Roof Pitch Calculator

Two factors, one pitch

A common rafter is the hypotenuse over 12 in of run and the pitch of rise, so its length per foot of run is √(1 + (pitch ÷ 12)²). The worked roof at 6/12: factor 1.118, so a 12 ft run cuts a common rafter of 13.4164 ft rising 6 ft at 26.6°. A hip or valley rafter crosses the corner diagonally — 12√2 ≈ 16.97 in of plan run per 12 in of common run at the same rise — giving √(2 + (pitch ÷ 12)²): exactly 1.5 at 6/12, so the hip rafter runs 18 ft. Both factors are verified against published framing references (see the methodology page).

Pitch also stretches area: a 1,500 sq ft footprint at 6/12 carries 1,677.05 sq ft of actual surface — 16.77 roofing squares. Take the squares to the Roofing Shingle Calculator to turn them into bundles with waste applied.

The guide Roof pitch and the pitch factor derives both factors from a single foot of run, tabulates the surface a roof carries beyond its footprint at each pitch, and follows the squares through the shingle pipeline to whole bundles. Read it if the factor is new to you. The rest of this page explains what this calculator does with the numbers you give it, step by step, and how to read what comes back.

What the calculator computes, step by step

Every estimator on this site follows the five-stage pipeline documented on the methodology page: geometry, coverage, waste, package rounding, and a user-priced cost. This is one of the site's four trade-geometry tools, and it runs the first stage in full, takes one step into the second, and deliberately stops there. Nothing on this page is padded with a waste allowance, rounded up to a package, or priced; those stages belong to the Roofing Shingle Calculator, which takes the squares this page produces as its starting point.

1. Normalize the pitch. If the pitch field holds a number, that number is the pitch in inches of rise per 12 in of run, and the measured fields are ignored. Otherwise the engine's pitchFromRiseRun turns the measured pair into the same form with (rise ÷ run) × 12. Because pitch is a ratio, the pair can be in any unit — inches, feet, metres — as long as both numbers share it. A fractional result is an ordinary input, and the ceiling is 24 in of rise per 12: anything steeper is refused.
2. Settle the run. The length field is read as the horizontal run from the outside of the wall plate to the ridge centerline, or, if the selector says span, as the full building width, which the engine halves. Runs up to 500 ft are accepted. In metric mode the metres you type are divided by the exact 0.3048 m per foot before any of this runs.
3. Compute the two factors. The slope factor √(1 + (pitch ÷ 12)²) comes from the roofing engine's pitchFactor, the same function the shingle calculator calls, and the hip/valley factor √(2 + (pitch ÷ 12)²) from hipValleyFactor. Both are evaluated from the pitch every time; there is no stored table to go stale, which is why a pitch of 7.5/12 works as well as a whole one.
4. Scale the run. rafterCalc multiplies: common rafter = run × slope factor, hip or valley rafter = run × hip factor, and ridge rise = run × pitch ÷ 12. The roof angle, atan(pitch ÷ 12), is reported alongside as a readout — it depends on the pitch alone and never on the run.
5. Area and squares — the coverage step, as far as it goes. With a footprint entered, roofArea multiplies it by the slope factor to get the true sloped surface and divides that by the 100 sq ft roofing square. On a purchasing tool this is where a product's coverage would divide the quantity; here the divisor is a definition, and the pipeline hands off. Waste, the round-up to whole bundles, and a price you type all happen on the shingle calculator.

Why each input matters

Pitch drives both factors and the angle, and it is the only input that does. It is entered as inches of rise per 12 in of run, so 6 means a 6/12 roof; a decimal such as 7.5 is a 7.5/12 roof. Degrees are not a pitch, and the field cannot tell the difference — see the misreadings below.

Measured rise over run is the alternative for a roof whose pitch you do not know: two readings in the same unit, which the tool normalizes. The direct pitch field wins whenever it holds a value, so clear it before relying on the measured pair. The pair sets only the pitch; the length of the run is a separate entry.

The run-or-span selector and the length are the most consequential pair on the form. Every length the tool returns is the run multiplied by a factor, so the length scales the common rafter, the hip rafter, and the rise in exact proportion, and the selector decides whether the number you typed is halved first. A span of 32 ft and a run of 16 ft describe the same roof; a run of 32 ft describes one twice as large.

The footprint is optional and feeds only the area line. It is the horizontal outline of the roof as seen from above, overhangs included — not the floor area of the house and not a measurement taken along the slope. Leave it blank and the result stops at the rafters and the angle; fill it and the sloped area and the squares appear beneath them.

The units toggle changes what the fields expect and how the result is presented, not what is computed. In metric mode, metres are divided by 0.3048 and square metres by 0.09290304 — both exact definitions — before the engine sees them, and the rafter lengths and area are multiplied back for display. The squares line is unchanged, because a square is a fixed 100 sq ft unit in either system.

The figures this page relies on

• The slope factor, √(1 + (pitch ÷ 12)²) — arithmetic: Pythagoras on one foot of run, computed by the roofing engine each time it runs. The engine's own ceilings are a pitch of 24 in 12 and a run of 500 ft — practical limits, not specifications.
• The hip/valley unit run, 12√2 = 16.97 in per 12 in of common run — arithmetic: the diagonal of a 12 × 12 in square, which is why the factor is √(2 + (pitch ÷ 12)²). The engine's source notes check it against two published framing references: the Swanson Tool Co. Blue Book, which prints the hip and valley unit run as 17, and the roofobservations.com hip-and-valley derivation.
• The roofing square, 100 sq ft — a definition recorded in the site's materials data: an industry unit, not a measured value. Manufacturer spec sheets quote a product's actual coverage per square at or slightly under that figure (Owens Corning Guide Specifications, Section 07 31 13), so the product sheet is the last word on a tight order.
• Inches per foot, 12; metres per foot, 0.3048; square metres per square foot, 0.09290304 — exact definitions, used to form the unit run, to convert metric entries into the engine's feet, and to present metric results back.
• Coverage per bundle and waste — none on this page. The bundles-per-square figure (a manufacturer figure, adjustable in the form) and the roofing waste convention live on the shingle calculator, where the coverage, waste, and round-up stages run. This page holds no product figure and no allowance.

Pitch-angle chart (printable)

Every row is generated at build time by the same rafterCalc engine the form calls. The last column is the common factor scaled to a 10 ft run; scale it to your own run, or multiply the factor directly. The Print the pitch chart button strips the site chrome so the chart and any results on screen print on one sheet for the job box.

Worked examples

Every figure in this table was produced at build time by the same rafterCalc and roofArea functions the form calls. The inputs are chosen to exercise different parts of the form: a span rather than a run, a measured pitch, a low slope and a steep one, a roof with two planes meeting at one ridge, and a metric entry converted exactly before the engine ran, which is what the metric toggle does.

The worked roof. A 12 ft run at 6/12 is the hint under the form. The slope factor is 1.118, so the common rafter is 12 × 1.118 = 13.42 ft, the hip factor is exactly 1.5, so the hip or valley rafter is 18 ft, and the ridge sits 6 ft above the plate at 26.6°. The 1,500 sq ft footprint becomes 1,677.05 sq ft of surface, 16.77 squares — the figure to carry to the shingle calculator.

The span. A 32 ft wide building at 4/12, entered with the selector on span: the engine halves it to a 16 ft run. At this pitch the slope factor is only 1.0541, so the common rafter is 16.87 ft, the hip 23.25 ft, the rise 5.33 ft, and the angle 18.4°. The 1,800 sq ft footprint carries 1,897.37 sq ft, 18.97 squares — 5.4% more than the footprint, which is what a low pitch costs in shingles.

The measured pitch. A level laid on the rafter reads 5 of rise over 8 of run. The tool normalizes that to (5 ÷ 8) × 12 = 7.5/12, a fractional pitch no printed chart carries, and on a 14 ft run returns a slope factor of 1.1792, a common rafter of 16.51 ft, a hip of 21.65 ft, a rise of 8.75 ft, and an angle of 32°. No footprint was entered, so the result stops there and no area line appears.

The low-slope porch. 2/12 on an 18 ft run. The slope factor is 1.0138, barely above one, so the common rafter at 18.25 ft is only 0.25 ft longer than the run. The hip, at 25.63 ft, is not: at a low pitch the diagonal dominates the hip factor, which stays close to √2 (1.424). The rise is 3 ft, the angle 9.5°, and the 700 sq ft footprint carries 709.66 sq ft, 7.1 squares.

The steep roof. 10/12 on a 9 ft run. The slope factor is 1.3017: a common rafter of 11.72 ft, a hip of 14.77 ft, a rise of 7.5 ft, and an angle of 39.8°. The 1,100 sq ft footprint carries 1,431.88 sq ft, 14.32 squares. The same footprint at the porch pitch would carry 1,115.17 sq ft; the pitch alone adds 316.71 sq ft of surface to be covered.

Two planes, one ridge. A 40 ft long building whose ridge is off-centre: the front run is 12 ft at 8/12, and the rear run is 20 ft to the same ridge. The front plane returns a rise of 8 ft and a common rafter of 14.42 ft. The rear plane shares that rise, so its pitch is found with the measured fields — 8 over 20, which the tool normalizes to 4.8/12 — and its common rafter is 21.54 ft at 21.8°. Each plane gets its own footprint, run times ridge length with the overhangs left out to keep the arithmetic visible: 480 sq ft in front carries 576.89 sq ft, 800 sq ft behind carries 861.63 sq ft, and the roof totals 1,438.51 sq ft, 14.39 squares. There is no single-pitch shortcut: the whole 1,280 sq ft footprint at the front pitch gives 1,538.37 sq ft and at the rear pitch 1,378.6 sq ft, one high and one low.

The metric roof. In metric mode, a 3.5 m run at 7/12 reaches the engine as 11.4829 ft. The slope factor is 1.1577 — a pure ratio, the same in either system — and the common rafter is 13.29 ft, which the result shows as 4.052 m, with the hip at 5.354 m and the rise at 2.042 m. The 120 m² footprint is 1,291.67 sq ft; it carries 1,495.37 sq ft, presented back as 138.92 m², and 14.95 squares. The toggle changed what you typed and what was printed back; it never changed the path through the engine.

How to read the result

The headline line is Common rafter, in feet with the inches in brackets, or in metres in metric mode: the slope distance from the outside of the wall plate to the ridge centerline. Beneath it, Pitch N-in-12 repeats the pitch the engine actually used — the figure to check first when the measured fields were in play — with the slope factor and the roof angle beside it. Rise at the ridge is the vertical distance the ridge sits above the plate. Hip/valley factor carries the hip or valley rafter length. Sloped roof area appears only when a footprint was entered, and it is the line to carry forward: the squares are the shingle calculator's input. Read the pitch line to confirm the roof, the rafter lines to lay out stock, and the squares to size the order. The copy button places a short plain-text summary of the result on the clipboard, and the print button adds the chart.

Common misreadings

Degrees in the pitch field. The field wants inches per 12, and it reads whatever it is given as that. A roof you know to be about 20° entered as 20 becomes a 20/12 roof: the result reports 59°, a slope factor of 1.9437, and a 23.32 ft common rafter on a 12 ft run. Translate through the chart's angle column instead: 20° sits nearest the 4/12 row (18.4°).

Span entered as run. The 32 ft building above cuts a 16.87 ft common rafter. Type the same 32 with the selector still on run and every length doubles — a 33.73 ft rafter, a 46.49 ft hip, a 10.67 ft rise — while the angle stays at 18.4°, because the angle depends on the pitch alone. A rafter that looks far too long for the building with a plausible angle beside it usually means the selector.

Rise and run in different units. The measured pair is a ratio, and the engine cannot see units. An attic measurement of 4 ft of rise over 8 ft of run is a 6/12 roof, and its common rafter on that run is 8.94 ft. Type the rise in feet and the run in inches — 4 over 96 — and the pitch becomes 0.5/12, a nearly flat roof whose rafter is 8.01 ft. The slip in the other direction, 48 in of rise over 8 ft of run, is steeper than the 24-in-12 ceiling and is refused with the message "That rise over run is steeper than 24-in-12, the steepest supported pitch." — the one case the engine can catch.

Metric figures in the imperial fields. The metric roof above is a 3.5 m run with a 120 m² footprint. Type those numbers with the toggle still on Imperial and the engine sees a 3.5 ft run and a 120 sq ft footprint. The common rafter comes back as 4.05 ft — the same digits as the correct 4.052 m, because the factor is a unit-free ratio, so only the unit on the line gives it away. The squares line does not hide it: 1.39 squares instead of 14.95, because a square is a fixed number of square feet.

Sloped area entered as the footprint. The factor is applied once, to a horizontal measurement. A surface measured along the slope — the worked roof's 1,677.05 sq ft, say — belongs in the footprint field with a pitch of 0, whose factor is exactly 1: the area comes back unchanged at 1,677.05 sq ft. Fed in with the real pitch it is stretched a second time; the guide shows that doubling in numbers.

The rafter length as the board length. The figure is the slope distance to the ridge centerline. The ridge-board deduction, the birdsmouth, the overhang, and the tail cut are layout details the framer applies on top, so the stock is longer than the figure, and how much longer depends on choices this tool does not see.

Where the model stops

The engine applies one pitch to one run and returns the geometry of that plane. A roof whose planes differ is run once per plane, as the two-plane example shows; dormers and intersecting roofs are not laid out, rafters are not counted, and spacing is not modeled. The footprint is yours to measure, and the factor scales whatever you give it, so overhangs left out of the footprint stay out of the area. The lengths run to the ridge centerline with no deductions or additions. Nothing on this page carries a waste allowance, a round-up, or a price: those stages run on the Roofing Shingle Calculator, where the waste is a single flat percentage, as it is everywhere on the site. And, as the note under the form says, 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, and the dimensions you enter should already carry that review. The methodology page lists the simplifications every estimator shares.

Related tools and guides

The Roofing Shingle Calculator carries the squares from this page through waste to whole bundles at your price. The Stair Calculator applies the same rise-run trigonometry to stringers, the Feet & Inches Calculator chains the tape-measure math for layout, the Board Foot Calculator totals the rafter stock once you have chosen lengths, and the Construction Unit Converter moves any figure between feet and metres. For the factor derived step by step and followed through to bundles, read roof pitch and the pitch factor, or browse all guides.

Frequently asked questions

Roof figures are computed locally and never transmitted. Formula sources and the shared pipeline are documented on the methodology page.