# Pressure Altitude Calculator

> Converts between pressure and altitude in the ICAO International Standard Atmosphere: pressure altitude from station pressure (or from QNH/altimeter setting plus field elevation), and the ISA pressure and temperature at a given altitude.

- Calculator id: `pressure-altitude` · Category: Weather & Environment (`weather`) · Tool name: `convert_pressure_altitude`
- Canonical page: https://tttkmbb.com/weather/pressure-altitude · This document: https://tttkmbb.com/weather/pressure-altitude.md · JSON definition: https://tttkmbb.com/weather/pressure-altitude.json

## Purpose

Converts between pressure and altitude in the ICAO International Standard Atmosphere: pressure altitude from station pressure (or from QNH/altimeter setting plus field elevation), and the ISA pressure and temperature at a given altitude.

**Use when:** You need pressure altitude for aviation performance, the standard pressure or temperature at an altitude, or station pressure from a sea-level-reduced reading and elevation.

**Do not use when:** You need true altitude on a non-standard day (that requires temperature correction), altitudes above 11 km (stratosphere), or the density altitude (use air-density).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `pressure` | number |  | optional | Station pressure in pressure_unit, or the QNH/altimeter setting when elevation_m is also given. Omit to only evaluate altitude_m. (> 0, max 1200) |
| `pressure_unit` | enum: hpa \| kpa \| inhg \| mmhg |  | optional, default "hpa" | Unit of the pressure input. |
| `elevation_m` | number | m | optional | Elevation of the station. When given, `pressure` is interpreted as QNH (sea-level-reduced altimeter setting) and station pressure is derived. (min -500, max 9000) |
| `altitude_m` | number | m | optional | Optional geopotential altitude at which to report the ISA pressure and temperature. (min -500, max 11000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `pressure_altitude_m` | number | m | ISA altitude at which the standard pressure equals the station pressure. |
| `pressure_altitude_ft` | number | ft | Pressure altitude in feet. |
| `station_pressure_hpa` | number | hPa | Absolute pressure at the station (input, or derived from QNH and elevation). |
| `station_pressure_inhg` | number | inHg | Station pressure in inches of mercury. |
| `isa_pressure_hpa` | number | hPa | Standard-atmosphere pressure at altitude_m (only when altitude_m is given). |
| `isa_pressure_inhg` | number | inHg | Same in inches of mercury. |
| `isa_temperature_c` | number | °C | 15 °C minus 6.5 °C per 1000 m. |

## Formula

`p(h) = 1013.25 × (1 − 0.0065·h/288.15)^5.25578 hPa; h(p) = 44330.8 × [1 − (p/1013.25)^0.190267] m; station pressure from QNH: p_station = QNH × (1 − 0.0065·elevation/288.15)^5.25578; T_ISA = 15 − 0.0065·h °C`

ICAO Standard Atmosphere troposphere (sea level 1013.25 hPa, 15 °C, lapse 6.5 K/km, g = 9.80665 m/s², M = 28.9644 g/mol), valid to 11 000 m (226.32 hPa). The NWS pressure-altitude formula uses slightly different rounded constants (145366.45 ft, exponent 0.190284) and agrees within 0.1 %.

## Data Sources

- Wikipedia – International Standard Atmosphere (ICAO Doc 7488) — https://en.wikipedia.org/wiki/International_Standard_Atmosphere (reference, retrieved 2026-09-24)
- NWS El Paso – Pressure altitude formula — https://www.weather.gov/media/epz/wxcalc/pressureAltitude.pdf (government, retrieved 2026-09-24)

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-altitude?`
- `POST https://tttkmbb.com/api/v1/calculate/pressure-altitude` 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-altitude · OpenAPI operationId `convert_pressure_altitude` 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-altitude", "inputs": {…}}`

## Example

- Station pressure 900 hPa: inputs `{"pressure":900,"pressure_unit":"hpa"}` → `{"pressure_altitude_m":988.5,"pressure_altitude_ft":3243,"station_pressure_hpa":900,"station_pressure_inhg":26.577}`
- ISA at 1500 m: inputs `{"altitude_m":1500}` → `{"isa_pressure_hpa":845.56,"isa_pressure_inhg":24.97,"isa_temperature_c":5.25}`

```
GET https://tttkmbb.com/api/v1/calculate/pressure-altitude?pressure=900&pressure_unit=hpa
```

## Limitations

You need true altitude on a non-standard day (that requires temperature correction), altitudes above 11 km (stratosphere), or the density altitude (use air-density). ICAO Standard Atmosphere troposphere (sea level 1013.25 hPa, 15 °C, lapse 6.5 K/km, g = 9.80665 m/s², M = 28.9644 g/mol), valid to 11 000 m (226.32 hPa). The NWS pressure-altitude formula uses slightly different rounded constants (145366.45 ft, exponent 0.190284) and agrees within 0.1 %. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What is the difference between QNH and station pressure?**

Station pressure is the actual pressure at the site; QNH (altimeter setting) is that pressure reduced to sea level through the ISA so that an altimeter reads field elevation. Give elevation_m to convert between them.

**Is pressure altitude the true altitude?**

Only on a standard day. Warmer-than-ISA air makes true altitude higher than pressure altitude (about 4 ft per 1000 ft per °C of deviation); aviation performance charts nevertheless use pressure altitude.

**Why is 1013.25 hPa the reference?**

It is the ISA sea-level pressure (29.92 inHg); set the altimeter to it and it displays pressure altitude directly.

## Related

- [Air Density Calculator](https://tttkmbb.com/weather/air-density.md) — Density altitude from temperature, pressure and humidity.
- [Boiling Point at Altitude Calculator](https://tttkmbb.com/weather/boiling-point-altitude.md) — Boiling point of water at the resulting pressure.
- [Pressure Converter](https://tttkmbb.com/conversion/pressure.md) — Convert pressure units (hPa, inHg, psi, kPa).