Roof Pitch Calculator

Roof pitch is the rise for every 12 inches of horizontal run: pitch = 12 × rise ÷ run. A roof that rises 4 ft over an 8 ft run is 12 × 4 ÷ 8 = 6/12, which is an angle of arctan(0.5) ≈ 26.57° and a 50% grade. This roof pitch calculator converts pitch, angle and percent, and adds rafter length, pitch factor and roofing squares.

How to use the roof pitch calculator

1. Pick what you know: Rise & run (measured with a level and tape), Pitch x/12 (from plans), Angle (from an angle finder or phone level) or Percent grade.
2. Type the value. Rise and run can be in any unit as long as both use the same one, and fractions such as 7 1/2 work.
3. For framing and ordering, fill in the rafter run (half the building span), the overhang and the roof footprint seen from above. Leave them blank if you only need the conversion.
4. Read the pitch, angle, percent grade, ratio, pitch factor and hip/valley factor, plus rafter length, roof area and roofing squares. The chart highlights your pitch among the common ones, and Show steps gives the trigonometry.

Roof pitch formulas

Every way of describing a roof slope comes from the same right triangle, with the run as the horizontal leg and the rise as the vertical leg.

The pitch factor is the Pythagorean theorem with the run set to 1: the sloped length is √(1² + slope²). Multiply any horizontal distance by it to get the length along the roof. The hip or valley factor does the same for the diagonal where two planes of the same pitch meet at a right angle in plan; the 288 is 12² + 12², because the hip runs diagonally across a 12 × 12 square.

Worked example: from rise and run

1. Measure 4 ft of rise over 8 ft of run.
2. Pitch: 12 × 4 ÷ 8 = 6, so the roof is 6/12.
3. Angle: arctan(4 ÷ 8) = arctan(0.5) ≈ 26.57°.
4. Grade: 4 ÷ 8 × 100 = 50%. Ratio: 1 : 2.
5. Pitch factor: √(1 + 0.5²) = √1.25 ≈ 1.118, so every foot of run is about 1.118 ft along the slope.

A level held 12 in out from the roof surface gives the same result directly: if the gap below the 12 in mark is 6 in, the pitch is 6/12.

Worked example: from an angle

An angle finder reads 30°. The slope is tan 30° ≈ 0.5774, so the pitch is 12 × 0.5774 ≈ 6.93/12, just under 7/12. The grade is about 57.74%. Angles rarely land on whole pitches, which is why the calculator shows two decimals.

Worked example: rafter length and roofing squares

A gable roof has a 7/12 pitch, a 28 ft span (a 14 ft run on each side), 1 ft overhangs and a footprint of 1,800 sq ft including the overhangs.

1. Pitch factor: √(1 + (7 ÷ 12)²) ≈ 1.1577.
2. Rafter length: (14 + 1) × 1.1577 ≈ 17.37 ft, about 17 ft 4 3/8 in, measured along the slope before the ridge deduction.
3. Roof area: 1,800 × 1.1577 ≈ 2,083.87 sq ft.
4. Squares: 2,083.87 ÷ 100 ≈ 20.84. With 10% extra for cutting and starter courses, about 22.92 squares.

Treat the area as an estimate. Dormers, valleys and planes with a different pitch need to be measured and added separately.

Roof pitch chart

Notice that the angle does not grow in step with the pitch: going from 1/12 to 2/12 adds about 4.7°, while going from 11/12 to 12/12 adds about 2.5°. That is the arctangent flattening out. Doubling the pitch never doubles the angle.

Pitch, slope and angle: the names

Roofers usually say pitch for the x/12 figure, but some older texts define pitch as rise ÷ span (the full width of the building), which makes a 6/12 roof a “1/4 pitch”. Slope is the same rise-over-run idea written as a ratio or a percent, and the angle is the one between the roof and the horizontal. The calculator gives all of them so you can match whatever your plans or supplier use.

Common roof pitch mistakes

• Using the span instead of the run. The run is half the span on a symmetrical gable. Using the full span halves the pitch.
• Measuring the run along the slope. Run is horizontal. A tape laid on the shingles measures the rafter, not the run.
• Mixing units. 7 in of rise over 1 ft of run is 7/12, not 7/1.
• Using one multiplier for a mixed roof. A pitch factor only applies to planes with that pitch; work out each pitch separately.
• Cutting rafters to the line length. Deduct half the ridge board and add the tail before cutting.

Roof pitch practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What angle is a 4/12 roof pitch?

arctan(4 ÷ 12) ≈ 18.43°. Its grade is 33.33%, and its pitch factor is about 1.054.

How do I convert degrees to roof pitch?

Multiply the tangent of the angle by 12. For 35°, tan 35° ≈ 0.7002, so the pitch is about 8.4/12.

What is a roof pitch multiplier?

It is the pitch factor, √(1 + (pitch ÷ 12)²). Multiply the flat footprint by it to get the sloped roof area: at 6/12 the factor is about 1.118, so 2,000 sq ft of footprint is about 2,236 sq ft of roof.

How many squares is my roof?

Divide the roof area in square feet by 100. A roof of 2,083.87 sq ft is about 20.84 squares before any extra for waste.

Is a 12/12 roof 45 degrees?

Yes. When rise equals run, tan θ = 1, so θ = 45°, the grade is 100% and the pitch factor is √2 ≈ 1.414.

Related calculators

• Slope calculator for slope, grade and angle from two points
• Trigonometry calculator for tangent and arctangent
• Stair calculator for risers, treads and stringers
• Pythagorean theorem calculator for rafter lengths
• Square footage calculator for the roof footprint