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Calculation breakdown
These values reflect the editable inputs and assumptions above.
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Calculation report
Includes formulas, entered assumptions, limitations and sources.
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Choose the roof measurement you know#
Enter pitch as rise per 12 horizontal units, angle in degrees, slope percent, or measured rise and run. The workbench converts all four into the same right-triangle geometry. US and metric inputs describe the same physical roof.
Pitch, angle and slope formulas#
Let slope s = rise ÷ horizontal run. Pitch is 12s, percent grade is 100s, and roof angle is arctan(s). The sloped-length and area multiplier is √(1 + s²).
A 6
pitch has s = 0.5, an angle of about 26.565°, a 50% grade and a factor of 1.118034. A 12 ft horizontal run therefore has a 6 ft rise and a geometric diagonal of approximately 13.416 ft before an eave overhang is added.Run, span and overhang are different inputs#
Run is the horizontal distance to the ridge for the roof face being measured. Full span is twice the run only for a symmetrical gable. A shed roof or unequal roof face must use its actual run.
The horizontal eave overhang increases the reported slope length. It does not expand the optional roof-area dimensions. Enter projected roof length and width including all eave and gable projections when estimating area.
Worked example: sloped roof area#
A roof projection of 40 × 30 ft with a uniform 6
pitch has 1,200 ft² of horizontal area. Multiply by 1.118034 for approximately 1,341.641 ft² of roof surface. A separately chosen 10% roofing allowance gives 1,475.805 ft², or 14.758 roofing squares of 100 ft² each. This is area, not a count of shingle bundles.Use the Square Footage Calculator to break a projection into non-overlapping shapes before applying the pitch factor. Different pitches require separate calculations.
What this geometry does not determine#
The slope length is not a finished rafter cut length. The tool does not deduct ridge-board thickness, locate birdsmouth cuts, size structural members, check loads or approve roofing products for a minimum slope. Roof shape, openings and cutting allowances still need the actual plan.
Sources#
Johnson Level’s CALC-1500 manual provides construction examples for pitch, rise, horizontal run and diagonal. Unit definitions follow NIST SP 811.