Roof pitch and the pitch factor

A roof's pitch is the number that turns a floor plan into a roof. The footprint is measured flat, but shingles and rafters lie on the slope, which is always longer than the flat distance beneath it. The pitch factor closes that gap. This guide explains how the site's roofing tools read a pitch, how they compute the factor rather than look it up, and how it flows through the same pipeline as every other estimator here: geometry, coverage, waste, a round-up to whole packages, and a price you supply. Every figure below is produced at build time by the engines behind the Roof Pitch Calculator and the Roofing Shingle Calculator.

Pitch is rise per 12 inches of run

In US framing, pitch is written as inches of vertical rise for every 12 inches of horizontal run: a 6/12 roof climbs 6 in over each foot it travels inward, and a 12/12 roof climbs 12 in and sits at 45°. The run is the horizontal distance from the outside of the wall plate to the ridge centerline — half the span on a symmetrical gable. Because pitch is a ratio, any measured rise-over-run pair will do; the engine's pitchFromRiseRun normalizes it with (rise ÷ run) × 12. A rise of 4 over a run of 8 is a 6/12 roof, 20 in over 48 in is 5/12, and 1 ft over 6 ft is 2/12.

The one rule is that rise and run must share a unit. Enter that last roof as 12 in of rise over 6 ft of run and the ratio silently becomes 24/12 — the steepest pitch the engine accepts, and 12 times steeper than the roof you measured. The engine cannot see units; it sees two numbers. Measuring 12 in along a level and reading the vertical drop, as the tool page describes, gives a rise that is already in per-12 form. The roof angle is atan(rise ÷ 12): 26.6° at 6/12. It is a readout, not an input; degrees typed into the pitch field are read as inches per 12.

The pitch factor

The factor is Pythagoras on one foot of run. Over 12 in of run the roof rises rise inches, so the slope distance is √(12² + rise²), and dividing by 12 gives the length per unit of run: √(1 + (rise ÷ 12)²). The roofing engine's pitchFactor evaluates that expression every time it runs — there is no stored table. A flat roof gives exactly 1; 4/12 gives 1.0541; 6/12 gives 1.118; 12/12 gives 1.4142, which is √2; and 24/12, the steepest pitch the engine accepts, gives 2.2361. Fractional pitches are ordinary inputs: 5.5/12 gives 1.1, a value no printed chart carries.

The last column is the factor in plain language: a 6/12 roof carries about 11.8% more surface than its footprint, a 12/12 roof about 41.4% more.

From footprint to roof area and squares

roofArea multiplies the horizontal footprint by the factor and divides by the size of a square. The footprint is the horizontal outline of the roof including overhangs, not the heated floor area, and you supply it. A 1,500 sq ft footprint at 6/12 becomes 1,677.05 sq ft of roof surface, or 16.77 squares. A 2,000 sq ft footprint at 4/12 becomes 2,108.19 sq ft (21.08 squares), and a 900 sq ft footprint at 12/12 becomes 1,272.79 sq ft (12.73 squares).

A roofing square is 100 sq ft of roof surface — an industry definition, not a measured property of any product. Manufacturer spec sheets quote a product's actual per-square coverage as slightly under, or exactly, 100 sq ft depending on the product (Owens Corning Guide Specifications, Section 07 31 13, as cited in the site's materials data), so the product sheet is the last word on a tight order.

In metric mode the tool divides square metres by the exact 0.09290304 m² per sq ft, applies the factor in feet, and converts back. A 140 m² footprint is 1,506.95 sq ft; at 8/12 it carries 1,811.13 sq ft, which is 168.26 m² of roof surface and 18.11 squares. A square stays a 100 sq ft unit whichever system leads the display.

From squares to bundles

The shingle calculator's roofingEstimate runs the rest of the pipeline. Coverage: one bundle covers 100 ÷ bundles-per-square sq ft. The default is 3 bundles per square — the figure the Owens Corning guide specification gives for its three-tab and common architectural shingles, and the baseline GAF states for its architectural line. The same specification lists premium lines at 4 to 6 bundles per square, which is why the field is an adjustable default rather than a constant; the engine accepts up to 8. Waste: the area is multiplied by (1 + waste% ÷ 100) before any rounding, with a default of 10% — a trade convention, not a manufacturer figure — and 15% suggested for cut-up roofs with hips, valleys, and dormers. Round-up: the adjusted area is divided by per-bundle coverage and rounded up to a whole bundle. Price: a per-bundle price you enter, times the count; the site never supplies one.

The 1,500 sq ft footprint at 6/12 with 10% waste and 3 bundles per square: 16.77 squares become 18.45 after waste, and the order is 56 bundles (0.22 squares left over from the round-up). At 15% for a cut-up roof the same footprint needs 58 bundles. A 1,200 sq ft footprint at 10/12 on a product packed 4 bundles to the square covers 1,562.05 sq ft (15.62 squares) and needs 69 bundles. And the case the factor exists to prevent: run the 1,500 sq ft roof with the pitch left at zero and the engine orders 50 bundles, 6 short of the real 6/12 order. Where the coverage figures come from is covered in coverage figures and their sources, and the waste step in waste factors, explained.

The hip and valley factor

A hip rafter runs from the building corner up to the ridge, crossing the plan at 45°. In plan its run is the diagonal of a 12 × 12 in square, 12√2 = 16.97 in of hip run for every 12 in of common run — the 17 in unit run framing references print for hips and valleys. The hip climbs the same rise as the common rafter beside it, so per foot of common run its length is √((12√2)² + rise²) ÷ 12, which simplifies to √(2 + (rise ÷ 12)²). The engine's hipValleyFactor computes exactly that: 1.5 at 6/12, 1.453 at 4/12, 1.7321 at 12/12. A valley is the same geometry folded inward and uses the same factor. Both expressions are checked against published framing references — the Swanson Tool Co. Blue Book and the roofobservations.com hip-and-valley derivation — as the engine's source notes record.

Rafter lengths from run or span

rafterCalc takes a pitch and either the run or the full span (which it halves) and returns geometry to the ridge centerline: common rafter run × pitch factor, hip or valley rafter run × hip factor, ridge rise run × rise ÷ 12, and the angle. Runs up to 500 ft are accepted.

• A 12 ft run at 6/12: common rafter 13.42 ft, hip or valley rafter 18 ft, ridge rise 6 ft, angle 26.6°.
• A 28 ft span at 4/12: the engine halves it to a 14 ft run, giving a common rafter of 14.76 ft, a hip of 20.34 ft, and a rise of 4.67 ft.
• A 10 ft run at 12/12: the rise equals the run at 10 ft, the common rafter is 14.14 ft, and the hip is 17.32 ft.
• A 4 m run at 8/12, entered in metric: the tool divides by the exact 0.3048 m per ft to get 13.12 ft, runs the same arithmetic, and reports a common rafter of 4.807 m, a hip of 6.254 m, and a rise of 2.667 m.

These are lengths of lines, not of boards: the ridge-board deduction, birdsmouth, overhang, and tail cut are layout details the framer applies on top, so the stock you buy is longer than the figure. This site estimates geometry and material quantities only: it does not size rafters or any other member, determine spans, loads, or bearing, or rule on code compliance. Those judgments belong to a licensed engineer, architect, or code official.

Where the model stops

One pitch applies to one run: a roof with planes at different pitches is estimated one pitch at a time, adding the bundle counts. The footprint is yours to measure, and the factor scales whatever you give it — overhangs left out of the footprint stay out of the order. Waste is a single flat percentage, as it is everywhere on the site. Starter strips and ridge caps are separate products, not covered by field-shingle waste. Underlayment, fasteners, flashing, and ventilation are not modeled at all. And nothing here is structural: the rafter figures are slope geometry, and the engine carries no information about what any rafter is asked to hold.

Common misreadings

Degrees in the pitch field. The field wants inches per 12. A roof angle typed as a pitch is either rejected — anything over 24 — or accepted as a far steeper roof than you have. Use the angle column above to translate.

Span entered as run. Typing the full building width as the run doubles every length. The 28 ft span at 4/12 above cuts a 14.76 ft common rafter; the same number entered as a run returns 29.51 ft.

Sloped area entered as footprint. The factor is applied once, to a horizontal measurement. Feed the 1,677.05 sq ft sloped result back in as a footprint at 6/12 and the tool reports 1,875 sq ft — the factor applied twice, overstating the roof by 197.95 sq ft. If you measured the slope directly, enter that area with a pitch of zero, whose factor is exactly 1.

Frequently asked questions

The Roof Pitch Calculator returns rafter lengths, angle, area, and squares from a pitch and a run; the Roofing Shingle Calculator carries the squares through waste to whole bundles at your price. The siding calculator uses the same 100 sq ft square, and the stair calculator applies the same rise-over-run trigonometry to a flight of stairs. More concept guides are collected on the guides page.

Every roof figure on this page is computed at build time by the same engines that run the calculators, and nothing you enter in those tools leaves your browser. The full estimation pipeline is documented on the methodology page.