Roof Underlay & Breather Membrane: Slope Length, Courses, Laps & Rolls for a Pitched Roof

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 8 inputs are read from the form on every keystroke: Roof Length along the Eaves, Horizontal Run, Eaves to Ridge, Roof Pitch, Roof Slopes of This Size, Roll Width, Roll Length, Head Lap between Courses and Allowance for End Laps, Valleys & Cutting.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Rolls to Order together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Slope Length, Eaves to Ridge, Courses per Slope, Membrane Length Laid, Membrane Length with Allowance, True Roof Area, Plan Area (for Comparison), Membrane Area Laid and Membrane beyond the Roof Area (Laps & Top Course) — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

The plan says 80 m². The pitch makes it 98, and the laps and top course make the membrane 120.

How to use it

1. Work through the input groups in order — Roof and Membrane. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Rolls to Order in the dark results panel — that is the headline figure, expressed in rolls.
4. Check the supporting rows underneath (Slope Length, Eaves to Ridge, Courses per Slope, Membrane Length Laid, Membrane Length with Allowance, True Roof Area, Plan Area (for Comparison), Membrane Area Laid and Membrane beyond the Roof Area (Laps & Top Course)) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Rolls to Order before a trial is booked, so machine time and material in Nonwovens & Technical Textiles are committed against a calculated figure rather than an estimate.
• Costing and quotation — Rolls to Order is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Roof Length along the Eaves) shows how much of the gap in Rolls to Order each variable explains.
• Teaching and study — the accepted ranges bracket normal Nonwovens & Technical Textiles practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• Pitch, run, head lap and allowance are yours: the head lap and how a membrane is carried over the ridge or fixed at the eaves are the membrane maker's instructions and the local building rules, and the tool has no figure of its own for either. Courses run parallel to the eaves, the full roof length each; the top course is counted whole even where it overhangs the ridge. The allowance covers end laps where a course is longer than a roll, valleys, hips, openings and cutting, so a complex roof needs a larger figure or a slope-by-slope count. **This is a quantity take-off; it does not choose a membrane or check ventilation.**
• Every input is bounded to the range normal practice occupies (Roof Length along the Eaves 1 to 500 m, Horizontal Run, Eaves to Ridge 0.5 to 50 m and Roof Pitch 5 to 75 °, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Standards and further reading

• EN 13859-1, Flexible sheets for waterproofing, definitions and characteristics of underlays, Part 1: underlays for discontinuous roofing.
• The membrane maker's installation instructions, which set the head lap, end lap and fixing for the pitch.
• The local building regulations and roofing code of practice, which decide where a vapour-permeable underlay may be used and how the roof is ventilated.

Questions people ask