Tapered Roof Insulation Average Thickness and Quantity
Average thickness, board-feet, and average R for a slope-to-drain tapered layout.
Example
You enter
- Taper run length to drain (ft) 40
- Taper slope (in/ft) 0.25
- Thickness at the low (start) edge (in) 0.5
- Field area (ft²) 2000
- Insulation R per inch 5.7
You get
- Avg thk (in) 5.5
- Board feet 11000
- Average R the taper delivers 31.35
Checked against published worked examples from: Johns Manville.
Details, formula, and sources
Scopeavg = start + slope x run / 2; board-feet = area x avg; avg R = avg x R-per-inch. A 40 ft run at 1/4 in per foot off a 1/2 in start averages 5.5 in, so a 2,000 sf field is 11,000 board-feet at ~R-31; a shallower 1/8 in/ft taper averages 3.0 in - 6,000 bf and only R-17. The slope has to serve both drainage (>= 1/4 in/ft) and the code R. Distinct from a flat assembly R-value.
Formula or tableavg_thk_in = start_thk_in + slope_in_per_ft x run_ft / 2; board_feet = area_sf x avg_thk_in; avg_r = avg_thk_in x r_per_in.
Source and editionTapered-insulation identity by name (average of a linear taper; board-feet and average R from the average thickness); first-principles arithmetic.
Free accessThe average-thickness arithmetic is public first-principles; the taper layout and R-per-inch come from the manufacturer's design.
What governsEstimate. AHJ and licensed professional govern.
API field namesrun_ft, slope_in_per_ft, start_thk_in, area_sf, r_per_in, avg_thk_in, board_feet, avg_r
- Taper layout slope (>= 1/4 in/ft for drainage) and start thickness from the manufacturer's designinsulation manufacturer
- R per inch the insulation's R-value per inch (~5.7 for polyiso, aged)insulation manufacturer