Calculate the diagonal rafter that supports the inside corner where two equal-pitch roofs meet. Get its line length, cut length, tail, ridge deduction and cut angles from the common run and pitch.
A valley rafter sits beneath the internal angle formed by two intersecting roof planes. It supports the ends of jack rafters and carries the framed corner while the finished valley above it directs water down to the eave. For the main roof members, the standard rafter length calculator handles the commons; this page solves the diagonal valley, and the matching hip rafter length calculator covers the same plan geometry at an outside corner. The distinction matters for installation and flashing even where the length equations coincide.
On a regular intersection with equal pitches, the valley bisects the plan angle and runs at 45 degrees. Its horizontal run is therefore the common run multiplied by sqrt(2), while the rise is unchanged. Because that rise is spread over a longer run, the valley is shallower than the common rafter. Its angle is atan(tan(common pitch angle) / sqrt(2)), and its line length is sqrt(valley run squared + rise squared). At a 6/12 common pitch, for example, the valley acts at 4.24/12 over its own run and stands at 19.5 degrees.
Enter the common run for the roof plane, its pitch, the horizontal overhang where the valley reaches the eave, ridge or intersecting member thickness. Work from the plans' controlling intersection rather than measuring a convenient shingle valley on an existing roof. Surface valleys can be offset by roofing build-up and do not necessarily reveal the centerline of the framing member below.
The output distinguishes the theoretical line length from the cut length. The diagonal tail is overhang x sqrt(2) / cos(valley angle), and the ridge deduction is (ridge thickness / 2) x sqrt(2) / cos(valley angle) when the end condition uses that centerline deduction. Angles are stated from the top edge of the board so the plumb and seat cuts can be transferred without silently changing reference. If another framing method states an angle from vertical or from the board's end, convert it before marking.
| Common pitch | Valley rise per 12 in of valley run | Valley angle | Valley length per 1 ft of common run |
|---|---|---|---|
| 4/12 | 2.83/12 | 13.3° | 17.44 in |
| 5/12 | 3.54/12 | 16.3° | 17.69 in |
| 6/12 | 4.24/12 | 19.5° | 18.00 in |
| 8/12 | 5.66/12 | 25.2° | 18.76 in |
| 10/12 | 7.07/12 | 30.5° | 19.70 in |
| 12/12 | 8.49/12 | 35.3° | 20.78 in |
Suppose the intersecting roof has a 12 ft common run at 6/12. The common rafters rise 6 ft over that run. The valley's horizontal distance is not 12 ft; it is the diagonal across a square plan corner, 12 ft multiplied by sqrt(2), which is 16 ft 11 5/8 in rounded to the nearest sixteenth. Combining the diagonal run with the same 6 ft rise produces a valley line length of exactly 18 ft and a valley pitch angle of 19.5 degrees.
For a board with a 12 in horizontal overhang and a 1.5 in ridge member, the tail contributes 18 in along the valley slope. The ridge deduction contributes a subtraction of 1 1/8 in. Add and subtract those from the 18 ft line length to get a 19 ft 4 7/8 in cut length. Verify which end condition your framing plan uses before cutting: some valley layouts terminate at another structural member rather than at a conventional ridge centerline.
The 12 ft common run becomes 16 ft 11 5/8 in in plan because 12 x sqrt(2) = 16.9706 ft. The rise remains 6 ft.
Combine the diagonal run and rise as a right triangle: sqrt(16.9706^2 + 6^2). The result is the clean benchmark for this pitch and run.
Add an 18 in diagonal tail for a 12 in horizontal overhang, then subtract a 1 1/8 in ridge deduction for a 1.5 in ridge board.
Mark the plumb and seat cuts from the top edge of the board, then test the valley in position before using it as a pattern. Its ends should bear as intended, the birdsmouth or lower connection should not float, and its top should support the intersecting planes without pushing either plane out of line. Because the valley is concealed after the roof is built, correct a twisted or crowned board now rather than relying on jack rafters to pull it into place.
Treat the structural valley and the weather surface as related but separate systems. Woven shingles, closed-cut valleys and open metal valleys place different demands on the surface above the board, and underlayment laps are critical where two drainage paths merge. Follow the roofing manufacturer's instructions and local code for flashing width, fasteners and ice-barrier requirements. No length calculation can compensate for a valley surface that directs water under the roof covering.
This calculator assumes the two roof planes have the same pitch, their wall plates form the expected plan geometry, and the valley follows the 45-degree bisector. It provides conventional framing geometry for board layout and material estimation. It does not size the valley member for structural load. Valleys collect load from both roof planes, so member size, species, grade, supports and any doubled or engineered construction must come from the project design, span resources and local code.
Unequal pitches move the valley away from the 45-degree plan line and create different angles on each side. A dormer intersection may also involve sleepers, a valley board laid over an existing roof, or a structural valley with a different support condition. Do not force those cases into the equal-pitch equation. Establish the actual intersection in plan and elevation, then calculate each side from that geometry or follow the engineered framing plan.
Every result on this page comes from the method described above, using standard framing geometry and the published data credited below. Found a number that looks wrong? Use Report an Error — every report is read.
The valley lies where two roof surfaces drain toward each other. A hip carries an outside corner and sheds water away on both sides, while a valley concentrates runoff and needs compatible flashing or a woven or metal valley system.
The equal-pitch geometry is the same: hip run equals common run x sqrt(2), and hip or valley length is sqrt(hip run^2 + rise^2). The difference is application and installation, not this basic length triangle.
No. Dividing 6 by sqrt(2) gives 4.24 because the same rise is spread over a longer diagonal run. The valley angle is 19.5 degrees even though both intersecting common rafters are at a 6/12 pitch.
Only if both roof planes have the same pitch and the valley bisects their plan angle at 45 degrees. Unequal pitches shift the valley line and require plan geometry for the actual intersection.
Both matter. The valley board supports the jack rafters and roof planes, while the finished valley surface and flashing manage the concentrated water. A correct board length does not excuse incompatible flashing, underlayment or shingle detailing.
Recheck the common run, ridge or intersection point, and both plate lines. In remodeling, unequal wall heights, sagging plates and roof planes that are not truly equal pitch are common causes.
The full common rafter: length, angles, birdsmouth and materials.
Line and cut lengths and angles for the diagonal rafter on a hip roof.
First jack length and the common difference for your spacing.
Single-slope rafters between two different wall heights.
Seat cut, heel height and HAP, checked against the IRC one-quarter limit.
Plumb, seat and cheek angles — plus the saw settings to cut them.
Convert pitch, rise/run, degrees and percent, both ways.
How far a board can span — IRC tables by species, grade and load.
The lumber size a span actually needs. The inverse of the span tool.
Two pitches, one roof — upper and lower rafter lengths.
The full pitch × run table, printable for the workshop wall.
Figure any rafter by hand — formula and framing-square methods.