Roof Pitch Calculator

Roof Pitch is evaluated from Rise, Run and Full Roof Span. The calculation reports Roof Pitch, Slope Angle and Rafter Length.

Results

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About the Roof Pitch Calculator

Roof Pitch is treated here as a quantitative relation between Rise, Run and Full Roof Span and Roof Pitch, Slope Angle, Rafter Length and Total Rafter Length.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Pitch = rise / run x 12 (expressed as X/12)
Angle = arctan(rise / run) x (180/pi)
Rafter length per foot of run = sqrt(rise^2 + run^2) / run x 12
Total rafter length = (span / 2) x rafter length per foot of run / 12
Area multiplier = sqrt(rise^2 + run^2) / run
→ multiply flat (plan view) roof area by this factor to get actual sloped roof area.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Pitch = rise / run x 12 (expressed as X/12)
Angle = arctan(rise / run) x (180/pi)
Rafter length per foot of run = sqrt(rise^2 + run^2) / run x 12
Total rafter length = (span / 2) x rafter length per foot of run / 12
Area multiplier = sqrt(rise^2 + run^2) / run
→ multiply flat (plan view) roof area by this factor to get actual sloped roof area.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Standard residential: 6/12 pitch, 28-ft span

Inputs

rise: 6 run: 12 span_ft: 28

Roof Pitch: 6 X/12. Slope Angle: 26.57 deg. Rafter Length: 13.416 in/ft. Total Rafter Length: 15.65 ft. Roof Area Multiplier: 1.118 x

With Rise = 6, Run = 12 and Full Roof Span = 28 as the stated inputs, the result is Roof Pitch = 6 X/12, Slope Angle = 26.57 deg and Rafter Length = 13.416 in/ft. Each value corresponds to the declared output fields.

Example 2: Steep Victorian: 12/12 pitch, 32-ft span

Inputs

rise: 12 run: 12 span_ft: 32

Roof Pitch: 12 X/12. Slope Angle: 45 deg. Rafter Length: 16.971 in/ft. Total Rafter Length: 22.63 ft. Roof Area Multiplier: 1.4142 x

With Rise = 12, Run = 12 and Full Roof Span = 32 as the stated inputs, the result is Roof Pitch = 12 X/12, Slope Angle = 45 deg and Rafter Length = 16.971 in/ft. Each value corresponds to the declared output fields.

Example 3: Shed roof: 4/12 pitch, 12-ft span

Inputs

rise: 4 run: 12 span_ft: 12

Roof Pitch: 4 X/12. Slope Angle: 18.43 deg. Rafter Length: 12.649 in/ft. Total Rafter Length: 6.32 ft. Roof Area Multiplier: 1.0541 x

With Rise = 4, Run = 12 and Full Roof Span = 12 as the stated inputs, the result is Roof Pitch = 4 X/12, Slope Angle = 18.43 deg and Rafter Length = 12.649 in/ft. Each value corresponds to the declared output fields.

Example 4: Low slope addition: 2/12 pitch, 20-ft span

Inputs

rise: 2 run: 12 span_ft: 20

Roof Pitch: 2 X/12. Slope Angle: 9.46 deg. Rafter Length: 12.166 in/ft. Total Rafter Length: 10.14 ft. Roof Area Multiplier: 1.0138 x

With Rise = 2, Run = 12 and Full Roof Span = 20 as the stated inputs, the result is Roof Pitch = 2 X/12, Slope Angle = 9.46 deg and Rafter Length = 12.166 in/ft. Each value corresponds to the declared output fields.

Common Use Cases

Calculate roof pitch for a new construction project
Determine rafter length for a shed or garage
Convert roof pitch to degrees for material selection