Dachneigungsrechner

How to use it: enter rise and run in the same units - rise is the vertical height the roof gains, run is the horizontal distance it covers over that height (for a full roof, run is usually half the building width, to the ridge centerline). Pitch, angle, and rafter length update as you type.

Formula. Pitch ratio is rise divided by run; carpentry "X in 12" notation scales that ratio to a run of 12; angle comes from the inverse tangent; rafter length is the hypotenuse of the rise/run triangle:

Pitch ratio = rise ÷ run, X in 12 = pitch ratio × 12, Angle = atan(rise ÷ run), Rafter length = √(rise² + run²)

Worked example. With the defaults above (1200 mm rise, 3600 mm run): pitch ratio = 1200 ÷ 3600 = 0.3333; in the common notation that's 0.3333 × 12 = 4.00, i.e. a "4 in 12" roof; angle = atan(0.3333) ≈ 18.43°; rafter length = √(1200² + 3600²) = √14,400,000 ≈ 3794.7 mm.

Traditional fractional pitch. Older references sometimes describe pitch as a fraction of the span instead of "X in 12" - a "1/4 pitch" roof rises a quarter of the total building width. Since run is half the span, fractional pitch = (X in 12) ÷ 24. The reference chart below converts between all three notations for common roof pitches:

The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.

Rise

1200 mm

Run

3600 mm

Primary result: Pitch: 4.00 in 12.

• Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
• Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
• When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.

This is triangle geometry only. The rafter length shown is the theoretical line-length of the rise/run triangle - it does not subtract a ridge-board reduction, add eave or gable overhang, or account for a birdsmouth notch at the wall plate, all of which change the actual lumber length you'd cut.

It also does not size rafters structurally (span tables, snow/wind load, species and grade). Use it for layout and pitch, and have spans checked against your local code or an engineer for anything load-bearing.