What this calculator does
Roof pitch is the rise over the run, and everything else follows from it. A 2.4 metre rise over a 4 metre run gives a 30.96 degree pitch, a 4.665 metre rafter and a slope factor of 1.166.
The slope factor is the figure that matters for ordering materials. A roof covering 120 square metres in plan actually has 139.9 square metres of surface at that pitch, so ordering to the plan area would leave you 20 square metres short. The steeper the roof, the larger the gap.
The formula
The pitch angle is the arctangent of rise over run. The rafter length is the hypotenuse by Pythagoras. The slope factor is the rafter length divided by the run, which is the multiplier converting plan area to true roof area. The run is half the span for a symmetrical gable, not the full width.
| Term | Meaning |
|---|---|
| Rise | Vertical height from the wall plate to the ridge. |
| Run | Horizontal distance from wall to ridge, which is half the span on a symmetrical roof. |
| Slope factor | True area divided by plan area. Always greater than 1. |
| Pitch ratio | Rise to run expressed as 1 in something, a common builder shorthand. |
The inputs explained
| Field | What to enter |
|---|---|
| Rise (m) | Vertical rise in metres. |
| Run (half the span) (m) | Horizontal run in metres. For a symmetrical gable roof this is half the building span, not the whole width. |
| Plan area of the roof (m²) | Plan area of the roof in m², measured as though looking straight down. |
When to use it
Ordering roofing material
Material covers the true sloped area, which exceeds the plan area by the slope factor.
Cutting rafters
The rafter length and angle are what the carpenter needs, before any allowance for overhang and birdsmouth.
Checking a pitch against a product
Roofing products have minimum pitches below which they leak, so the angle has to be confirmed.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does pitch affect the roof area?
A range of rises over the same run.
| Rise | Pitch angle | Slope factor | True roof area |
|---|---|---|---|
| 1.2 m | 16.70° | 1.044 | 125.3 m² |
| 2 m | 26.57° | 1.118 | 134.2 m² |
| 2.4 m | 30.96° | 1.166 | 139.9 m² |
| 4 m | 45.00° | 1.414 | 169.7 m² |
Questions
What is the run on a roof?
The horizontal distance from the wall to the ridge, which on a symmetrical gable roof is half the building span. Using the full span is the most common error here and halves the calculated pitch.
What is the slope factor for?
Converting plan area to actual roof surface area. A roof measuring 120 m² from above has more surface than that because it is tilted. Multiply the plan area by the slope factor before ordering tiles, sheeting or underlay.
What is the minimum pitch for a roof?
It depends entirely on the covering. Some profiled metal sheeting works down to around 5 degrees, while plain clay tiles usually need 35 degrees or more. Going below a product minimum causes leaks under wind-driven rain, so check the manufacturer specification.
How do I convert pitch to a ratio?
Divide the run by the rise to get the second number in a 1 in X expression. A 2.4 m rise over a 4 m run is 1 in 1.67. American practice instead quotes rise in inches per 12 inches of run, so the same roof is roughly a 7 in 12 pitch.
For counting roof trusses, see the roof truss calculator. For shingle quantities, see the roof shingle calculator.