Metric results use decimals. Fraction rounding never changes geometry.
Birdsmouth geometry depends on wall/top-plate dimensions, rafter depth, bearing requirements, connection details, and applicable construction rules. This calculator does not determine a birdsmouth cut.
Actual framing length may require adjustments for ridge, bearing, seat cuts, and connection details. This model uses ridge centerline geometry and makes no ridge-board deduction.
Common rafter slope length to wall line
160.9969 in · 13.416408 ft
Pitch 6:12 · roof slope angle from horizontal 26.57°
Common rafter to wall line 13' 5" (≈ 161"; 160.9969 in)
Horizontal run 12' 0" (≈ 144"; 144 in) · rise 6' 0" (≈ 72"; 72 in)
The plumb line is vertical; tool/saw angle conventions vary by reference surface. The displayed roof slope angle is measured from horizontal, not a saw setting.
Simple symmetrical gable roof with a ridge centered over the span. Geometric layout estimate only.
Actual framing length may require adjustments for ridge, bearing, seat cuts, and connection details. This model uses ridge centerline geometry and makes no ridge-board deduction.
Calculated slope lengths do not include all field adjustments for ridge details, bearing cuts, fascia/subfascia, fastening, waste, or site-specific conditions.
Construction note: This calculator provides geometric layout estimates. It does not determine structural capacity, lumber sizing, connection design, load requirements, or code compliance.
Full-precision inches internally; fractions are display only.
Birdsmouth geometry depends on wall/top-plate dimensions, rafter depth, bearing requirements, connection details, and applicable construction rules. This calculator does not determine a birdsmouth cut.
The plumb line is vertical; tool/saw angle conventions vary by reference surface. The displayed roof slope angle is measured from horizontal, not a saw setting.
Rafter Length & Roof Pitch Calculator Roof span: 24 ft; 24' 0" (≈ 288"; 288 in) Pitch: 6:12; input mode ratio Half-span run: 12' 0" (≈ 144"; 144 in) Rise: 6' 0" (≈ 72"; 72 in) Roof slope angle from horizontal: 26.57° Common rafter slope length to wall line: 13' 5" (≈ 161"; 160.9969 in) Horizontal overhang: 12 in; 1' 0" (≈ 12"; 12 in) Tail vertical fall: 0' 6" (≈ 6"; 6 in) Rafter tail slope length: 1' 1 7/16" (≈ 13 7/16"; 13.4164 in) Total geometric slope to fascia: 14' 6 7/16" (≈ 174 7/16"; 174.4133 in) Imperial fraction precision: nearest 1/16 inch (display only); metric uses decimals Half-span run = roof span ÷ 2 = 288 ÷ 2 = 144 in Rise = run × (pitch rise / 12) = 144 × (6 / 12) = 72 in Common rafter = √(run² + rise²) = 160.99689438 in Roof slope angle from horizontal = atan(pitch rise / 12) × 180 / π = 26.5650511771° Tail vertical fall beyond wall = horizontal overhang × pitch ratio = 6 in Tail slope = horizontal overhang × √(1 + pitch ratio²) = 13.416407865 in Total geometric slope to fascia = common slope + tail slope = 160.99689438 + 13.416407865 = 174.413302245 in Simple symmetrical gable roof; ridge centered over span. Span is between exterior wall/support lines. Geometric layout estimate only. Actual framing length may require adjustments for ridge, bearing, seat cuts, and connection details. This model uses ridge centerline geometry and makes no ridge-board deduction. Calculated slope lengths do not include all field adjustments for ridge details, bearing cuts, fascia/subfascia, fastening, waste, or site-specific conditions. Birdsmouth geometry depends on wall/top-plate dimensions, rafter depth, bearing requirements, connection details, and applicable construction rules. This calculator does not determine a birdsmouth cut. The plumb line is vertical; tool/saw angle conventions vary by reference surface. The displayed roof slope angle is measured from horizontal, not a saw setting. Construction note: This calculator provides geometric layout estimates. It does not determine structural capacity, lumber sizing, connection design, load requirements, or code compliance. OpenStax: Right Triangle Trigonometry: https://openstax.org/books/contemporary-mathematics/pages/10-8-right-triangle-trigonometry This Old House: Understanding and Determining Roof Pitch: https://www.thisoldhouse.com/roofing/determining-roof-pitch NIST Guide to the SI: length conversions: https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8
Enter roof span and pitch to calculate common-rafter length, rise, run, roof angle, and optional horizontal overhang geometry.
Enter the roof span between exterior wall/support lines, select pitch ratio or angle, then enter an optional horizontal overhang. Choose a convenience pitch or your own positive decimal rise per 12. Unit changes preserve physical measurements. Copy Rafter Results exports inputs, geometry, formulas and scope notes; Print / Save PDF includes the roof diagram. Reset restores 24 ft, 6:12, 12 in overhang, US and nearest 1/16 inch.
Common-rafter run = roof span / 2. Roof span is the horizontal distance between the two exterior wall/support lines used for this geometry. The simple symmetrical gable roof assumes a centered ridge. A 24 ft span gives a 12 ft run, not a 24 ft common-rafter run.
Geometry extends to the ridge centerline. No half-ridge-board subtraction, heel height or offset is applied. Actual framing length may require adjustments for ridge, bearing, seat cuts, and connection details. This model uses ridge centerline geometry and makes no ridge-board deduction.
Here roof pitch means rise per 12 units of horizontal run: pitchRatio = pitchRisePer12 / 12. A 6:12 pitch gives a ratio of 0.5. Historical uses of “pitch” can differ; this page consistently uses rise per run.
Positive decimal rises such as 6.5:12 are supported. Buttons for 3:12, 4:12, 5:12, 6:12, 8:12, 10:12 and 12:12 are conveniences only. The denominator remains 12; no preset is a structural or code recommendation.
This Old House explains rise measured over 12 horizontal inches (opens in a new tab). Its roof-material and design guidance is outside this geometry model.
Rise = commonRafterRun × pitchRatio. For the default, 12 ft × (6 / 12) = 6 ft. Rise is the vertical difference from the modeled wall line to the ridge centerline, not an added heel height or birdsmouth dimension.
angleDegrees = atan(pitchRatio) × 180 / π. The engine returns 26.5650511771° for 6:12, displayed as 26.57°. The reference is horizontal. Do not use the rounded displayed angle for subsequent calculations.
Common rafter length = √(commonRafterRun² + rise²), equivalently run × √(1 + pitchRatio²). The default gives 13' 5" (≈ 161"; 160.9969 in). The label is Common rafter slope length to wall line.
This is a geometric hypotenuse, not required lumber length or a stock order. OpenStax explains right-triangle tangent and hypotenuse relationships (opens in a new tab).
You can check common-rafter geometry as a right triangle using the supported run and rise. This verifies only the mathematical relationship, not lumber length, structural capacity or hip-and-valley geometry.
Horizontal overhang is the horizontal distance beyond the wall line, not distance along the sloped rafter. Tail vertical change = horizontal overhang × pitchRatio. Tail slope length = √(horizontal overhang² + tail vertical change²).
At 6:12, 12 in horizontal overhang gives 0' 6" (≈ 6"; 6 in) vertical fall and 1' 1 7/16" (≈ 13 7/16"; 13.4164 in) tail slope. Adding 12 in directly to the common slope would confuse horizontal and sloped lengths. Blank or zero overhang gives zero tail.
Total geometric slope to fascia = commonRafterLength + tailSlopeLength. Raw default lengths give 14' 6 7/16" (≈ 174 7/16"; 174.4133 in). Common slope, tail slope and total slope remain separate results.
Calculated slope lengths do not include all field adjustments for ridge details, bearing cuts, fascia/subfascia, fastening, waste, or site-specific conditions. Fascia/subfascia thickness, ridge board, bearing and cut details are not modeled.
Pitch to angle: θ = atan(pitchRisePer12 / 12) × 180 / π. Angle to pitch: pitchRisePer12 = tan(θ × π / 180) × 12. For 45°, the equivalent pitch is 12:12 within floating-point tolerance.
Switching input modes retains the unrounded physical pitch; formatted displays do not feed the conversion. Editing the angle defines a new physical pitch. Invalid inputs clear results rather than retaining the previous geometry.
Imperial construction displays show rounded feet/inches, reduced inch fractions and secondary decimal inches. Choose nearest 1/8, 1/16 or 1/32 inch; default is 1/16. Whole-inch carries are handled. The default tail at 1/16 is 13 7/16".
Fractions are display only. Internal geometry is full-precision inches; tail and total slope use raw values. Metric output uses decimal millimeters, not imperial fractions. NIST defines the international foot as 0.3048 m and the inch as 25.4 mm.
The existing construction parser/formatter is reused. Unmarked mixed numbers use the selected unit. Explicit ft/in/mm/cm/m suffixes and feet/inches notation specify their own unit; for example 24 ft, 24′, 24′ 6″ and 24 1/2 are supported. Arithmetic expressions are not accepted.
To check its decimal representation, convert the displayed tape-measure fraction separately. The displayed fraction is rounded; converting it does not recover full-precision geometry or supply an exact cut specification.
The roof visual identifies the centered ridge, wall lines, half-span run, rise, common rafter and horizontal overhang tail. Physical ratios inform its proportions, with clamps to keep the schematic legible. It is not a scaled framing drawing; the caption supplies every quantity as text.
Roof slope angle is measured from horizontal. The plumb line is vertical; tool/saw angle conventions vary by reference surface. The displayed roof slope angle is measured from horizontal, not a saw setting.
No numerical plumb-cut reference or saw-setting instruction is provided. A vertical plumb line and a tool dial can use different reference surfaces. This page does not prescribe cut geometry.
Birdsmouth geometry depends on wall/top-plate dimensions, rafter depth, bearing requirements, connection details, and applicable construction rules. This calculator does not determine a birdsmouth cut.
Actual framing length may require adjustments for ridge, bearing, seat cuts, and connection details. This model uses ridge centerline geometry and makes no ridge-board deduction. No birdsmouth notch depth, seat-cut depth, heel height, bearing length, ridge thickness or automatic stock-length suggestion is calculated.
Pitch 6:12; run 12' 0" (≈ 144"; 144 in); rise 6' 0" (≈ 72"; 72 in); angle 26.565051°; common slope 13' 5" (≈ 161"; 160.9969 in); horizontal overhang 1' 0" (≈ 12"; 12 in); tail 1' 1 7/16" (≈ 13 7/16"; 13.4164 in); total slope 14' 6 7/16" (≈ 174 7/16"; 174.4133 in).
Pitch 4:12; run 10' 0" (≈ 120"; 120 in); rise 3' 4" (≈ 40"; 40 in); angle 18.434949°; common slope 10' 6 1/2" (≈ 126 1/2"; 126.4911 in); horizontal overhang 0' 0" (≈ 0"; 0 in); tail 0' 0" (≈ 0"; 0 in); total slope 10' 6 1/2" (≈ 126 1/2"; 126.4911 in).
Pitch 12:12; run 10' 0" (≈ 120"; 120 in); rise 10' 0" (≈ 120"; 120 in); angle 45°; common slope 14' 1 11/16" (≈ 169 11/16"; 169.7056 in); horizontal overhang 0' 0" (≈ 0"; 0 in); tail 0' 0" (≈ 0"; 0 in); total slope 14' 1 11/16" (≈ 169 11/16"; 169.7056 in).
Pitch 6.9282032303:12; run 12' 0" (≈ 144"; 144 in); rise 6' 11 1/8" (≈ 83 1/8"; 83.1384 in); angle 30°; common slope 13' 10 1/4" (≈ 166 1/4"; 166.2769 in); horizontal overhang 0' 0" (≈ 0"; 0 in); tail 0' 0" (≈ 0"; 0 in); total slope 13' 10 1/4" (≈ 166 1/4"; 166.2769 in).
Pitch 6:12; run 3,000 mm; rise 1,500 mm; angle 26.565051°; common slope 3,354.1 mm; horizontal overhang 300 mm; tail 335.41 mm; total slope 3,689.51 mm.
Simple symmetrical gable/common-rafter geometry with a centered ridge. Not a hip, valley, gambrel, mansard, truss or full roof model. No structural rafter sizing, allowable span, species/grade, snow/wind/dead/live load, fastening or connection design is performed. No result verifies code compliance.
Construction note: This calculator provides geometric layout estimates. It does not determine structural capacity, lumber sizing, connection design, load requirements, or code compliance. Calculated slope lengths do not include all field adjustments for ridge details, bearing cuts, fascia/subfascia, fastening, waste, or site-specific conditions. Actual framing length may require adjustments for ridge, bearing, seat cuts, and connection details. This model uses ridge centerline geometry and makes no ridge-board deduction.
Software bounds: span 0.000001–100,000,000 normalized inches; overhang 0–100,000,000 inches; pitch rise 0.000001–1,000,000 per 12; derived lengths at most 1,000,000,000,000 inches. Angle must also be greater than 0° and less than 90° and resolve within the pitch bounds. These are software limits, not construction criteria. Input strings are capped at 64 characters; the shared fraction parser bounds denominators to 4096. Invalid measurements clear geometry and disable copy/print.
Calculations remain local to this page session, without saved projects, numeric URL persistence or network calculations.
Divide span by two, calculate rise as run × pitch rise / 12, then take √(run² + rise²). This gives geometric slope to the wall line.
For a symmetrical gable with centered ridge, the horizontal distance from one exterior wall line to the ridge is half the distance between the two wall lines.
Multiply the half-span run by the pitch ratio, expressed as rise per 12 horizontal units divided by 12.
Take atan(pitch rise / 12) and convert radians to degrees. The angle is measured from horizontal.
Multiply tan(angle in radians) by 12. Input mode changes preserve the unrounded pitch.
Horizontal overhang adds a sloped tail equal to overhang × √(1 + pitch ratio²). Total geometric slope is the raw common slope plus raw tail slope.
The input is horizontal beyond the wall line. The calculated tail slope is a different length at positive pitch.
They provide familiar construction measurement references alongside decimal results. Fraction precision is display only; metric results use decimals.
No. It does not calculate bearing or birdsmouth cuts, select lumber size or recommend stock length. Field and structural details require separate work.
No. It is a geometric estimate only and does not verify capacity, loads, connections, allowable spans or applicable building rules.
Reviewed October 4, 2026. These references explain right-triangle geometry, rise-per-run terminology, measurement concepts and exact length conversions. No source endorses BuzCalculator; structural and code design rules are not imported.