Check the same triangle
Enter a 6/12 pitch and 12-foot run in the rafter length calculator. The pitch method and the rise-and-run method should agree because they describe the same right triangle.
How to Figure Rafter Length
A common rafter follows the hypotenuse of a right triangle. Identify the horizontal run and vertical rise for one roof plane, solve the triangle, then handle any overhang as a separate extension of the run.
Have two sides or a pitch and run? Use the rafter calculator →
The rafter triangle: rise, run, and length
Figuring rafters starts with one right triangle for one roof plane. Run is the level distance from the outside wall line to the ridge centerline. Rise is the vertical distance from that same wall-line elevation to the ridge-line elevation. The geometric rafter length is the sloped hypotenuse connecting those two points.
Keep these definitions tied to the same reference points. The rafter's line length is not the building span, and the run is not the distance measured up the roof. On a centered, symmetrical gable, each side usually has half the total span as its run. A shed roof or an off-center ridge needs its actual horizontal run instead. Hips and valleys follow different plan geometry and should not be treated as common rafters.
Method 1: Figure rafter length from rise and run
When rise and run are known in the same unit, use the Pythagorean theorem: rafter length = √(run² + rise²). Square each leg, add the results, and take the square root. Do not add rise and run directly; the diagonal is shorter than that sum.
Set the two legs
For a roof plane with 12 feet of horizontal run and 6 feet of vertical rise, keep both values in feet. The triangle represents the reference line from the wall line to the ridge, before an eave tail.
Square and add
Twelve squared is 144. Six squared is 36. Add them to get 180 square feet in the intermediate calculation. The units return to feet after taking the square root.
Take the square root
√180 is 13.4164 ft. PitchCalc displays that result as13.4 ft. Keep extra precision through later geometry and round the displayed line length only at the end.
Method 2: Figure rafter length from pitch and run
Pitch supplies the rise-to-run ratio. For an X/12 pitch, calculate rise as run × (pitch ÷ 12), then use the hypotenuse formula. With a 6/12 pitch over a 12-foot run, rise is 12 × (6 ÷ 12), or 6 feet. The triangle is now the same 6-by-12 example, so its rafter line length is 13.4164 feet, displayed as 13.4 feet.
The direct route is run × pitch multiplier. A 6/12 multiplier is 1.118, so 12 × 1.118 = 13.4 ft at the site's displayed precision. Use the roof pitch chart to look up common multipliers. If the pitch itself is unknown, get rise and run from the roof pitch calculator before figuring the member.
Do not confuse ratio inches with feet
The 6 and 12 in 6/12 define a dimensionless ratio. They do not force the actual roof to have a 12-inch or 12-foot run. Scale that ratio to the real run, keeping real rise and run in one unit.
Method 3: Work backward from a known length
A renovation or field check may give you the rafter line length and one leg. Rearrange the same triangle instead of guessing the other leg. If length and run are known, rise = √(length² − run²). If length and rise are known, run = √(length² − rise²). Use wall-to-ridge measurements from matching endpoints. In the calculator’s inverse modes, exclude the rafter tail from the length input and enter its horizontal overhang separately.
The rafter length must exceed either positive leg. If a claimed 12-foot rafter is paired with a 13-foot run, the triangle is impossible; the value may be a nominal stock length, a different reference point, or a bad measurement. When length equals run, rise is zero. That is a flat triangle, not a pitched rafter. The formulas and rounding rules are listed on the methodology page.
Overhangs and rafter tails
In this centered gable example, the wall-to-wall span is 24 ft and each run is 12 ft. A 6 ft rise gives a 13.4 ft wall-to-ridge line. Adding a 1 ft horizontal overhang extends the run to 13 ft, giving a 14.5 ft total sloped line. The overhang belongs outside the wall line, not inside the span or the original run.
An eave overhang extends the horizontal run beyond the exterior wall line while following the same pitch. If the main run is 12 feet and the horizontal overhang is 1 foot, solve the sloped line over a total 13-foot run, or calculate the tail's sloped extension separately with the same multiplier. Measure a horizontal projection, not the already sloped tail.
This produces a geometric reference-line length only. It does not locate a birdsmouth, size a seat cut, set a plumb cut, deduct for ridge-board thickness, establish fascia geometry, or select lumber. Those details depend on the framing layout, member depth, connection, loads, product, and code. A line-length answer is useful for geometry and estimating, but it is not a cut list or structural design.
Common mistakes when figuring rafters
Most bad rafter numbers come from mismatched reference points or units, not from the square-root operation.
Using span instead of run
Span crosses the whole building. A common rafter covers one roof plane. On a centered symmetrical gable, divide span by 2 to get run. Verify the ridge location on an asymmetrical or altered roof.
Mixing inches and feet
Convert all real lengths before solving. Six feet is 72 inches, while 6 inches is 0.5 foot. Decimal feet are not feet-and-inches notation: 12.5 feet means 12 feet 6 inches.
Measuring from different endpoints
Rise, run, and length must describe one triangle. Mixing wall-line run with a rafter length that includes the tail creates a result that cannot reconcile until the overhang is separated.
Trusting a sagging ridge
Existing framing may have settled, bowed, or been altered. A measured ridge height can describe current geometry without describing the intended plan. Compare multiple rafters and available drawings before turning one field reading into a layout.
What to do with the rafter length
Label the result as a geometric line length and record whether it includes the horizontal overhang. Keep the unrounded value for follow-on calculations. To check rise, run, pitch, inverse modes, and overhang in one place, open the rafter calculator.
Before cutting material, establish the actual ridge, wall, bearing, and fascia details; lay out plumb and seat cuts separately; and verify the design against the plans, product requirements, and local code. Triangle math answers how long the reference line is. It does not decide whether the proposed member or connection is safe.
Figuring rafters FAQ
Short answers for checking rafter triangles, pitch, span, and overhang.
How do I figure rafter length from rise and run?
Use the Pythagorean theorem: rafter length = √(run² + rise²). A 12-foot run and 6-foot rise produce a geometric line length of 13.4164 feet, displayed as 13.4 feet.
How do I calculate rafter length from roof pitch?
First find rise by multiplying run by pitch divided by 12, then solve the right triangle. You can also multiply run directly by the pitch multiplier. At 6/12, a 12-foot run times 1.118 is about 13.4 feet.
Is roof span the same as rafter run?
No. Span is the full horizontal width between supports. On a centered, symmetrical gable roof, one common rafter usually has a run equal to half the span. Verify the actual ridge location before using that shortcut.
Does calculated rafter length include the overhang?
Only if you extend the horizontal run by the overhang before solving. The extension follows the same pitch. The result is still a geometric line length and does not include fascia details, ridge deductions, or cut layout.
Does this method tell me where to make a birdsmouth or plumb cut?
No. Triangle math gives a reference line length only. Birdsmouth, seat and plumb cuts, ridge details, connections, lumber sizing, loads, and code compliance require a separate framing layout and structural check.