Roof pitch calculator: rise and run, x/12 and degrees

Quick answer

A 6/12 roof rises 6 in for every 12 in of horizontal run. That is an angle of 26.6 degrees, a slope of 50 percent and a pitch multiplier of 1.118: the roof surface is 11.8 percent larger than the area it covers. A 12/12 roof is 45 degrees with a multiplier of 1.414.

What this calculator does

Roof pitch is written in several ways. In the United States and Canada it is usually the rise in inches for every 12 in of horizontal run, such as 4/12 or 6/12. In the United Kingdom, Australia and most metric countries it is usually an angle in degrees. Engineers and drainage drawings often use a percentage. All of them describe the same thing: how much the roof rises over a horizontal distance.

The calculator converts between these notations. It also gives the pitch multiplier, which turns an area measured from above into the area of the sloping roof, and the hip or valley factor. With a horizontal run it gives the total rise and the length of a rafter along the slope.

It does not size rafters, check snow or wind loads, or tell you whether a roofing product is allowed on your pitch. Those depend on your building code and the instructions of the manufacturer.

How to measure roof pitch

You do not need to climb onto the roof. The safest place to measure is inside the attic, on the underside of a rafter, or on a gable end or a shed roof you can reach from a ladder standing on firm ground.

1. Hold a level horizontally with one end touching the underside of a rafter, or the top of the roof surface. Make sure the bubble is centred.
2. Measure 12 in along the level from the point where it touches, and mark that point. With a metric level, use 1000 mm, or any length you can measure accurately.
3. At the mark, measure straight up (or down) at a right angle to the level, to the rafter or the roof surface. That distance is the rise.
4. Enter the rise and the run you measured. With a run of 12 in, the rise in inches is the pitch: 5 in means 5/12.

This is the method that the home inspectors' association InterNACHI and the shingle manufacturer IKO describe. InterNACHI suggests a long level or a straight board when you measure on top of the roof, because shingles are uneven. A longer run also gives a more accurate result: an error of 1/8 in over 12 in changes the pitch by 1/8, but over 24 in only by 1/16. If you use a longer level, enter its length as the run. A digital angle finder or an inclinometer app gives the angle directly; enter it with the Angle option.

How to use it

1. Choose metric or US units. The units apply to the rise, the run and the optional rafter length; the pitch, angle and percentage are the same in both.
2. Under What you know, choose Rise and run, Pitch, Angle or Slope in percent, and enter the value.
3. To get a rafter length, choose Yes under Rafter length and enter the horizontal run of the rafter: for a simple gable roof, half the span, measured to the centre of the ridge.
4. Select Calculate.

How the result is calculated

Every notation is a way of writing the slope: the rise divided by the run.

1. Slope = rise ÷ run. From a pitch in 12: slope = pitch ÷ 12. From a percentage: slope = percent ÷ 100. From an angle: slope = tan(angle).
2. Pitch in 12 = 12 × slope. Percentage = 100 × slope. Angle = arctan(slope).
3. Pitch multiplier = √(1 + slope²), which is the same as 1 ÷ cos(angle). It is the length along the roof for one unit of horizontal run.
4. Hip or valley factor = √(2 + slope²): the length of a hip or valley rafter for one unit of common run, where two roof planes of the same pitch meet at a right angle in plan.
5. Rise over a run = run × slope. Rafter length = run × pitch multiplier, measured along the slope without overhang or any allowance for the ridge board.

The angle is shown to 0.1 degree and the pitch to 0.01 in 12. Pitches are often rounded to whole numbers on drawings; a measured rise of 5 7/8 in over 12 in is 5.88/12, which a roofer would call a 6/12 roof.

Worked example

US units: a 12 in level held against a rafter, with 6 in measured from the level to the rafter. Slope = 6 ÷ 12 = 0.5. Pitch: 12 × 0.5 = 6, so 6/12. Angle: arctan(0.5) = 26.57 degrees, shown as 26.6. Slope in percent: 50 percent. Pitch multiplier: √(1 + 0.25) = 1.118. Hip or valley factor: √(2 + 0.25) = 1.5.

Metric: a 1000 mm level with a rise of 500 mm gives the same slope of 0.5: an angle of 26.6 degrees, a pitch of 6 in 12, 50 percent, a multiplier of 1.118 and a hip or valley factor of 1.5.

With a rafter: a gable roof spans 24 ft, so the horizontal run of each common rafter is 12 ft. At 6/12 the rise to the ridge is 12 × 0.5 = 6 ft, and the rafter length along the slope is 12 × 1.118 = 13.42 ft, or 13 ft 5 in to the nearest 1/16 in, before the overhang is added.

From an angle: a roof of 30 degrees has a slope of tan 30° = 0.577, so it is a 6.93/12 pitch, 57.7 percent, with a multiplier of 1.155.

Roof pitch chart

The chart is calculated with the same formulas as the calculator and rounded for display.

What the pitch decides

The pitch limits which roof coverings you can use. The International Residential Code, section R905.2.2 in the 2021 edition, allows asphalt shingles only on slopes of 2/12 or steeper, and requires two layers of underlayment from 2/12 up to 4/12; for clay and concrete tile, section R905.3.2 sets 2 1/2/12. GAF calls 4/12 and steeper a standard slope. Tile manufacturers in the United Kingdom and Australia state minimum pitches in degrees: Marley gives 17.5 degrees for its Modern concrete tile with a 100 mm headlap, and Monier says most of its concrete tiles can go down to 15 degrees. Check the instructions of your product.

To find the area of the roof and the bundles of shingles to buy, use the pitch with the roofing calculator on this site, which multiplies the area seen from above by the pitch multiplier.

• Roofing calculator: roof area and shingle bundles

Common mistakes

• Measuring the rise along the roof instead of straight up from a level. The run must be horizontal and the rise vertical.
• Entering the pitch as degrees. A 6/12 roof is 26.6 degrees, not 6 degrees.
• Confusing slope with the traditional pitch. Carpentry manuals such as the US Army field manual FM 5-426 define pitch as the rise divided by the full span, so a 6/12 roof is a 1/4 pitch and a 4/12 roof a 1/6 pitch; IKO and InterNACHI point out the same difference. This calculator follows everyday usage, where "pitch" means the rise per 12 of run, and run is half the span of a symmetrical gable.
• Using the rafter length from the calculator as the board length. Add the overhang, and subtract half the thickness of the ridge board, before cutting.
• Measuring on a sagging rafter or near a joint. Measure at two or three places and use the average.