Roof pitch is how steep a roof is, and you calculate it by dividing the rise (the vertical height) by the run (the horizontal distance). A roof that rises 2.5 m over a run of 5 m has a pitch of 0.5, which is a 26.6 degree angle, a slope of 50% and “6 in 12” in the ratio used on many drawings. The same single number can be written four ways, so it helps to know how to move between them.
Note: this is general information for estimating. Roof design, tile and slate choice, structural sizing, and building regulations or planning permission depend on your building and location. Check manufacturer guidance and ask a structural engineer, architect or your local building control team before building or altering a roof.
What roof pitch means: rise, run and span
Pitch describes the slope of a roof surface. Three measurements come up:
- Rise: the vertical height from the top of the wall plate (where the rafter sits on the wall) to the ridge, which is the highest line of the roof.
- Run: the horizontal distance from the outer face of the wall to a point directly below the ridge. On a symmetrical gable roof, the run is half of the span.
- Span: the total width of the building between the outside faces of the walls that support the roof.
If your house is 10 m wide and has a symmetrical gable roof, the span is 10 m and the run is 5 m. If the ridge is 2.5 m above the wall plate, the rise is 2.5 m.
The pitch is the relationship between rise and run, so a taller roof over the same run is steeper. Pitch is not the same as roof height, though. A wide building with a shallow pitch can have a higher ridge than a narrow building with a steep pitch, because rise depends on both pitch and run.
It is also useful to separate pitch from rafter length. The rafter is the sloping timber, and it is longer than the run because it runs along the slope. Pitch tells you the angle, and rafter length tells you how much timber and roof covering you need.
The basic formula
For any roof, the pitch can be expressed from rise and run:
- Slope (as a decimal) = rise ÷ run
- Slope as a percentage = rise ÷ run × 100
- Angle in degrees = the inverse tangent of (rise ÷ run)
- Pitch as x in 12 = rise ÷ run × 12
- Rafter length = the square root of (rise² + run²)
Take the example of a rise of 2.5 m over a run of 5 m. The House of Calculator roof pitch tool gives:
| Measure | Result |
|---|---|
| Slope as a decimal | 0.5 |
| Angle | 26.57 degrees |
| Slope as a percentage | 50% |
| Pitch as x in 12 | 6 in 12 |
| Pitch as 1 in N | 1 in 2 |
| Rafter length (eaves to ridge) | 5.59 m |
You can check the rafter length with Pythagoras: 2.5² + 5² = 6.25 + 25 = 31.25, and the square root is 5.59. The angle comes from a tangent calculation, which is on most scientific calculators as “tan⁻¹” or “arctan”. The tool also does this for you in any of four units: metres, millimetres, feet or inches.
Because only the ratio of rise to run matters, the units do not change the answer. A rise of 1,600 mm over a run of 4,000 mm gives the same 0.4 slope, 21.8 degrees and 40% as 1.6 m over 4 m. Just keep rise and run in the same unit before dividing.
Converting between degrees, x in 12, percent and 1 in N
Roof pitch is written differently in different places. UK drawings and tile manufacturers usually quote degrees, American plans often use “x in 12” (inches of rise per 12 inches of run), and some builders and engineers use a percentage or a ratio. The table converts the common values, using the tangent of the angle:
| Angle | Pitch as x in 12 | Slope (%) | Pitch as 1 in N |
|---|---|---|---|
| 15° | 3.22 in 12 | 26.8% | 1 in 3.73 |
| 20° | 4.37 in 12 | 36.4% | 1 in 2.75 |
| 22.5° | 4.97 in 12 | 41.4% | 1 in 2.41 |
| 25° | 5.60 in 12 | 46.6% | 1 in 2.14 |
| 30° | 6.93 in 12 | 57.7% | 1 in 1.73 |
| 35° | 8.40 in 12 | 70.0% | 1 in 1.43 |
| 40° | 10.07 in 12 | 83.9% | 1 in 1.19 |
| 45° | 12.00 in 12 | 100% | 1 in 1 |
And the other way, from the x in 12 ratio to degrees:
| Pitch as x in 12 | Angle | Slope (%) |
|---|---|---|
| 3 in 12 | 14.0° | 25.0% |
| 4 in 12 | 18.4° | 33.3% |
| 5 in 12 | 22.6° | 41.7% |
| 6 in 12 | 26.6° | 50.0% |
| 8 in 12 | 33.7° | 66.7% |
| 9 in 12 | 36.9° | 75.0% |
| 12 in 12 | 45.0° | 100% |
Two things to notice. First, 45 degrees is not “half of 90 degrees steepness” in any practical sense; it is a 100% slope, where rise equals run. Second, the relationship is not linear. Going from 30 to 35 degrees raises the slope from 57.7% to 70%, which is a larger jump than going from 15 to 20 degrees. When you convert, always use the tangent and not a simple proportion. If you need a refresher on percentages, our How to calculate percentages guide covers the basics.
The roof pitch calculator has four modes for this reason: you can enter rise and run, an angle in degrees, a ratio in x in 12, or a percentage slope, and it returns the others. The common way to use it is to put in the value you have on a drawing, and read off the value you need on the site.
Worked example: an 8 m wide house with a 35 degree roof
Suppose you are planning a symmetrical gable roof on a house with a span of 8 m and a design pitch of 35 degrees. The run is half the span, so 4 m.
- Find the rise. Rise = run × tan(35°) = 4 × 0.7002 = 2.80 m.
- Find the rafter length. Rafter = run ÷ cos(35°) = 4 ÷ 0.8192 = 4.88 m, measured from the eaves to the ridge line.
- Find the x in 12 value. 12 × tan(35°) = 8.4, which is an 8.4 in 12 pitch.
- Check with Pythagoras. 2.8² + 4² = 7.84 + 16 = 23.84, and the square root is 4.88, which agrees.
These figures were worked by hand and checked against the formula. If the roof overhangs the wall at the eaves, you need extra rafter length. The House of Calculator tool lets you add an overhang. For the 2.5 m by 5 m example, a horizontal overhang of 0.3 m increases the rafter from 5.59 m to 5.926 m, because the overhang follows the slope and adds 0.3 ÷ 5 × 5.59 = 0.335 m. Note that overhang is measured horizontally, so check how your drawings measure it, and always confirm timber lengths with your carpenter or truss supplier.
From pitch to roof area
Once you know the rafter length, you can estimate the surface area of the roof, which drives the quantity of tiles, slates, felt and battens. For a simple gable roof with two equal slopes:
Roof area = rafter length × length of the ridge × 2
Using the 2.5 m rise and 5 m run example, with a rafter of 5.59 m and a ridge 8 m long, the area is 5.59 × 8 × 2 = 89.4 square metres. Compare that with the plan area of the house, which is the span multiplied by the length: 10 × 8 = 80 square metres. The roof surface is larger than the floor plan by a factor of about 1.12, which is the rafter length divided by the run (5.59 ÷ 5). That ratio is the “pitch factor” and it grows as the roof gets steeper. For a 30 degree roof, the factor is 1 ÷ cos(30°), which is 1.155. For 45 degrees it is 1.414.
This is a rough estimate. Hips, valleys, dormers, chimneys and overhangs all change the area, and coverings need an allowance for overlaps and waste. Use supplier calculators and measurements for an order. Our How to measure for flooring and fencing guide shows how to approach measuring for similar jobs, and the method for an area-based material is the same as in How much paint, wallpaper or tile do you need?.
How to measure the pitch of an existing roof
There are several ways to find the pitch of a roof you already have:
- From a gable end or drawings. If you can see the profile, measure the rise and run from a scale drawing or a photograph taken straight on, then use the formula.
- In the loft, with a level and a tape. Hold a spirit level horizontally against a rafter, measure 300 mm along the level, then measure vertically from the end of the level to the rafter. The ratio of that vertical measurement to 300 mm is the slope. For example, a vertical gap of 150 mm over 300 mm is a 0.5 slope, or 26.6 degrees.
- With a digital angle finder or a phone app. These read the angle directly. Check the calibration and place the device flat on the rafter, not on a rough surface.
- From the ground. You can estimate with a clinometer or a camera angle, but this is less accurate, so use it only for rough planning.
Do not climb on a roof to measure it. Measuring from inside the loft, from a ladder that is properly secured, or from drawings is safer. If a roof must be accessed, use a professional.
Why roof pitch matters
Pitch influences several things about a roof and a building:
- Roof covering. Each type of tile, slate or sheet has a minimum pitch that its manufacturer specifies, below which water can be driven back under the covering. The minimum varies by product and by exposure, so use the manufacturer’s data for your choice and location. Some coverings, such as single-ply membranes, are designed for flat or very low pitches.
- Drainage. A steeper roof sheds rain, snow and debris faster. A very shallow roof needs more careful detailing to avoid pooling.
- Loft space. A steeper pitch gives more headroom in the roof space, which affects whether a loft conversion is practical.
- Structure and wind. The pitch affects the forces on the roof, including wind uplift and the loads on rafters and trusses. This is a matter for a structural engineer.
- Appearance and planning. The pitch should suit the style of the building and the area. A local planning authority may have a view, particularly for an extension or a conservation area.
- Cost. A steeper roof has more surface area, so more material and labour. A move from 30 to 45 degrees increases the surface area by around 22% for the same span, because the pitch factor goes from 1.155 to 1.414.
Check the manufacturer’s data sheet, the relevant building regulations, and any planning conditions before fixing a pitch.
Common mistakes when calculating roof pitch
- Using the span instead of the run. For a symmetrical gable roof, the run is half the span. Using the full width halves the pitch.
- Mixing units. Rise and run must be in the same unit. Mixing millimetres and metres gives a nonsense answer.
- Treating the angle as a linear scale. Slope is the tangent of the angle, so double the angle is not double the slope.
- Confusing pitch and slope percentage. A 45 degree pitch is a 100% slope, not 45%.
- Forgetting the overhang. The rafter must be longer than the eaves-to-ridge length if the roof overhangs the wall.
- Measuring rafter length along the wrong line. Rafter length is along the slope, and run is horizontal. They are not interchangeable.
- Ignoring the minimum pitch for the covering. Choose the pitch and the covering together, and check the manufacturer’s guidance.
- Relying on a rough estimate to order materials. Use a quantity take-off from the supplier, with allowances for waste.
Try the calculator
Enter your rise and run, or an angle, ratio or percentage, into the Roof Pitch Calculator to see the other values, the rafter length, and the effect of an overhang.
Frequently asked questions
How do you calculate roof pitch?
Divide the rise by the run. For a rise of 2.5 m over a run of 5 m, the slope is 0.5, which is a 50% slope, an angle of 26.6 degrees and a 6 in 12 pitch. Use the inverse tangent to turn the slope into an angle.
What is a 6 in 12 pitch in degrees?
A 6 in 12 pitch is a slope of 0.5, which is 26.57 degrees. It means the roof rises 6 inches for every 12 inches of horizontal run.
What is the run of a roof?
The run is the horizontal distance from the outside of the wall to a point directly below the ridge. On a symmetrical gable roof it is half the span, so a 10 m wide house has a 5 m run.
How do I convert degrees to a pitch ratio?
Take the tangent of the angle to get the slope, then multiply by 12 for the x in 12 ratio, or by 100 for a percentage. For example, 30 degrees has a tangent of 0.577, which is 6.93 in 12 or a 57.7% slope.
What is the minimum pitch for a tiled roof?
It depends on the type of tile or slate and the exposure of the site, and manufacturers publish minimum pitches for each product. Check the data sheet for your covering and ask a roofer or building control if you are unsure.