How to Calculate Roof Pitch: Formula, Chart and Examples

Roof pitch tells you how steep a roof is. You need it to describe a roof to a builder, to compare plans, to work out the length of rafters and to check what a roofing material expects. The calculation is only a division, but the terms and the units can be confusing. This guide explains them with the formula, a full chart and worked examples.

What roof pitch means

Pitch compares two distances. The rise is how far the roof climbs vertically. The run is the horizontal distance over which it climbs. For a simple gable roof, the run is half the width of the building, because each side of the roof covers half the span.

In the United States pitch is usually written as a ratio over 12. A 6/12 roof rises 6 units for every 12 units of run. The units can be inches, feet, centimetres or metres, as long as rise and run use the same one. The ratio stays the same either way.

You will also see slope expressed as an angle in degrees or as a percent. They describe the same steepness in different ways, and we show how to convert between them below.

Three ways to get rise and run

You need two numbers: a rise and a run. Here are three ways to find them. Whichever you choose, take care. Do not climb a roof unless you know how to do it safely and have the right equipment. If in doubt, use one of the safer methods or ask a professional.

1. From the attic, with a level and a tape. This is usually the safest way. Find a rafter and hold a level horizontal against its underside. Mark 12 inches along the level, then measure straight down or up from that 12 inch mark to the rafter. That distance is the rise for a 12 inch run, which is the x in x/12.
2. From plans or drawings. Building plans often list the pitch or show the ridge height and the width. If you have them, read the rise and run from the drawing and apply the formula.
3. From building dimensions. For a simple gable roof, take half the width of the building as the run. Measure or find the height from the top of the wall to the ridge as the rise. This only works if the roof is a single straight slope on each side.

Whichever way you measure, use the same unit for both numbers, and measure more than once to check.

The roof pitch formula, step by step

Once you have rise and run, the rest is arithmetic. These are the formulas our Roof Pitch Calculator uses.

• Pitch (x/12) = rise / run x 12
• Angle = arctan(rise / run), shown in degrees
• Percent slope = rise / run x 100
• Rafter length along the slope = the square root of (run squared + rise squared), with no overhang

If you already know the pitch and want the rise for a given run, turn the first formula around: rise = pitch / 12 x run.

Take the steps in order. Divide the rise by the run. Multiply by 12 to get the x in x/12. If you want the angle or the percent slope, start again from the plain division rise / run and apply the formula for each.

Roof pitch chart: pitch, angle and percent slope

This chart lists common pitches with their angle and percent slope, using the formulas above.

Notice that 12/12 is exactly 45 degrees and a 100% slope, because the rise equals the run. The chart stops at 12/12. Steeper roofs have angles above 45 degrees and slopes above 100%.

Worked example

Take a simple gable roof on a building that is 24 ft wide. Each side of the roof covers half the width, so the run is 12 ft. The ridge is 6 ft above the top of the walls, so the rise is 6 ft.

• Pitch = 6 / 12 x 12 = 6, so the roof is 6/12.
• Angle = arctan(6 / 12) = 26.57 degrees.
• Percent slope = 6 / 12 x 100 = 50.00%.
• Rafter length along the slope = the square root of (12 x 12 + 6 x 6) = the square root of 180, which is about 13.42 ft, with no overhang.

Now the second mode. Suppose you know the pitch is 6/12 and the run is 20 ft, and you want the rise. Rise = 6 / 12 x 20 = 10 ft.

Here is one more. A roof with an 8/12 pitch over a 15 ft run has a rise of 8 / 12 x 15 = 10 ft. The rafter length along the slope is the square root of (15 x 15 + 10 x 10) = the square root of 325, about 18.03 ft. The chart gives its angle as 33.69 degrees and its percent slope as 66.67%.

Converting pitch to angle and percent

Because all three measures come from the same rise / run, you can convert between them whenever you like.

• Pitch to percent slope: divide the x by 12 and multiply by 100. For 6/12 that is 6 / 12 x 100 = 50.00%.
• Pitch to angle: take the arctan of x / 12. For 6/12 that is arctan(0.5) = 26.57 degrees.
• Percent slope to pitch: divide the percent by 100 and multiply by 12. A 50% slope becomes 6/12.

If you do not have a scientific calculator, use the chart or our Roof Pitch Calculator, which shows all three at once.

Common mistakes

• Mixing units. Rise in inches and run in feet gives a wrong ratio. Convert one so both match.
• Using the full width as the run. On a gable roof the run is half the width.
• Treating rafter length as the run. The rafter runs along the slope, so it is longer than the run.
• Forgetting overhang. The rafter length from the formula has no overhang, so the real board is longer.
• Assuming a single slope. Hips, valleys and dormers need to be worked out section by section.

Pitch is only one part of a roofing job. The minimum pitch a roofing material accepts depends on the material, so check the manufacturer’s instructions and your local rules before you decide. This guide and the calculator do not make that judgement. For more tools for the home, see the Home and Energy Calculators page.

Frequently asked questions

Tools used in this guide

• Roof Pitch Calculator

Related articles

Photo: Verstappen Photography on Unsplash