Roof pitch calculator: angle, roof squares and rafter length
Enter a pitch any way you have it. Get degrees, percent, the slope multiplier, roof squares and rafter length, with the math shown.
How it works
Enter the pitch as rise and run, x:12, degrees, percent, rise and span, or a traditional fraction like 1/4. The calculator turns it into one slope ratio and uses it for the roof area and the rafter. Each section updates as you type and shows its math with your numbers in "Show your work".
How we calculate it
These are the lines in the "Show your work" panels, in the same order. s is the slope ratio, rise ÷ run, with both in the same unit.
Pitch
- Slope ratio: s = x ÷ 12. From other inputs: rise ÷ run, 2 × rise ÷ span, tan(angle), percent ÷ 100, or 2 × traditional pitch.
- Pitch: 12 × s, shown as x:12. At 6:12, s = 0.5000.
- Angle: θ = atan(s). atan(0.5) = 26.57°.
- Grade: 100 × s = 50.0 %.
- Multiplier: m = √(1 + s²) = √1.25 = 1.1180. This is the rafter length per unit of run.
- Per foot: 12 in × m = 13.416 in of rafter per 12 in of run.
- Traditional: rise ÷ span = s ÷ 2 = 0.25 = 1/4, on a symmetric gable.
Roof area
- Plan area: hip (L + 2 × overhang) × (W + 2 × overhang); gable (L + 2 × rake) × (W + 2 × eave). Overhangs are measured level and widen both sides, corners included. Or enter a plan area you already know.
- Sloped area: plan area × m.
- Squares: sloped ft² ÷ 100. One roofing square is 100 ft² of roof surface (ASTM D1079). Metric areas convert at 1 m² = 10.7639104 ft².
- With waste: sloped area × (1 + waste % ÷ 100). The 10 % default is a rule of thumb.
- This assumes every roof plane has the same pitch. Measure dormers and other pitches separately.
Rafter length
- Run: (span − ridge thickness) ÷ 2.
- Line length: run × m, from the wall plate to the ridge.
- Tail: horizontal overhang × m.
- Total: line length + tail, before cuts.
- Total rise: run × s.
- Plumb cut = θ. Seat cut = 90° − θ.
- Birdsmouth, ridge plumb-cut allowance and fascia are not included.
Feet and inches are rounded once, on the total, to the nearest 1/16 in. The math uses unrounded values, so the last digit may differ from multiplying the rounded numbers shown. Minimum slopes for the material you pick come from the 2024 IRC, Section R905. Sources: right-triangle trigonometry; traditional pitch from InterNACHI, "Measuring Roof Slope and Pitch"; roofing square from ASTM D1079; minimum slopes from the 2024 IRC, Chapter 9.
Roof pitch chart
| Pitch | Degrees | Percent | Multiplier | Traditional |
|---|---|---|---|---|
| 1:12 | 4.76° | 8.3 % | 1.0035 | 1/24 |
| 2:12 | 9.46° | 16.7 % | 1.0138 | 1/12 |
| 3:12 | 14.04° | 25.0 % | 1.0308 | 1/8 |
| 4:12 | 18.43° | 33.3 % | 1.0541 | 1/6 |
| 5:12 | 22.62° | 41.7 % | 1.0833 | 5/24 |
| 6:12 | 26.57° | 50.0 % | 1.1180 | 1/4 |
| 7:12 | 30.26° | 58.3 % | 1.1577 | 7/24 |
| 8:12 | 33.69° | 66.7 % | 1.2019 | 1/3 |
| 9:12 | 36.87° | 75.0 % | 1.2500 | 3/8 |
| 10:12 | 39.81° | 83.3 % | 1.3017 | 5/12 |
| 11:12 | 42.51° | 91.7 % | 1.3566 | 11/24 |
| 12:12 | 45.00° | 100.0 % | 1.4142 | 1/2 |
| 13:12 | 47.29° | 108.3 % | 1.4743 | 13/24 |
| 14:12 | 49.40° | 116.7 % | 1.5366 | 7/12 |
| 15:12 | 51.34° | 125.0 % | 1.6008 | 5/8 |
| 16:12 | 53.13° | 133.3 % | 1.6667 | 2/3 |
| 17:12 | 54.78° | 141.7 % | 1.7341 | 17/24 |
| 18:12 | 56.31° | 150.0 % | 1.8028 | 3/4 |
| 19:12 | 57.72° | 158.3 % | 1.8727 | 19/24 |
| 20:12 | 59.04° | 166.7 % | 1.9437 | 5/6 |
| 21:12 | 60.26° | 175.0 % | 2.0156 | 7/8 |
| 22:12 | 61.39° | 183.3 % | 2.0883 | 11/12 |
| 23:12 | 62.45° | 191.7 % | 2.1619 | 23/24 |
| 24:12 | 63.43° | 200.0 % | 2.2361 | 1 |
Generated from the same formulas as the calculator. The row for your pitch is highlighted.
How to measure roof pitch
In the attic, hold a 12 in level against a rafter and measure the drop from the end of the level to the rafter. That number is x in x:12. Or lay a phone inclinometer on the roof surface and enter the reading in degrees.
Questions
How do I find my roof pitch from the ground or the attic?
In the attic, hold a 12 in level against the underside of a rafter, with one end touching it. Measure straight down from the other end of the level to the rafter. That drop in inches is the x in x:12. On the roof, lay a phone inclinometer on the surface and enter the reading in degrees. Counting siding courses on the gable end is only a rough check.
Is 3/12 too low for shingles?
Not under the code. The 2024 IRC (R905.2.2) allows asphalt shingles down to 2:12. From 2:12 up to, but not including, 4:12, it requires double underlayment (R905.1.1). NRCA recommends 3:12 as a practical minimum, as quoted in JLC. The shingle maker's installation instructions and your local code also apply. Pick a material in the calculator to see its minimum.
What is the difference between pitch and slope? Is 1/4 pitch the same as 6:12?
Yes, on a symmetric gable. Slope is rise ÷ run, written like 6:12. Traditional pitch is rise ÷ span. The span is twice the run, so 6 in of rise per 12 in of run is 6 ÷ 24 = 1/4 pitch (InterNACHI). Choose "Traditional pitch" in the calculator to convert either way.
How many squares is my roof, and does my quote look right?
A square is 100 ft² of roof surface. Take the footprint including overhangs, multiply by the slope multiplier, and divide by 100. Then add waste, often 10-15 %. A 50 × 30 ft hip-roof ranch at 6:12 with 1 ft overhangs is 52 × 32 × 1.1180 = 1,860 ft². That is 18.6 squares, or about 20.5 with 10 % waste. If a quote is far above your number, ask what it includes, such as sheds, porches or a higher waste factor.
How long is a rafter for a 24 ft span at 6:12?
With a 1-1/2 in ridge board and a 1 ft 4 in overhang, the run is (288 − 1.5) ÷ 2 = 143.25 in. The line length is 143.25 × 1.118034 = 160.158 in, or 13' 4-3/16". The tail is 16 × 1.118034 = 17.889 in, or 1' 5-7/8", so the total is 14' 10-1/16" before cuts. Birdsmouth and ridge plumb-cut allowances are not included. The calculator does not size rafters or check spans.