Convert rise and run into pitch, multiplier, angle and slope percentage — and the sloped area of any footprint.
Roof Pitch Calculator
Inputs
Pitch is conventionally expressed per 12 inches of run.
Results
Pitch
6.00/12
multiplier = √(rise² + run²) ÷ run; angle = arctan(rise ÷ run)
Calculated with BuildCalculators.com
Roof pitch is the ratio of vertical rise to horizontal run, conventionally expressed per 12 inches of run — a 6/12 roof rises 6 inches over every 12 inches across. It determines the roof area, which materials are permitted, how hard the roof is to walk, and therefore what the labour costs.
From that one ratio you get the multiplier, the angle in degrees and the slope as a percentage. Different trades ask for different ones.
pitch = (rise ÷ run) × 12, expressed as x/12m = √(rise² + run²) ÷ runθ = arctan(rise ÷ run)slope % = (rise ÷ run) × 100area = footprint × mFrom inside the loft, hold a spirit level horizontally against a rafter. Mark 12 inches along the level, then measure vertically from that mark up to the rafter. That measurement is the rise, and you have the pitch without going near the roof surface.
Roofers say 6/12. Engineers say 26.6 degrees. Drainage specifications say 50% slope. All three describe an identical roof — they are just different expressions of rise over run, and this calculator gives all of them at once.
Water moves off a steep roof fast and lingers on a shallow one. Asphalt shingles need at least 2/12 to shed water reliably and 4/12 for a standard installation; below that, water can drive back under the courses regardless of workmanship.
Up to about 6/12 a roofer can walk the surface. From 7/12 to 9/12 it gets difficult, and above 9/12 it needs roof jacks, staging and harnesses. That is why two roofs of identical area can differ substantially in quoted labour.
The most common residential pitch in the US.
6/12 — multiplier 1.1180
Walkable, suits every common roofing material, and adds 11.8% to the footprint area.
A low-pitch roof, common on garages and extensions.
4/12 — multiplier 1.0541
The minimum for a standard shingle installation. Below this, doubled underlayment is required.
A 45 degree roof — steep, common on older and gothic-styled houses.
12/12 — multiplier 1.4142
The roof is 41.4% larger than its footprint, and needs full staging. Both material and labour rise sharply.
| Pitch | Multiplier | Angle | Slope % | Walkable |
|---|---|---|---|---|
| 1/12 | 1.0035 | 4.8° | 8.3% | Yes |
| 2/12 | 1.0138 | 9.5° | 16.7% | Yes |
| 3/12 | 1.0308 | 14.0° | 25.0% | Yes |
| 4/12 | 1.0541 | 18.4° | 33.3% | Yes |
| 6/12 | 1.1180 | 26.6° | 50.0% | Yes |
| 8/12 | 1.2019 | 33.7° | 66.7% | With care |
| 9/12 | 1.2500 | 36.9° | 75.0% | Staging |
| 10/12 | 1.3017 | 39.8° | 83.3% | Staging |
| 12/12 | 1.4142 | 45.0° | 100% | Staging |
| 16/12 | 1.6667 | 53.1° | 133% | Staging |
| Material | Minimum pitch | Notes |
|---|---|---|
| Asphalt shingles | 2/12 | Doubled underlayment below 4/12 |
| Wood shakes | 4/12 | Steeper is better for longevity |
| Standing seam metal | 1/12 | Some systems go lower |
| Corrugated metal | 3/12 | |
| Clay or concrete tile | 2.5/12 | Underlayment critical |
| Slate | 4/12 | |
| EPDM or TPO membrane | 0.25/12 | The low-slope solution |
Pitch is not a cost in itself, but it drives two that matter: how much material the roof needs, and how difficult it is to work on.
Going from 4/12 to 10/12 on the same footprint adds 23% to the roof area, and therefore 23% to every material priced by the square. On a 1,500 ft² house that is roughly three and a half extra squares.
Roofs above 9/12 typically carry a steep-pitch surcharge of 20–50% on labour, because the crew needs roof jacks, staging and fall protection, and simply moves more slowly.
Below 2/12 the saving in area reverses: the roof needs a membrane system rather than shingles, and membrane costs more per square than asphalt. The cheapest roof to cover is a moderate pitch, not a flat one.
A 6/12 pitch is a 50% slope, not a 6% one. Drainage and civil documents usually specify percentage; roofers always say x/12. Mixing them up is a factor-of-eight error.
The rafter length is the hypotenuse, not the rise. Measuring along it and treating that as rise gives a pitch that is too shallow. Rise is always measured vertically.
Additions, dormers and porch roofs frequently differ from the main roof. Each plane needs its own multiplier, worked out and added separately.
Installing shingles below 2/12 voids most manufacturer warranties and will leak eventually regardless of how well it is done. Pitch determines what is permitted, not just what is preferred.
From inside the loft, hold a spirit level horizontally against a rafter, mark 12 inches along the level, then measure vertically from that mark to the rafter. That vertical measurement is the rise, giving you rise/12.
26.6 degrees. The conversion is arctan(rise ÷ run) — arctan(6 ÷ 12) = 26.565°.
They describe the same thing differently. A 6/12 pitch is a 50% slope, because the rise is half the run. Roofers use x/12; drainage and civil documents use percentage.
2/12 is the absolute minimum for asphalt shingles, and manufacturers require doubled underlayment between 2/12 and 4/12. Below 2/12 the roof needs a membrane system instead.
Up to about 6/12 most roofers walk comfortably. From 7/12 to 9/12 it gets difficult, and above 9/12 needs roof jacks, staging and fall protection — which is why steep roofs carry a labour surcharge.
A 4/12 roof is 5.4% larger than its footprint; 6/12 is 11.8% larger; 12/12 is 41.4% larger. On a 1,500 ft² footprint that is a difference of over five squares between 4/12 and 12/12.
Between 4/12 and 8/12 for US residential, with 6/12 the most common single value. It sheds water well, suits every standard material, and remains walkable.
Yes, and they frequently do. Porch roofs, dormers and additions often differ from the main roof. Each plane needs its own multiplier calculated separately.
Roof Replacement Cost by Material — Installed prices run from $350 a square for three-tab asphalt to $3,000 for slate — but ranked by cost per year of roof life, the order changes. Both rankings, with the arithmetic shown.
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This calculator uses published constants from named industry sources, each asserted in an automated test that runs on every build. The formula is printed with the result above, and any correction we make is logged on the changelog.
It is a planning estimate. It does not replace an engineer, a site visit or a written quote — confirm quantities with your supplier before ordering.