	Required	Description
`force_n`	number	N	yes	Force acting perpendicular to the surface, in newtons (weight = mass × 9.80665). Range: ≥ 0
`area_m2`	number	m²	yes	Contact area in square metres (1 cm² = 0.0001 m²). Range: > 0

Outputs

Output	Type	Unit	Description
`pressure_pa`	number	Pa	P = F / A in pascals (N/m²).
`pressure_kpa`	number	kPa	Pressure in kilopascals.
`pressure_bar`	number	bar	Pressure in bar (1 bar = 100,000 Pa).
`pressure_psi`	number	psi	Pressure in pounds-force per square inch (1 psi = 6894.757 Pa).
`pressure_atm`	number	atm	Pressure in standard atmospheres (1 atm = 101,325 Pa).

Example

500 N on 0.02 m²: {"force_n":500,"area_m2":0.02} → {"pressure_pa":25000,"pressure_kpa":25,"pressure_bar":0.25,"pressure_psi":3.6259,"pressure_atm":0.2467}

700 N (71 kg person) on 0.05 m² (two feet): {"force_n":700,"area_m2":0.05} → {"pressure_pa":14000,"pressure_kpa":14,"pressure_psi":2.0305,"pressure_atm":0.1382}

GET https://tttkmbb.com/api/v1/calculate/pressure-force-area?force_n=500&area_m2=0.02

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/pressure-force-area (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/pressure-force-area · Markdown: https://tttkmbb.com/physics/pressure-force-area.md · JSON definition: https://tttkmbb.com/physics/pressure-force-area.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="pressure-force-area"
OpenAPI operationId: calculate_pressure
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

HyperPhysics – Pressure (reference)
NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors) (standard)

FAQ

Is this absolute or gauge pressure?

Neither in particular: it is simply force over area. Gauge readings on tyres or vessels are relative to atmospheric pressure (add 101.325 kPa for absolute).

Why does a small area give a huge pressure?

Pressure is inversely proportional to area: the same weight on a stiletto heel (about 1 cm²) exerts hundreds of times the pressure of a flat shoe.

Related calculators

Force Calculator — Compute the force from mass and acceleration or weight.
Density Calculator — Density of the material exerting the load.
Ideal Gas Law Calculator — Gas pressure from volume, temperature and amount.