Source: https://guthlabs.ai/docs/instruments/barometric-formula-pressure-vs-altitude-general/

instrument / verified-clean

# Barometric Formula (Pressure vs Altitude, general)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/barometric-formula-pressure-vs-altitude-general/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/barometric-formula-pressure-vs-altitude-general/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/barometric-formula-pressure-vs-altitude-general/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/barometric-formula-pressure-vs-altitude-general/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Earth & Space (astronomy, orbital mechanics, meteorology, geology, geodesy, oceanography)

**Tranche**: tranche-5

**Evidence ID**: t5-158

**Ledger rows**: 1

No ledger note is attached.

## Review findings

NEEDS_REVIEW because the temperature, pressure, altitude, and reference-datum units are not explicitly specified. The displayed formula is standard for the isothermal ideal-gas atmosphere under the stated constant-parameter assumptions, and the honest-label warning appropriately identifies its simplification.

### Formula and scope findings

- The formula is correct only for an isothermal atmosphere with constant molar mass M, gravitational acceleration g, and temperature T; it is not a general barometric or ISA-layer formula.

- The specification does not state that temperature must be absolute temperature in kelvin, although using Celsius or Fahrenheit directly would make the formula invalid.

- The reference pressure P0 must be defined at the same reference datum from which altitude h is measured; calling it sea-level pressure is insufficient for locations with nonstandard reference elevations.

### Unit assumptions

- P0 and output P use the same pressure unit, such as pascals or kilopascals.

- Altitude h is in metres and is measured relative to the datum where P0 applies.

- Temperature T is in kelvin; Celsius must be converted with T_K = T_C + 273.15.

- M is in kg/mol, g is in m/s², and R is in J/(mol·K).

- Test calculations use M = 0.0289644 kg/mol, g = 9.80665 m/s², and R = 8.314462618 J/(mol·K).

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-temperature input produces division by zero in the exponent and must be rejected. The specification does not state an input-domain validation rule for T <= 0.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "P0_Pa": 101325,
    "temperature_K": 288.15,
    "altitude_m": 0
  },
  "expected_outputs": {
    "P_Pa": 101325
  },
  "working": "1. Exponent = -(Mgh)/(RT) = -(0.0289644 × 9.80665 × 0)/(8.314462618 × 288.15) = 0.\n2. exp(0) = 1.\n3. P = 101325 × 1 = 101325 Pa."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`