Measurement & project guide
Resolve rise, run and roof area without mixing them
Enter pitch, an angle, a percent grade or a measured rise and run. Then use the slope factor on the correct horizontal footprint. The geometry is useful only when the measurement basis is clear.
- A Horizontal run
- B Vertical rise
- C Sloped length
Before you calculate
- Pitch or angle
- Pitch is rise per 12 horizontal units; an angle is measured from horizontal. A 6:12 pitch is not six degrees.
- Run and overhang
- State whether the input is ridge-to-eave run or full span, and whether the entered overhang is horizontal.
- Roof footprint
- Use the horizontal projected area for the slope multiplier. Separate roof planes with different pitches.
Read the result before using it
- Pitch, angle and grade
- Equivalent descriptions of one slope: ratio, degrees and percent.
- Slope factor
- The multiplier from horizontal area or run to sloped area or length.
- Order area
- An area with your entered allowance. Valleys, hips, penetrations and product courses need a real roof takeoff.
Check before ordering or handing over
- Measure from a safe location; do not access a roof just to obtain a calculator input.
- Check every plane's pitch and footprint on the roof drawing.
- Use the roofing manufacturer's slope limits, coverage and installation instructions.
Detailed results and planning tools
View calculations, report and comparisons
Calculation breakdown
These values reflect the editable inputs and assumptions above.
| Quantity | Value |
|---|
Calculation report
Includes formulas, entered assumptions, limitations and sources.
Compare scenarios
Keep up to three alternatives to compare measured values and assumptions.
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.
Frequently asked questions
What does a 6:12 roof pitch mean?
The roof rises 6 units for every 12 units of horizontal run. Its angle is approximately 26.565 degrees and its slope is 50 percent.
Is roof run the same as full span?
No. A symmetrical gable has a run equal to half its full horizontal span. Shed roofs and unequal roof faces require their actual measured run.
How do I calculate sloped roof area?
Multiply horizontal projected roof area by the square root of one plus slope squared. This applies when all included roof faces share one pitch and projection areas do not overlap.
Is the slope length a rafter cut length?
No. It is right-triangle geometry only. Ridge thickness, birdsmouth cuts, structural sizing and connection details are excluded.
Does the eave overhang input increase roof area?
It increases the reported geometric slope length only. The two projected roof-area dimensions must already include all overhangs.