Free · Roofing calculators 🏠
Roof Slope Area & Entered Unit Cost
Convert horizontal projected area into a uniform-pitch surface area and apply an entered price per area unit.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A horizontal projection of 80 m² at a 9:12 rise-to-run pitch has surface area 100 m². At 30 per m², the entered area-based cost is 3,000.
Pitch = rise/run = tangent(angle); surface area = horizontal area ÷ cosine(angle); cost = surface area × entered unit cost
Worked example
Enter these known values and leave the other values blank.
- Horizontal projected length
- 10 m
- Horizontal projected width
- 8 m
- Rise for 12 units of run
- 9 :12
- Entered cost per selected area unit
- 30 USD / m²
- Horizontal projected area
- 80 m²
- Slope angle from horizontal
- 36.87 deg
- Rise-to-run slope as percent
- 75 %
- Uniform-slope surface area
- 100 m²
- Area-based cost
- 3000 USD
Assumptions and limitations
- Horizontal projected dimensions or area are positive. The model assumes the same slope magnitude over the full projection; different-pitch sections need separate calculations.
- Slope ranges from zero to less than 90 degrees. A flat surface has the same area as its horizontal projection.
- Include overhangs in the horizontal projection if they should count. Dormers, complex transitions, waste, overlaps, penetrations and extra material layers are not added automatically.
- Entered unit cost and total cost are nonnegative arithmetic inputs. The tool does not estimate structural capacity or choose a roofing system.
Common questions
Is 9:12 pitch the same as nine degrees?
No. It means rise/run = 9/12 = 0.75, or 75% slope. Its angle is the inverse tangent of 0.75.
Should I use the sloped length as the projected length?
No. Enter horizontal projected dimensions. The cosine factor then converts the projection to the sloped area.
References
- OpenStax: right-triangle slope relationships
- NIST: exact length and volume conversions
- Calculation definition and unit reference
Bookify includes the valid flat-roof and zero-cost boundaries while retaining positive projected area and slopes below 90 degrees.
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