Herramientas prácticas para trabajos de precisión
Calculadora de Pendiente de Techo
Visualice la pendiente del techo como elevación/recorrido, en grados y con un diagrama de triángulo a escala.
How it works
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:
| X in 12 | Angle | Traditional (fractional) pitch |
|---|---|---|
| 2 in 12 | 9.5° | 1/12 pitch |
| 3 in 12 | 14.0° | 1/8 pitch |
| 4 in 12 | 18.4° | 1/6 pitch |
| 5 in 12 | 22.6° | 5/24 pitch |
| 6 in 12 | 26.6° | 1/4 pitch |
| 7 in 12 | 30.3° | 7/24 pitch |
| 8 in 12 | 33.7° | 1/3 pitch |
| 9 in 12 | 36.9° | 3/8 pitch |
| 10 in 12 | 39.8° | 5/12 pitch |
| 12 in 12 | 45.0° | 1/2 pitch |
Current-input example
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.
Before using the result
- 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.
Limitations
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.
Frequently asked questions
What does "4 in 12" mean?
It's carpentry shorthand for the pitch ratio scaled to a 12-unit run: for every 12 units the roof runs horizontally, it rises 4 units. It's unit-independent - 4 in 12 is the same slope whether you measure in millimetres or inches.
Is the rafter length the actual board length I should cut?
No - it's the straight-line hypotenuse between your rise and run points. Real rafters are usually longer (for overhang past the wall) and get a birdsmouth cut and ridge-side trim, so treat this number as the geometric baseline, not a cut list.
What does a "1/4 pitch" or "1/3 pitch" roof mean?
These describe rise as a fraction of the total building width (span) rather than as "X in 12". A 1/4 pitch roof is a 6-in-12 roof (26.6°); a 1/3 pitch is 8-in-12 (33.7°). See the reference chart above for the full conversion.
How do I find run if I only know the building width?
For a simple gable roof, run is typically half the building width - the horizontal distance from the wall plate to the ridge centerline. Measure to the ridge, not the far wall, if the roof isn't symmetric.
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