How to calculate roof pitch, with the pitch factor table
Rise over run, the x/12 notation, the conversions to degrees and percent, a pitch factor table from 1/12 to 18/12, four ways to measure on site, and a worked area example.
To calculate roof pitch, measure how many inches the roof rises over 12 inches of horizontal run. That number over 12 is the pitch: a roof that climbs 7 inches in 12 is a 7/12. From there, angle = atan(rise ÷ 12), percent = rise ÷ 12 × 100, and the pitch factor that turns plan area into true area is √(1 + (rise ÷ 12)²).
The rest of this guide is the math, a full table from 1/12 to 18/12, the ways to take the reading, and what a wrong pitch does to your squares.
Rise over run and the x/12 notation
Pitch is a ratio. Rise is the vertical climb, run is the horizontal distance it climbs over. North American roofers fix the run at 12 inches and state the rise against it, so you write 4/12, 4:12 or "a 4 in 12" and everyone on the crew means the same plane.
Fixing the run at 12 is what makes the number usable on site. You don't need to measure a whole rafter. Any 12 inches of level run, anywhere on the plane, gives you the rise directly in inches. Half-inch readings are normal on older framing: 8.5/12 is a real pitch, not a rounding error.
If you measured over a different run, scale it back to 12: pitch = rise ÷ run × 12. A rise of 15 inches over a run of 24 inches is 15 ÷ 24 × 12 = 7.5, so 7.5/12.
Metric readers: rise:12 is a North American notation; most other markets state roof slope in degrees, and the formulas below convert either way.
Converting between degrees, rise:12 and percent
Three notations describe the same slope, and you'll meet all three. A phone inclinometer reads in degrees, a level and tape give you rise:12, and engineered drawings for low-slope work often show percent. The formulas:
- rise:12 to degrees: angle = atan(rise ÷ 12)
- degrees to rise:12: rise = tan(angle) × 12
- rise:12 to percent: percent = rise ÷ 12 × 100
- percent to rise:12: rise = percent ÷ 100 × 12
Set your calculator to degrees, not radians, before you run atan or tan. That one setting is behind most "the math doesn't work" moments.
Worked conversion 1: 7/12 to degrees and percent
Angle = atan(7 ÷ 12) = atan(0.583) = 30.3°. Percent = 7 ÷ 12 × 100 = 58.3%. A 7/12 roof is a 30.3° roof with a 58.3% slope.
Worked conversion 2: a 22° phone reading to rise:12
Rise = tan(22°) × 12 = 0.404 × 12 = 4.8. That's 4.8/12, so call it 5/12. Check it against the table: 5/12 is 22.6°, and a phone laid on granules can easily be half a degree off.
Worked conversion 3: a 30% slope on a drawing to rise:12 and degrees
Rise = 30 ÷ 100 × 12 = 3.6, so 3.6/12. Angle = atan(0.30) = 16.7°. Between a 3/12 and a 4/12, closer to 4.
The pitch factor formula
Satellite imagery, a site plan or a tape run around the eaves gives you plan area: the roof's footprint seen from straight above. Shingles cover the sloped surface, which is larger. The pitch factor is the ratio between the two.
Pitch factor = √(1 + (rise ÷ 12)²)
It comes straight from Pythagoras. Over 12 inches of run, a 6/12 rafter climbs 6 inches, so the sloped length is √(12² + 6²) = √180 = 13.416 inches. Divide by the 12-inch run and you get 1.118. Every square foot of plan area on a 6/12 plane is 1.118 square feet of roof.
True area = plan area × pitch factor. The same factor converts a rake's horizontal run into its sloped length.
The pitch factor table, 1/12 to 18/12
Every value below is computed from the formulas above: angle and percent rounded to one decimal, the factor to three.
| Pitch | Angle | Percent | Pitch factor |
|---|---|---|---|
| 1/12 | 4.8° | 8.3% | 1.003 |
| 2/12 | 9.5° | 16.7% | 1.014 |
| 3/12 | 14.0° | 25.0% | 1.031 |
| 4/12 | 18.4° | 33.3% | 1.054 |
| 5/12 | 22.6° | 41.7% | 1.083 |
| 6/12 | 26.6° | 50.0% | 1.118 |
| 7/12 | 30.3° | 58.3% | 1.158 |
| 8/12 | 33.7° | 66.7% | 1.202 |
| 9/12 | 36.9° | 75.0% | 1.250 |
| 10/12 | 39.8° | 83.3% | 1.302 |
| 11/12 | 42.5° | 91.7% | 1.357 |
| 12/12 | 45.0° | 100.0% | 1.414 |
| 13/12 | 47.3° | 108.3% | 1.474 |
| 14/12 | 49.4° | 116.7% | 1.537 |
| 15/12 | 51.3° | 125.0% | 1.601 |
| 16/12 | 53.1° | 133.3% | 1.667 |
| 17/12 | 54.8° | 141.7% | 1.734 |
| 18/12 | 56.3° | 150.0% | 1.803 |
Two things stand out. The factor barely moves at the low end (a 2/12 adds 1.4%), and it climbs fast past 12/12, where every extra inch of rise adds six to seven points. On a steep roof, a one-step misread costs more than it does on a ranch.
Measuring pitch on site
Any of these gives you a reading you can trust. Take it on the plane you're pricing, and take a second reading somewhere else on the same plane if the framing looks tired.
Level and tape on the rake
From a ladder at the gable end, hold a level against the rake board with one end touching it and the bubble centred. Mark 12 inches along the level from the contact point, then measure plumb from that mark to the rake board. The distance in inches is the rise per 12. A 24-inch level makes this easier than a torpedo.
Level and tape on the roof surface
On the roof, set one end of the level on the shingles, pointing up-slope, and lift the other end until the bubble is centred. Measure 12 inches along the level from the touching end, then measure plumb from that mark down to the roof. Do it across a few courses rather than on a raised tab or a lap; one high shingle edge throws the reading.
From the attic on a rafter
Hold the level against the underside of a rafter, bubble centred, and measure 12 inches out from the contact point. Measure plumb from the mark up to the rafter. On a truss roof, measure the top chord, never the bottom chord, which is flat or set at a different slope on a scissor truss.
Phone inclinometer
Most phones have a level or measure app that reads an angle. Lay the phone on a straight board or the level itself rather than directly on granules, read the angle in degrees, and convert with rise = tan(angle) × 12 or the table. Check the phone on a surface you know is level first; a case with a lip can add a degree.
A rafter square or speed square with a pitch scale works too, if you're used to reading one.
Measuring pitch from the street or your desk
When you can't get on the roof before you quote, read the pitch from the side. Satellite imagery shows the footprint, not the rise, so overhead images won't give you a number. Our free roof pitch finder lays pitch lines over Street View so you can match one to a gable rake from your desk; a square-on photo of the gable end works the same way if you measure rise and run on screen and apply rise ÷ run × 12. Finding roof pitch from satellite imagery and Street View covers the method step by step, including the angles that fool you.
Low-slope, standard and steep
These are general trade bands, not code definitions; your local code and the manufacturer's instructions decide what goes on a given slope.
| Band | Typical range | What it usually means on the job |
|---|---|---|
| Low-slope | Below 4/12 (under 2/12 is treated as flat work) | Membrane or roll roofing at the bottom; shingles near the top only with the extra underlayment the wrapper calls for |
| Standard | 4/12 to 8/12 | Walkable, shingle territory, normal production |
| Steep | Above 8/12 | Roof jacks, harnesses, slower tear-off and install, usually a steep charge |
Read the shingle wrapper for the minimum slope and the underlayment it requires at the low end. That's where warranty questions start.
Applying pitch to area: a worked example
Take a 50 × 26 ft ranch with a simple gable roof at 6/12 and a 1 ft overhang all round. The roof outline at the drip edge is 52 × 28 ft.
- Plan area: 52 × 28 = 1,456 sq ft.
- Pitch factor at 6/12: 1.118.
- True area: 1,456 × 1.118 = 1,628 sq ft.
- Squares: 1,628 ÷ 100 = 16.3 squares, before waste.
The rakes move with the same factor. Each rake covers half the 28 ft depth, so 14 ft of run: 14 × 1.118 = 15.7 ft of sloped length. Four rakes come to 62.6 ft of drip edge, not the 56 ft you'd get from the plan view. The eaves and the ridge are level, so they stay at 52 ft each.
Now misread it as 4/12: 1,456 × 1.054 = 1,535 sq ft, or 15.4 squares. That's 93 sq ft short, close to a square of material, before you've applied waste. For the waste step itself, roofing waste factor by roof type has the ranges.
Why per-facet pitch matters
One pitch for the whole roof only works when the whole roof shares it. Picture the same ranch with a 24 × 22 ft attached garage at 4/12, while the main roof is 9/12. The garage is 528 sq ft of plan area.
- Garage at its real 4/12: 528 × 1.054 = 557 sq ft.
- Garage priced at the main roof's 9/12: 528 × 1.250 = 660 sq ft.
That's 103 sq ft, about a square, from one assumption. Porches, dormers, additions and shed roofs over a back door all tend to carry their own pitch. Measure each plane, pitch each facet, then add them up. If you measure on satellite imagery in RoofStruct, you set the pitch per facet, and a facet left without one is counted flat until you fix it. How to measure a roof from satellite imagery walks through the tracing and the split. RoofStruct offers free, unlimited self-serve measuring and PDF reports, no card.
Where you trip
- Calculator in radians. atan(0.5) in radians is 0.46, not 26.6. Switch to degrees.
- Pitch factor on hips and valleys. They run diagonally across the plan, so the common factor undercounts them. When both adjoining planes share a pitch, hip or valley length = common run × √(2 + (rise ÷ 12)²). At 6/12 that's 1.5 per foot of common run, not 1.118.
- Pitch factor on eaves and ridges. Both are level. Leave them at plan length.
- Measuring the truss bottom chord. It's the ceiling, not the roof.
- One reading on a sagging plane. A dip mid-span reads flatter than the framing was built. Take readings near both ends.
- Rounding before you multiply. Round the pitch to the nearest half inch if you like, but carry the factor to three decimals until the final squares.
FAQ
What is a 6/12 roof pitch in degrees?
26.6°. Angle = atan(6 ÷ 12) = atan(0.5) = 26.6°. It's also a 50% slope with a pitch factor of 1.118.
How do I convert degrees to roof pitch?
Multiply the tangent of the angle by 12. A 35° reading is tan(35°) × 12 = 0.700 × 12 = 8.4, so between 8/12 and 8.5/12. Round to the nearest half inch and check it against the table.
What is the pitch factor for a 4/12 roof?
1.054. √(1 + (4 ÷ 12)²) = √1.111 = 1.054. Multiply plan area by it: 1,000 sq ft of plan area on a 4/12 is 1,054 sq ft of roof.
Is roof pitch the same as roof slope?
In everyday trade use, yes: both mean rise over 12 inches of run. Strictly, older carpentry texts define pitch as rise over the full span, so a 6/12 slope is a "1/4 pitch" in that system. If a set of old plans gives a fraction without the 12, check which one it means.
Do I apply the pitch factor to every line on the roof?
No. It applies to area and to rakes, which climb the slope along the common run. Eaves and ridges are level and stay at plan length. Hips and valleys need their own factor, √(2 + (rise ÷ 12)²) per foot of common run when both planes share a pitch.