How to use it
Fill in any two of the four boxes and the other two are worked out, along with the roof angle in degrees, the percent grade and the length of a regular hip or valley rafter. If you type a third value, it replaces the older of the first two.
Pitch can be typed as 6 or 6/12 (inches of rise per foot of run), as an angle such as 26.5°, or as a grade such as 50%.
Worked example
A 6/12 roof over a 14' run rises 7' 0". The common rafter, measured along the slope, is 15' 7 13/16". The roof angle is 26.57° and the grade is 50%. A regular hip or valley on that roof is 21' 0".
These are theoretical lengths from the outside of the wall plate to the centre of the ridge. Add the overhang and deduct half the ridge thickness before you cut.
The math
- Rise = run × pitch. At 6/12, every foot of run rises 6 inches.
- Diagonal = √(rise² + run²).
- Angle = arctan(rise ÷ run).
- Regular hip or valley = √(rise² + 2 × run²). It runs at 45° in plan between two roof planes of the same pitch.
The same boxes solve any right triangle: squaring a foundation, a stair stringer, a brace or a ramp.
Typing measurements
Every box takes feet, inches and fractions the way you would write them: 9' 1 1/8", 7 1/2", 2.5' or 300mm. Put a space between whole inches and a fraction. A box also takes a whole calculation, so 14' 6" / 2 works anywhere.
Questions
How do I find rafter length from pitch and run?
Rise equals run times pitch, and the rafter is the diagonal: the square root of rise squared plus run squared. A 6/12 roof over a 14' run rises 7' and the rafter measures 15' 7 13/16" before overhang and ridge deductions.
What does a 6/12 pitch mean?
The roof rises 6 inches for every 12 inches of horizontal run. That is an angle of 26.57 degrees, or a 50% grade.
How do I convert roof pitch to degrees?
Divide the rise by the run and take the arctangent. A 4/12 pitch is 18.43°, 6/12 is 26.57°, 8/12 is 33.69° and 12/12 is 45°. Type the pitch in the Pitch box and the angle appears in the results.
Is run the full width of the building?
No. For a gable roof with a centred ridge, run is half the span: the horizontal distance from the outside of the wall to the centre of the ridge.
How precise is the answer?
The math is done at full precision and only the displayed fraction is rounded, to the nearest 1/16 inch by default. You can change that from 1/2 down to 1/64. When rounding changes the value, the answer is marked with ≈.
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