How this calculation works
Run is the horizontal distance, not the sloping rafter length. Rise and run must share a unit. The sloping length follows the Pythagorean theorem.
Angle = arctan(rise ÷ run); pitch per 12 = rise ÷ run × 12A worked example
A rise of 3 and run of 4 gives an angle of approximately 36.869898°, pitch 9 per 12 and slope length 5.
Good to know
Geometric relationship only. Does not specify roofing suitability, overhangs, loads or structural member sizes.
A 45-degree roof has equal rise and run
When vertical rise equals horizontal run, their ratio is 1 and the angle is 45 degrees. Expressed as rise per 12 run units, the pitch is 12. A 6-per-12 pitch instead has ratio 0.5 and angle about 26.57 degrees.
That example shows why a pitch number is not a degree value. The ratio and the angle describe the same geometry using different forms.
Measure horizontal run, not the sloping length
Run is the horizontal projection. Entering a measured rafter length as the run changes the triangle and gives the wrong pitch. The tool separately reports the sloping length from the Pythagorean relationship.
Roof suitability depends on material, weather, details and structural requirements that this calculation does not assess. The geometric result alone does not establish a compliant roof design.
A few questions, answered
Do rise and run need the same units?
Yes. Their ratio is meaningful only when both use the same length unit.
Does this include overhangs?
Only if your measured rise and run deliberately include the geometry you want to evaluate. No overhang is inferred.