How to use the roof pitch calculator
Pick what you already know: the rise per 12 inches (the roofer's pitch, such as 6:12), the angle in degrees, the percent grade, a rise and run you measured, or how many feet of run it takes to climb one. Type it, and the page fills in all the others. The drawing shows a gable end with the rafter, the rise, the run and the angle, and it moves as you change the number.
Rafters and roof area turns a pitch and a building size into a rafter length and a roof surface area. Measure your roof gives three ways to find the pitch of a roof you already have. The chart lists the common pitches from 1:12 to 18:12. The Imperial | Metric switch changes lengths, the chart and the quick picks.
How roof pitch is figured
rise per 12 = 12 × slope · degrees = arctan(slope) · percent = 100 × slope
slope multiplier = √(1 + slope²) · rafter length = run × multiplier
A 6:12 roof rises 6 inches for every 12 inches of run. Its slope is 0.5, which is 26.57 degrees, 50 percent, or 1 in 2. The slope multiplier is 1.118, so a rafter over a 12 foot run is 12 × 1.118 = 13.416 feet, which is 13 ft 5 in to the nearest sixteenth of an inch.
Plain numbers and fractions you type, such as 7 1/2, are kept as exact fractions, so 6 over 12 prints as 6:12 and not 5.9999. Degrees and the multiplier need an arctangent and a square root, so they are shown to two and four decimal places.
Pitch, degrees, percent and ratio
| Pitch | Degrees | Percent | Multiplier |
|---|---|---|---|
| 3:12 | 14.04° | 25% | 1.0308 |
| 4:12 | 18.43° | 33.33% | 1.0541 |
| 6:12 | 26.57° | 50% | 1.118 |
| 8:12 | 33.69° | 66.67% | 1.2019 |
| 12:12 | 45° | 100% | 1.4142 |
Percent is the same slope times 100, so 100 percent is 45 degrees, not 90. Where roofs are described in degrees, the round numbers are easier to read. A 30 degree roof is 57.7 percent, which is 577 millimeters of rise for every meter of run, and its multiplier is 1.155.
The slope multiplier, rafters and roof area
The multiplier is how much longer the sloped side is than the flat distance under it. It turns a run into a rafter length, and a flat plan area into a roof surface area. A building 30 feet wide has a 15 foot run on each side, and at 6:12 each rafter is about 16.77 feet along the slope. A 1,500 square foot footprint at 6:12 has about 1,677 square feet of roof, or 16.8 roofing squares. A roofing square is 100 square feet.
That area is for a plain gable roof measured over the overhangs you include. It leaves out dormers, valleys, hips and waste. Shingles overlap, so a supplier's coverage numbers, not this page, decide what to order.
Measuring the pitch of a roof you have
Level and tape, from the attic. Hold a level flat with one end touching the underside of a rafter. At the 12 inch mark on the level, measure straight up to the rafter. A gap of 5 inches is a 5:12 roof, or 22.62 degrees.
Gable end, from the ground. Measure the width across the gable wall and the height from the top of the wall to the peak. A wall 30 feet wide with a peak 10 feet above the wall top has a 15 foot run and a 10 foot rise: 10 ÷ 15 gives 8:12. A laser measure, a long tape on a pole, or a straight-on photo scaled to a known width can give the heights.
Phone or angle finder. Lay it flat on a rafter or a straightedge and read the degrees. The page turns it into a pitch. If two methods give different pitches, trust the level and tape.
Code, minimums and what this page does not do
Roof coverings have minimum slopes. City building guides that summarize IRC R905.2 allow asphalt shingles on 2:12 and steeper, with double underlayment from 2:12 up to under 4:12. The edition your building department uses can differ, and the shingle maker's instructions can be stricter, so check both. Metal, membrane and tile roofs have their own limits.
This page does not size rafters, trusses, ridge beams or anything else that carries load. Use the span tables in your local code or an engineer for that.
Where the numbers come from
Everything here is geometry: a right triangle with the run along the bottom, the rise standing on it and the rafter as the long side. The math was checked against a separate program using exact fractions and a 40 digit arctangent, on thousands of random pitches, and against edge cases such as zero, blank and absurdly steep input. A roofing square comes from a reference page, and the shingle minimums come from two city and university roofing guides; they are not the code text itself.
Tips and common mistakes
- The run is half the span for a gable roof, measured to the ridge line, not the whole width.
- A common mistake is to read 100 percent as 90 degrees. It is 45 degrees.
- Rise and run can be typed in different units, such as 4 ft and 120 in. The page converts them.
- Overhang changes the rafter length but not the pitch.
- A pitch on a hip or valley rafter is not the pitch of the roof planes.
Questions
What is a 6/12 roof pitch in degrees?
26.57 degrees. It is also 50 percent.
What is a 4/12 pitch in degrees?
18.43 degrees, or 33.33 percent.
How do I convert degrees to pitch?
Take the tangent of the angle and multiply by 12. For 30 degrees that is 6.93 in 12.
Is a 45 degree roof a 12/12?
Yes. At 12:12 the rise equals the run, which is 45 degrees and 100 percent.
Can I use metric?
Yes. Switch to Metric for lengths in meters and centimeters, a chart in 5 degree steps, and millimeters of rise per meter.
Is my measurement saved or sent anywhere?
No. The math runs in your browser. If you press Share on Facebook or copy the link, the page saves the pitch number and the unit system for 90 days so the link can show them. Nothing else is kept.