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Roof Pitch Calculator

A roof pitch calculator turns two measurements — the rise and the run of a roof — into the pitch, the angle, and the slope percentage. Enter the rise in inches and the run in inches, and it shows the pitch written as x/12, the angle in degrees, and the slope as a percentage. It is a quick way to describe a roof when you are ordering materials, talking to a roofer, or checking whether a roofing product suits the slope you have. It also works for gable, hip, and shed roofs, and works out rafter lengths and the roofing area from the building size.

How it works

Roof pitch describes how steep a roof is, and it is written in a form that builders everywhere recognise: rise over a 12-inch run. A pitch of 6/12 means the roof rises 6 inches for every 12 inches it travels horizontally. A pitch of 4/12 rises 4 inches over the same distance, so it is gentler. A pitch of 12/12 rises 12 inches over 12 inches, so it climbs at 45 degrees — a steep roof by any measure. The first number is the one that changes; the 12 stays fixed, which makes pitches easy to compare at a glance.

To use the calculator you need two numbers. The run is the horizontal distance from the outside face of the wall to the centre line of the roof — for a symmetrical roof, that is half the span of the building. The rise is the vertical distance from the top of the wall plate to the peak of the roof. Both must be measured in the same units, and inches are the usual choice. The pitch is then the rise scaled to a 12-inch run: pitch = rise ÷ run × 12, written as that number over 12.

The same two numbers also give you the angle and the slope percentage, which are just the same steepness expressed differently. The angle is the arctangent of rise divided by run, converted to degrees — the angle between the roof surface and the horizontal. The slope percentage is rise divided by run, multiplied by 100. So a roof with a rise of 6 inches and a run of 12 inches has a pitch of 6/12, an angle of about 26.57 degrees, and a slope of 50%. All three numbers describe the same roof; roofers tend to use pitch, while product guides and planning documents often use angle or slope.

The pitch also gives you the rafter length and the roofing area. The slope factor is the rafter length divided by the run: for a 6/12 pitch it is about 1.118, which means every foot of horizontal run needs about 1.118 feet of rafter. A common rafter on a gable roof spans half the building width, so with a 24-foot span and a 6/12 pitch it is about 13.42 feet long. On a hip roof the corners need hip rafters, which run diagonally and are longer — about 18 feet for the same roof. A shed roof has a single slope across the full span, so its rafter is about 26.83 feet for a 24-foot span at 6/12. The roofing area is the footprint (roof length times span) multiplied by the slope factor: a 40 by 24 foot roof at 6/12 is about 1,073 square feet of roofing (approximate for a hip roof, since its sloped ends change the shape a little).

Pitch matters because it decides how a roof behaves. Steeper roofs shed rain and snow faster, which is why snowy regions often favour steeper pitches, and they give more usable space under the roof for a loft or an attic room. Gentler roofs are cheaper to build and easier to walk on, but water drains more slowly, so they need roofing materials rated for low slopes — below about 3/12, standard shingles are usually not suitable, and a membrane or metal system is needed instead. Pitch also affects how much roofing material you need: a steeper roof has more surface area than a flatter roof covering the same footprint, so the same house can need noticeably more shingles at 9/12 than at 4/12.

Measuring a roof from the ground is possible, but take care. The safest way is to measure inside the attic, where you can hold a level horizontally from the peak and measure down to the rafter for the rise, and along the level for the run. If you must measure from outside, use a level and a tape on a ladder with someone steadying it, and never walk on a wet or steep roof to take a reading. A small error in the rise — an inch or two — changes the pitch by a whole step, so measure twice and use the calculator to check that the result looks sensible before you order materials.

Worked example

Priya is planning a re-roof and wants to describe her roof to a supplier. She measures inside the attic: from the centre line of the roof to the outside wall is 12 inches of run on her level, and the peak sits 6 inches above the wall plate. She enters a rise of 6 inches and a run of 12 inches.

First, the pitch: 6 ÷ 12 × 12 = 6, so the pitch is 6/12. Next, the angle: arctan(6 ÷ 12) is arctan(0.5), which is about 26.57 degrees. Finally, the slope: 6 ÷ 12 × 100 = 50%. Priya can now tell the supplier she has a 6/12 roof at about 26.57 degrees, and the supplier knows at once that standard shingles will suit it, that it sheds water well, and roughly how much extra surface area the slope adds over a flat footprint.

If Priya's roof had been steeper — say a rise of 9 inches over the same 12-inch run — the same steps would give a 9/12 pitch, an angle of about 36.87 degrees, and a slope of 75%. The pattern is easy to see: doubling the rise doubles the slope percentage, while the angle grows more slowly, which is why pitch and slope are the clearer numbers to compare when you are choosing materials.

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