Article
Roof pitch
Roof pitch comes from two lengths: how far the ridge rises, and how far it sits from the eave in plan. The rest is trigonometry, not a reading from a photo.
The roof pitch calculator does this. Next door: ridge height.
The idea in brief
Roof pitch is the angle in a right triangle: one leg follows the ceiling line, the other rises to the ridge.
A taller ridge on the same building width makes a steeper roof. Two lengths from a tape or a drawing are enough.
On this page: Half-span is the horizontal run from the ridge to the wall, not the length of the sloping rafter. Rise is the height difference between ridge and eave. Arctangent is the angle whose tangent equals rise divided by half-span. Slope percent is that same ratio times 100.
When this helps
| Situation | What the card shows |
|---|---|
| You compare two roof options on the same building. | The horizontal run stays the same. You only change the ridge rise and get two different angles. |
| You want to see whether shingles, metal, or a membrane even apply at that pitch. | The card turns rise and horizontal run into an angle in degrees and a slope percent. |
| On an older house you have one length from a drawing and measure the other in the attic. | Those two lengths are enough. You do not need a guess from a photo. |
What to type
Half-span is half the building width in plan, ridge to wall, not the length of the sloping rafter. Rise is the height difference between ridge and eave. On an older house you often have one of those from a drawing and measure the other in the attic.
The card takes the arctangent of rise divided by half-span, and slope percent as rise / half-span × 100. A 2.8 m rise on 4.0 m is about 35° and 70%. A gentler 1.5 m on 3.5 m is about 23° and 43%.
What it is for
Pitch tells you whether a shingle, metal, or membrane product even applies, and how water will run. It is not a structural design and it is not a code check. If you compare two options on the same footprint, change only the rise and watch the angle. Rafter length is a different card.
A worked example
A 2.8 m rise on 4.0 m
Rise 2.8 m, half-span 4.0 m.
- Divide 2.8 by 4.0. You get 0.7.
- The angle is the arctangent of 0.7, about 35°.
- Slope percent: 70%.
Typical numbers from the card
| Inputs | Result |
|---|---|
| The ridge rises 2.8 m, and the horizontal run to the eave is 4.0 m. | The angle is about 35°, and the slope is about 70%. |
| The ridge rises 1.5 m, and the horizontal run to the eave is 3.5 m. | The angle is about 23°, and the slope is about 43%. |
Typical mistakes
| Mistake | What goes wrong | How to avoid it |
|---|---|---|
| You type the full building width even though the ridge is centered. | The angle comes out too small, because the horizontal run is twice as long as it should be. | If the ridge is centered, use half the building width. |
| You type the sloping rafter length instead of the horizontal run. | That is a different triangle. Half-span follows the ceiling line, not the roof surface. | Use the horizontal distance from ridge to wall, not the rafter length. |
| You mix up the angle in degrees with slope percent. | Those are two ways to write the same rise-to-run ratio. | The angle is in degrees. Slope percent is rise divided by run, times 100. |
Before you compare options
- Half-span is the horizontal run from ridge to wall, not the rafter length.
- Rise is the height difference between the ridge and the eave.
- If the ridge is centered, do not type the full building width.
- The card only does geometry. It does not check snow load and it does not replace a code check.
Frequently asked questions
What pitch is a 2.8 m rise on a 4.0 m half-span?
About 35° and 70% slope. That is the arctangent of 2.8 / 4.0.
Is half-span the rafter length?
No. It is the horizontal run. The rafter is longer because it follows the slope.
How is the angle different from slope percent?
Same triangle. The angle is in degrees; slope is rise over run times 100.
Does the card know snow load?
No. It only does geometry from the two lengths you type.
Where is ridge height?
On a separate page, when you know the angle and want rise, not the other way around.
Can I type the full building width?
Not if the ridge is centered. Use half the span, or the angle comes out too small.