A shed roof has one slope, one high wall, and one low wall, and the rafter runs the whole span in one piece. That makes the math simpler than a gable roof in one way and trickier in another: simpler, because there is no ridge and no birdsmouth in the middle, and trickier, because the run is the full span instead of half of it, so a small change in pitch moves the length more. The same right triangle still applies: the run is the span, the rise is the span times the pitch divided by 12, and the rafter length is the square root of the span squared plus the rise squared. This guide works through shed and lean-to roofs with real numbers, including the overhang and the spacing, and the rafter calculator checks any shed span and pitch if you enter the span as the building span and halve the answer in your head, or simply use the worked examples below.
The Shed Rafter Formula
On a gable roof the run is half the span. On a shed roof the run is the span, because the rafter crosses the whole building from the high wall to the low wall. A 12 ft shed span at 3/12 pitch has a 12 ft run and a 3 ft rise, so the rafter is the square root of 144 plus 9, which is the square root of 153, or 12 ft 4 7/16 in. A 10 ft shed at 4/12 pitch has a 10 ft run and a 3.33 ft rise, so the rafter is the square root of 100 plus 11.11, which is 10 ft 6 1/2 in. A 14 ft shed at 2/12 pitch has a 14 ft run and a 2.33 ft rise, so the rafter is the square root of 196 plus 5.44, which is 14 ft 2 5/16 in. A 16 ft shed at 4/12 pitch has a 16 ft run and a 5.33 ft rise, so the rafter is the square root of 256 plus 28.44, which is 16 ft 10 3/8 in. The low pitches keep the lengths close to the span: at 2/12 pitch the rafter is only 2 5/16 in longer than the span, while at 4/12 pitch on the same span it is 10 3/8 in longer.
| Shed span | Pitch | Rise | Rafter length |
|---|---|---|---|
| 10 ft | 4/12 | 3.33 ft | 10 ft 6 1/2 in |
| 12 ft | 3/12 | 3 ft | 12 ft 4 7/16 in |
| 14 ft | 2/12 | 2.33 ft | 14 ft 2 5/16 in |
| 16 ft | 4/12 | 5.33 ft | 16 ft 10 3/8 in |
The overhang on a shed roof is usually bigger than on a house roof, because the low slope needs more horizontal reach to throw water clear of the wall. An 18 in overhang at 3/12 pitch gives a 1 ft 6 9/16 in tail, so the 12 ft shed rafter becomes a board close to 14 ft long once the tail is added. A 24 in overhang at 4/12 pitch gives a 2 ft 1 5/16 in tail, so the 16 ft shed rafter becomes a board close to 19 ft long. Measure the overhang from the low wall, not from the high wall: the high end of a shed rafter usually ends flush with the high wall or with a small fascia, and the tail that matters is the one at the low end, where the water runs off.
Lean-To Roofs Against a Wall
A lean-to is a shed roof with one end carried by the wall of the house instead of by its own high wall. The math is the same, but the measurements change: the span is the distance from the house wall to the outside posts, and the rise is set by how high the ledger board sits on the house wall. A 10 ft lean-to at 3/12 pitch rises 2.5 ft over its 10 ft span, so the rafter is 10 ft 3 11/16 in long. An 8 ft lean-to at 4/12 pitch rises 2.67 ft, so the rafter is 8 ft 5 3/16 in. The ledger height is the number to set first: measure down from the eaves of the house roof to where the ledger will sit, check that the pitch that results is at least 3/12, and if it is not, lower the outside posts or raise the ledger. A lean-to that is too flat holds water and snow against the house wall, which is the worst place for a leak to start.
Shed Rafter Spacing and Size
Shed rafters usually sit at 16 in or 24 in on center, and the choice depends on the roofing. A shingled shed needs 16 in spacing, because the sheathing spans between the rafters and shingles need a solid deck. A metal roof shed can use 24 in spacing, because the metal panels are carried by purlins that run across the rafters, and the purlins spread the load. The lumber size follows the span: a 2×4 rafter is only a starting point for spans up to about 8 ft, a 10 ft shed span at 3/12 pitch should use 2×6 rafters, and a 12 ft span should use 2×6 at 16 in on center at a minimum. A 14 ft or 16 ft shed span needs 2×8 rafters, because the span is long and the pitch is low, and low-pitch rafters carry more of the snow load as bending than steep rafters do. The rafter spacing and size post compares the lumber sizes in full, including the 16 in and 24 in spacing choice.
Count the rafters the same way as a house roof: divide the shed length in inches by the spacing and add one. A 12 ft long shed at 16 in on center is 144 divided by 16, which is 9 spaces, plus one, which is 10 rafters. A 20 ft long shed at 24 in on center is 240 divided by 24, which is 10 spaces, plus one, which is 11 rafters. Order one spare board for a miscut, and pick the straightest board for the pattern rafter, because a shed roof shows a crooked rafter more than a house roof does: there is no second slope to hide it behind, and the fascia line is the first thing anyone sees.
What Goes Wrong on Shed Roofs
Three mistakes cover most shed roof trouble. The first is a pitch that is too flat: below 2/12 pitch, shingles will not shed water reliably, and the roof needs a low-slope membrane instead. If the shed is already built at 2/12 or flatter, do not re-shingle it: change the roofing to a membrane or rebuild the slope. The second is a tail that is too short: a shed roof with no overhang dumps water straight down the wall, and the wall rots from the top down. Give the low end at least 12 in of overhang, and 18 in is better. The third is rafters that are too small for the span, which shows up as a sag in the middle of the roof after the first heavy snow. Lake County snow load is 25 psf ground snow load per ASCE 7, and it applies to sheds as well as houses. If the roof already sags, sistering a second rafter alongside each one is the usual fix, and the screws for that work should be 3 in structural screws, long enough to pass through both 2x members.
Before you order lumber, run the numbers once more: the span, the pitch, the rise, the rafter length, the tail, and the count. The rafter calculator checks the gable version of the same triangle, and the rafter length chart lists the common lengths for the standard spans. A shed roof is a small job, but it is still a roof, and the same rule applies as on a house: cut one pattern rafter, test-fit it, and only then cut the rest.
Related reading: rafter calculator, plus our guides on rafter length chart and rafter spacing and size, and the roofing calculators hub.
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Frequently Asked Questions
How do you calculate rafter length for a shed roof?
A shed roof is a single slope, so the run is the full span instead of half of it. The rafter length is the square root of the span squared plus the rise squared, where the rise is the span times the pitch divided by 12. A 12 ft shed span at 3/12 pitch rises 3 ft, so the rafter is the square root of 144 plus 9, which is 12 ft 4 7/16 in.
What pitch should a shed roof be?
A 3/12 or 4/12 pitch is the usual choice for a shed in Lake County: steep enough to shed water and snow, shallow enough to keep the high wall low. A 2/12 pitch is the minimum for most shingles, and below that the roof needs a low-slope membrane instead of shingles. A steeper pitch costs more lumber and a taller high wall, but it sheds the Chicago area snow load of 25 psf far better than a flat roof does.
How long should shed roof rafters be for a 12 ft shed?
At 3/12 pitch, a 12 ft shed span gives a 12 ft 4 7/16 in rafter from the high wall to the low wall, before the overhang. With an 18 in overhang at the low end, the tail adds 1 ft 6 9/16 in, so the total board is close to 14 ft. At 4/12 pitch the same 12 ft span gives a 12 ft 7 13/16 in rafter, because the rise is 4 ft instead of 3 ft.
What is rafter spacing for a metal roof shed?
Rafters at 24 in on center are common for a metal roof shed, because the metal panels span the wider spacing and the shed carries a light load. Purlins run across the rafters and carry the panels, so the rafter spacing and the purlin spacing work together: 24 in rafter spacing with purlins at 24 in on center is a standard metal shed layout. For a shingled shed roof, 16 in on center is the safer spacing, because the sheathing needs the closer support.
Can I use 2×4 rafters for a shed roof?
Only on a very short span. A 2×4 rafter at 16 in on center is a starting point for spans up to about 8 ft, and even then only on a light shed with a steep pitch. A 10 ft shed span at 3/12 pitch should use 2×6 rafters, and a 12 ft span should use 2×6 at 16 in on center at a minimum. The cost saved by using 2×4 lumber is small against the cost of a sagging shed roof, and the snow load in Lake County is the same 25 psf whether the building is a house or a shed.
Zayn Robert is a content specialist focused on roofing, construction, and home improvement topics. He creates easy-to-understand guides that help homeowners learn about roof measurements, materials, maintenance, and repair decisions. His work combines detailed research with practical insights from roofing professionals at Zuniga Roofing Inc.