# 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.

- Calculator id: `pressure-force-area` · Category: Physics (`physics`) · Tool name: `calculate_pressure`
- Canonical page: https://tttkmbb.com/physics/pressure-force-area · This document: https://tttkmbb.com/physics/pressure-force-area.md · JSON definition: https://tttkmbb.com/physics/pressure-force-area.json

## Purpose

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.

**Use when:** 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).

## Input

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

## Output

| Field | 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). |

## Formula

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

## Data Sources

- HyperPhysics – Pressure — http://hyperphysics.phy-astr.gsu.edu/hbase/pres.html (reference, retrieved 2026-09-23)
- NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors) — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/pressure-force-area?force_n=…&area_m2=…`
- `POST https://tttkmbb.com/api/v1/calculate/pressure-force-area` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/pressure-force-area · OpenAPI operationId `calculate_pressure` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "pressure-force-area", "inputs": {…}}`

## Example

- 500 N on 0.02 m²: inputs `{"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): inputs `{"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
```

## Limitations

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). All values are computed from the formula above; no measurement or live data is involved.

## 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

- [Force Calculator](https://tttkmbb.com/physics/newtons-second-law.md) — Compute the force from mass and acceleration or weight.
- [Density Calculator](https://tttkmbb.com/physics/density-mass-volume.md) — Density of the material exerting the load.
- [Ideal Gas Law Calculator](https://tttkmbb.com/chemistry/ideal-gas-law.md) — Gas pressure from volume, temperature and amount.