Roof Pitch Calculator
Pitch (x:12), angle, slope percent, rafter length, and multiplier from rise and run.
What it does
Roof pitch describes steepness, and carpenters, architects, and shingle manufacturers each quote it differently. Pitch is the classic rise-over-run ratio in x:12 form; slope is the same ratio as a percent; angle is the degrees from horizontal.
The 12 in convention means 7:12 reads as 7 inches of vertical rise per 12 inches of horizontal run, which is also a 58.3 % slope and a 30.26° angle. All three describe one triangle.
Framers carry the multiplier shortcut: multiply any horizontal run by 1.1577 and you have the rafter length, no trigonometry on the roof deck. It is the secant of the pitch angle, tabulated in old carpentry manuals such as Army FM 5-426.
Steepness also decides materials: standard asphalt shingles want 4:12 or steeper, 2:12 to 4:12 needs doubled underlayment and special detail, and below 2:12 roofs want membrane systems.
How to use
- Pick the length unit for the display.
- Enter the rise (vertical climb).
- Enter the run, 12 in the x:12 convention.
- Read the pitch ratio.
- Read the angle and slope percent.
- Read the multiplier and rafter length.
Formula
- rise
- Vertical climb over the run.
- run
- Horizontal distance; the convention uses 12.
- multiplier
- Turns any horizontal run into its rafter length.
The x:12 convention reports rise per 12 units of run, so 7:12 means 7 up for every 12 across. Angle and slope follow from the same ratio: slope is rise over run as a percent, angle is the arctangent. The multiplier equals sqrt(1 + (rise/run)^2). Rafter length from this tool is the exact hypotenuse; add for overhang and ridge allowance and subtract for the birdsmouth on site.
Worked example
Example: 7 in of rise over 12 in of run
Defaults: rise 7 in, run 12 in, the classic x:12 setup.
- Pitch: 7:12.
- Angle: atan(7 / 12) = 30.26°.
- Slope: 7 / 12 = 58.3 %.
- Multiplier: sqrt(1 + 0.5833^2) = 1.1577.
- Rafter: 12 x 1.1577 = 13.89 in, same as sqrt(7^2 + 12^2).
- Tool shows 7:12, 30.26°, 58.3 %, 1.1577, 13.89 in.
Reference table
| Pitch | Angle | Slope | Multiplier | Rafter |
|---|---|---|---|---|
| 4:12 | 18.43° | 33.3 % | 1.0541 | 12.65 in |
| 5:12 | 22.62° | 41.7 % | 1.0833 | 13.00 in |
| 6:12 | 26.57° | 50.0 % | 1.1180 | 13.42 in |
| 8:12 | 33.69° | 66.7 % | 1.2019 | 14.42 in |
| 10:12 | 39.81° | 83.3 % | 1.3017 | 15.62 in |
Limits
- Geometry only: overhangs, ridge thickness, and birdsmouth cuts change lumber length.
- The rafter shown matches the run entered; a different run gives a different rafter.
- Pitch steeper than 12:12 flips the convention; framers write it as 12:rise.
- No structural guidance: spans, loads, and nailing come from code tables, not pitch math.
Common mistakes
- Confusing pitch (x:12) with slope percent.
- Measuring run along the sloped roof plane instead of the horizontal projection.
- Ordering rafters from the bare hypotenuse and forgetting overhang and ridge.
- Specifying standard shingles on a 2:12 or 3:12 roof; low slopes need membranes.
- Reading 12:12 as a normal pitch; it is a 45° roof, the steepest common convention.
Try it yourself
Quick checks. Answers sit tucked under each question.
9:12?
36.87°, 75 % slope, multiplier 1.25, rafter 15.00 in.
6:12?
26.57°, 50 % slope, multiplier 1.1180, rafter 13.42 in.
4:12?
18.43°, 33.3 % slope, multiplier 1.0541, rafter 12.65 in.
Questions
What does 6:12 pitch mean?
Six inches of rise per 12 inches of horizontal run: a 26.57° angle, 50 % slope, and a very common conventional roof.
Pitch versus slope versus angle?
Pitch is the x:12 ratio, slope is rise over run as a percent (6/12 = 50 %), and angle is the degrees from horizontal (26.57°). One triangle, three accents.
How do I measure pitch on an existing roof?
Hold a level horizontally with one end on the roof, mark 12 inches out, and measure straight down to the roof surface: that many inches is the first number.
What pitch can I shingle?
Standard asphalt shingles need 4:12 or steeper, 2:12 to 4:12 takes double underlayment and special detail, and below 2:12 use membrane systems.
How is rafter length figured?
Pythagoras: sqrt(rise² + run²), or the multiplier times the run. Both agree: 7 and 12 give 13.89 in.
Does the unit selector change the math?
No. Pitch, angle, slope, and the multiplier are ratios and unitless. Only the rafter label follows the unit chosen.
Sources
- University of Georgia: Applications of Mathematics in Construction
- U.S. Army FM 5-426: Carpentry, Roof Framing and Roofing (PDF)