Solve a single-slope rafter from the span and the difference between high and low plate heights—or from pitch. Get the slope length, tails at either end and plumb and seat angles for a shed or lean-to roof.
A shed or lean-to roof has one sloped plane instead of two planes meeting at a central ridge. That makes the basic geometry direct: the horizontal span is one side of a right triangle, the difference between the high and low plate heights is the other side, and the rafter forms the hypotenuse. If the rest of the building uses gable framing, the main roof rafter length calculator covers the common rafter case; after the shed rafter is seated, the birdsmouth calculator can help check the notch at the supporting plate.
Measure span between the same support references used in the framing plan, usually the relevant faces or centerlines of the two walls, ledgers or beams. Measure rise vertically between the bearing elevations, not by subtracting nominal wall heights that may start at different floor levels. The calculator then finds length as sqrt(span^2 + rise^2). Because there is only one slope, there is no automatic halving of the building width as there is when finding the run of a symmetric common rafter.
If the two plate heights are known, enter their difference as the rise. This is usually the most reliable method for a lean-to attached to an existing building, where the upper ledger elevation and the new outer wall plate determine the roof. If the architectural plan specifies pitch instead, enter span and pitch; rise is span multiplied by pitch / 12. A 3 ft rise over 12 ft, a ratio of 0.25 and a 3/12 pitch all describe the same slope.
Be precise about horizontal span. Roof pitch is rise per unit of horizontal run, not rise per foot measured along the sloping board. Likewise, an overhang entered as a horizontal eave projection must be extended when it is converted to board length along the slope. The result should show the bare line length separately from tails so you can audit the additions. That distinction is especially important on a shed roof because there may be an overhang at the low eave, the high side, or both.
| Pitch | Rise over 12 ft span | Roof angle | Line length |
|---|---|---|---|
| 1/12 | 1 ft 0 in | 4.8° | 12 ft 1/2 in |
| 2/12 | 2 ft 0 in | 9.5° | 12 ft 2 in |
| 3/12 | 3 ft 0 in | 14.0° | 12 ft 4 7/16 in |
| 4/12 | 4 ft 0 in | 18.4° | 12 ft 7 13/16 in |
| 6/12 | 6 ft 0 in | 26.6° | 13 ft 5 in |
Take a lean-to that spans 12 ft horizontally and drops 3 ft from its high bearing to its low plate. Its ratio is 3 / 12, so it is a 3/12 slope with a 14.0-degree angle. The rafter line length is sqrt(12^2 + 3^2) = sqrt(153) ft, which converts to 12 ft 4 7/16 in. This is the distance between the selected bearing references before any tail extensions are added.
Now suppose the roof projects 12 in horizontally beyond both supports. At this shallow angle, each 12 in horizontal projection becomes 12 3/8 in measured along the rafter. Adding both tails gives 14 ft 5 3/16 in. If the high end terminates against a wall with no overhang, add only the low tail; adding both by habit would leave an unwanted projection through or beyond the supporting wall.
Square the 12 ft span and the 3 ft rise, add the results and take the square root. The slope is equivalent to 3/12.
At a 14.0-degree roof angle, a 12 in horizontal tail becomes 12 3/8 in along the board. The example uses the same 12 in projection at both ends.
Add the two slope tails to the bare line length only if the design truly overhangs at both the high and low ends.
Both ends of a shed rafter are commonly laid out with plumb cuts suited to their supports, while the low plate may require a birdsmouth or another specified bearing detail. State and use angles from the top edge of the board consistently. Test the first rafter at both supports before cutting the set. On an addition, the existing wall may not be plumb and the ledger line may not be perfectly level; the pattern should reflect the chosen bearing points rather than an average of several conflicting measurements.
A shallow single slope moves all its water to one eave, so gutter capacity, flashing at the high wall and the roof covering's minimum slope are practical design issues, not finishing details. Some membranes and metal systems are made for low slopes; ordinary shingles may have special underlayment requirements or may be unsuitable at a given pitch. The length result does not certify the roof covering. Check the manufacturer's slope limits and local requirements before framing fixes the pitch.
Use this calculator for a single rectangular slope whose rafters run directly from one bearing line to another. It is ideal for checking board length, comparing a proposed plate height with a desired pitch, and planning tails before cutting. It does not account for deflected or cambered members, stepped supports, openings, dormers or a slope that changes pitch. Those conditions divide the roof into separate geometry problems.
It also does not size the rafter. A 12 ft clear span in a light garden shed and a 12 ft span carrying snow over a habitable addition cannot be treated as the same structural case merely because the board length matches. Spacing, species, grade, depth, bearing length, ledger fastening and lateral support all matter. Use the applicable code or span design for the actual building, and obtain engineering where the addition ties into an existing structure in a way the prescriptive code does not cover.
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.
Use the horizontal distance between the two support or plate lines for span, and the vertical difference between those plate heights for rise. The rafter length is the sloped hypotenuse: sqrt(span^2 + rise^2).
Divide rise by span and multiply by 12. A 3 ft rise over a 12 ft span is 3/12. Conversely, rise equals span multiplied by pitch / 12 when the pitch is known.
Yes, if the calculator fields are completed for both ends. A horizontal overhang becomes longer along the slope, so each tail is its horizontal projection divided by the cosine of the roof angle.
The upper end may bear on a ledger, wall, beam or header depending on the design. Keep the connection and support condition consistent with the plans and local code; the length geometry does not design that connection.
The calculator determines geometric length, not allowable span. Lumber depth and grade depend on span, spacing, snow and roof loads, support conditions and local code. A long single slope may need larger or engineered members.
Check whether one wall height was measured from a different floor or grade reference and confirm which faces of the supports define span. Small height errors change both pitch and the seat and plumb angles.
The full common rafter: length, angles, birdsmouth and materials.
Line and cut lengths and angles for the diagonal rafter on a hip roof.
Where two roof planes meet — valley length and its cut angles.
First jack length and the common difference for your spacing.
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.