Source: https://guthlabs.ai/docs/instruments/roof-attic-insulation-r-value-calculator/mechanism/

instrument mechanism / verified-clean

# Roof/Attic Insulation R-Value Calculator mechanism

The inspectable method record for Roof/Attic Insulation R-Value Calculator, kept separate from implementation and qualification.

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

## Model scope

The summation algorithm is standard for nominal stacked insulation layers, but the instrument needs a fixed, versioned material table and a fixed DOE recommendation convention before its outputs can be treated as unambiguous. Vectors 1 and 2 land exactly on the commonly tabulated DOE target entries R-30 and R-60. The honest-label warning is appropriate and should explicitly state that local code, assembly design, installation quality, and air sealing may change the result.

- R_total = ΣR_layer is correct when every layer R-value uses the same units and represents a series layer in the heat-flow path.

- The material-thickness calculation must use a material-specific R-per-unit-thickness table; a single generic conversion is invalid.

- The recommendation comparison is underspecified because DOE guidance commonly gives ranges and differs by attic/ceiling versus roof assembly, climate-zone version, and whether existing insulation is included.

- The calculator should define gap as total R-value minus recommended R-value; a negative result indicates a shortfall.

- The formula excludes framing thermal bridges, air films, air leakage, moisture effects, compression, and parallel heat-flow paths, so it computes insulation-layer R-value rather than necessarily the whole roof assembly effective R-value.

## Units and conventions

- All reported R-values are in h·ft²·°F/Btu, conventionally written as R-value.

- Thickness is explicitly supplied in inches or millimetres; millimetres are converted using 25.4 mm = 1 in.

- Material table values are assumed to be nominal R-value per inch at the stated material condition; loose-fill density, compression, temperature, and installation quality are not modeled.

- The test vectors use a selected DOE/ENERGY STAR attic-target convention: climate zone 1 → R-30, zone 2 → R-49, and zone 4 → R-60.

- The recommended target is treated as a single target, not as the midpoint or lower/upper endpoint of a published range.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "layers": [
      {
        "material": "fiberglass batt",
        "thickness": 9.375,
        "thickness_unit": "in"
      }
    ],
    "climate_zone": 1
  },
  "expected_outputs": {
    "total_R_value_h_ft2_F_per_Btu": 30,
    "recommended_R_value_h_ft2_F_per_Btu": 30,
    "gap_h_ft2_F_per_Btu": 0
  },
  "reference_data": {
    "material_rows": [
      {
        "material": "fiberglass batt",
        "R_per_in": 3.2,
        "source_convention": "widely tabulated standard value"
      }
    ],
    "climate_zone_row": {
      "climate_zone": 1,
      "recommended_attic_R": 30,
      "source_convention": "DOE/ENERGY STAR attic insulation target convention, 2023 guidance"
    }
  },
  "working": "Fiberglass contribution = 9.375 in × 3.2 R/in = 30.0 R. Total R = 30.0 R. Gap = total − target = 30.0 − 30.0 = 0.0 R."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

An extreme but numerically representable thickness causes the layer multiplication to overflow ordinary floating-point arithmetic. An implementation that accepts it without range validation can return Infinity or a non-finite gap instead of rejecting the input.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/roof-attic-insulation-r-value-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/roof-attic-insulation-r-value-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/roof-attic-insulation-r-value-calculator/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`