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Roof pitch calculator

Pitch, angle, and slope factor

A roof pitch calculator turns rise and run into the three numbers people mix up: a pitch such as 6:12, an angle in degrees, and a slope factor. The slope factor is the hypotenuse divided by the run. Multiply it by the horizontal plan area and you get an estimate of the sloped roof area for a roof that holds one pitch. Hips and valleys need extra material this factor does not add.

Inputs

Use the same unit for rise and run. A 6:12 pitch is a rise of 6 and a run of 12.

Result

Enter the rise and the run. Add a footprint if you want roof area.

Disclaimer: This is an estimate for planning. Measure the real space, read the product label, and confirm anything structural, legal, or financial with a qualified person. Nothing you type is sent to a server. Not a structural design and not a snow-load calculation.

Snow on the roof is not the slope factor. The roof snow load calculator is the planning estimate by ZIP code. Trail grade uses the same geometry outdoors at HikeSpan.

How to use

  1. Enter the rise and the run in the same unit. For the usual pitch notation, use inches of rise and a run of 12.
  2. Leave the footprint blank if you only want the pitch, the angle, and the slope factor.
  3. If you want area, enter both the length and the width of the horizontal plan, in feet. The sloped area is that rectangle times the slope factor.
  4. Press Calculate. A steeper pitch has a larger factor and more roof area than the plan.

How it's calculated

Pitch = rise : run
Slope factor = √(rise² + run²) ÷ run
Angle = arctan(rise ÷ run)
Sloped area ≈ plan area × slope factor

The slope factor is the slant length of the rafter triangle divided by the horizontal run. A 6:12 pitch has rise 6 and run 12. The hypotenuse is √(36 + 144) = √180 ≈ 13.416, and the factor is 13.416 ÷ 12 ≈ 1.118. Every square foot of plan area corresponds to about 1.118 square feet of roof surface at that pitch.

Snow on that roof is a different question. Design snow load by ZIP code is the roof snow load calculator, and it is an estimate, not this geometry. The plan area itself, if you are still measuring the footprint, can be checked on SqftKit’s area calculator.

Worked example

Rise 6, run 12. The pitch reads 6:12. The angle is arctan(6 ÷ 12) = 26.57 degrees. The slope factor is 1.118. A 20 by 30 foot plan is 600 square feet. The sloped area is 600 × 1.118 = 670.8 square feet. A 4:12 pitch is flatter: the factor is √(16 + 144) ÷ 12 = 1.054, and the same 600 square foot plan is about 632 square feet of roof.

Assumptions and sources

The factor is ordinary right-triangle geometry. It estimates the surface of a constant-pitch roof from the horizontal plan area, which is appropriate for a shed roof or a gable roof of one pitch. Hips, valleys, dormers, and overhangs change the cut list; add material for those separately. The plan dimensions are optional and are assumed to be in feet only because the area is labeled in square feet. Rise and run must share a unit with each other, which can be inches. Snow load is not computed here.

FAQ

What does 6:12 mean?

Six units of rise for every 12 units of run. Inches are the usual unit, so 6 inches of rise for each foot of horizontal run.

Is the slope factor the same as the pitch?

No. The pitch is the ratio 6:12. The slope factor is the slant length divided by the run, about 1.118 for a 6:12 pitch.

Does this include overhangs?

Only if the plan length and width you enter already include them. The factor does not add an overhang by itself.

Where do I estimate snow?

The roof snow load calculator uses ZIP code, pitch, and exposure for a planning estimate of design snow load. It is a different tool.

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