Shed Roof Truss Calculator

The only page dedicated to the single-slope family: mono truss geometry, lean-to connections into an existing wall, minimum drainage pitch, and a complete 12 ft shed example — one slope, solved end to end.

Mono Truss Calculator — One Slope, One Height Difference

A shed roof is a right triangle: span and pitch fix the rise, the rise fixes the low wall, and the hypotenuse is your rafter.

Span (ft)High wall height (ft)Pitch (x/12)Building length (ft)Truss spacing (in o.c.)

Total rise

3.00 ft

36 in of fall

Low wall height

7.00 ft

high wall minus rise

Rafter (top chord)

12 ft 6/16 in

12.369 ft exact

Truss count

on 16 ft at 24 in o.c.

✓ Asphalt shingles OK⚠ Double underlayment zone (below 4/12)Slope angle 14.0°

Mono Truss Geometry: The One-Slope Method

Every mono pitch roof truss is a right triangle wearing a roof: the span is the base, the pitch sets the rise, and the top chord is the hypotenuse. Where a gable truss negotiates two mirrored slopes, a mono truss has one slope and one height difference, so the entire geometry reduces to three formulas the calculator runs on every keystroke.

Rise = (pitch ÷ 12) × span

A 3/12 roof over 12 ft rises exactly 3 ft — one inch of fall per four inches of run. This single product drives everything else: the low-wall height, the rafter length, and how fast the roof dumps water toward its eave.

Low wall = high wall − rise

The height difference between walls is the rise, no more. A 10 ft high wall under that 3/12 example lands on a 7 ft low wall. When the low wall drops below about 4 ft the shed stops being usable on that side — the calculator flags it in red.

Rafter = √(span² + rise²)

The Pythagorean hypotenuse: √(144 + 9) = 12.369 ft for the 12 ft example, which orders as a 14 ft board per truss side. Note the rafter is longer than the span even on the flattest shed roof — the slope tax the pitch factor charges.

💡 Tip: count the trusses with the fencepost rule, not division. A 16 ft building at 24 in o.c. needs nine truss positions, not eight — floor(192 ÷ 24) + 1. The calculator’s count field applies this automatically, and getting it right the first time is the difference between one lumber delivery and two.

Four Shed-Roof Scenarios, Solved Differently

The same mono truss serves four very different builds, and each scenario hides a different failure mode. Pick the card that matches your project — the filter chips below highlight the scenarios that fit your constraints.

🛖

Freestanding Garden Shed

Simplest Build

12 ft span · 3/12–4/12 · both walls framed new

The win: No ledger work: two bearing walls, nine mono trusses on a 16 ft building at 24 in o.c., standard hardware throughout.
Watch this: The low wall is structural here — it carries a real horizontal sliding component at the roller end, so anchor it for shear, not just gravity.

🏠

Lean-To Against an Existing Wall

Optimal Strategy

10–16 ft span · 2/12–4/12 · ledger + bearing wall

The win: One wall of framing eliminated and roofline tucked under the eave — the classic firewood-and-mower bay for the least lumber.
Watch this: Two failure modes to design out: ledger fastening into the house rim, and the snow drift pocket that builds where the lean-to meets the wall.

🚜

Equipment Carport / RV Bay

High Clearance

14–20 ft span · 2/12–3/12 · 10–12 ft high side

The win: Mono trusses keep one wall low for cost while the high side clears equipment — the profile RV ports are built from.
Watch this: Open sides mean full wind uplift on the high wall: uplift straps and heavier anchors are not optional, and purlins want closer spacing.

🐄

Animal Shelter / Run-In

Open Front

10–12 ft span · 3/12–4/12 · open high front

The win: The high open front lets animals and machinery in while the low back wall sheds weather away from the stall line.
Watch this: The open front is a cantilevered wind catch — knee braces or the first pair of trusses need temporary and permanent bracing until sheathing ties the plane.

❌ Don’t attach blind: if the lean-to ties into a wall you don’t own structurally — a neighbor’s garage, a rental, a masonry veneer that looks load-bearing — the ledger becomes someone else’s problem and your liability. Freestanding with a close gap and separate flashing is the honest fallback.

Lean-To Truss Connection: Tying Into an Existing Wall

The lean-to lives or dies at its ledger — the horizontal member fastened to the existing wall that carries the high end of every truss. Everything else is ordinary shed framing. Three checks make the connection trustworthy, and each has a number attached.

①

The ledger fastener schedule

Vertical load flows from hangers through the ledger into the wall's studs or rim. The common starting point is 1/2 in lag screws at 16 in on center, staggered top and bottom, into doubled rim joist material or solid blocking — but the honest method is to divide the total end reaction by the fastener count and compare against the lag screw's withdrawal and shear values for your wall type. A 16 ft lean-to at 40 psf total load carries roughly 10.7 kip at the ledger: nine lags at 16 in spacing, each rated near 1.2 kip in shear, is the order of magnitude that passes — toenails into sheathing is the detail that fails.

②

The snow drift wedge

Where a lean-to meets a taller wall, wind-blown snow packs into the triangular wedge and can pile to several times the ground snow depth. Code drift tables treat this as a separate load case, and it lands hardest on the trusses nearest the wall. Practically: if the drift case governs, the interior trusses closest to the house want the heavier top-chord assumption — worth running in the solver as a separate load scenario before ordering.

③

Flashing and the headroom check

The roof must shed water down-slope past the ledger, which means Z-flashing over the ledger and a terminate-into-wall sequence that keeps water outside the building envelope — the connection detail inspectors reject most is flashing skipped 'because the roof covers it'. And before any of it: verify the high wall height leaves the finished headroom the space needs, because the ledger line is fixed the day the first hanger goes up.

⚠️ Height check: many lean-tos die at the eave line — the plan puts a 10 ft high wall against a house whose eave sits at 9 ft 6 in. Measure the available height before choosing the pitch, because the pitch is what you flex: dropping from 3/12 to 2/12 buys back a foot of clearance on a 12 ft span (24 in to 24 in… exactly the rise difference: 3 ft vs 2 ft).

Minimum Slope for a Shed Roof: The Drainage Floor by Material

Flat is not a slope. Every roofing membrane has a pitch floor below which water laps back into laps and seams, and mono roofs flirt with that floor by design. The table below is the material-versus-slope map — stay above your row and the roof sheds; drop below it and warranty language starts with the word “excluded.”

Pitch	Angle	Material floor
0.5/12	2.4°	Standing-seam metal only (with sealed laps)
1/12	4.8°	Metal roofing; rolled roofing floor
2/12	9.5°	Asphalt shingle minimum — double underlayment required
3/12	14.0°	Shingles comfortable; the lean-to workhorse
4/12	18.4°	Standard underlayment rules apply again

Single-slope shed roof with metal panels draining toward a gutter on a garden workshop

One slope, one drainage directionPhoto: Unsplash

Why mono roofs drift toward flat

The temptation is structural: flatter means less rise, which means a shorter high wall or a wider span under the same eave line, which means cheaper. The calculator’s pitch slider shows the trade honestly — at 2/12 a 12 ft span costs 2 ft of height; at 4/12 it costs 4 ft.

The counter-pressure is the table: below 2/12 asphalt is out, below 1/12 exposed-fastener metal is out, and every step down moves you to a membrane whose price per square foot rises faster than the framing saved. The 3/12 sweet spot exists because it is the cheapest slope that still lets ordinary shingles do ordinary work.

12 Foot Shed Roof Truss: The Complete Worked Example

A 12 ft shed at a 3/12 pitch against a 10 ft wall is the canonical first mono-pitch build. Here is the whole calculation — geometry, lumber lengths, truss count, and loads — with every number reproducible in the calculator above and the preloaded solver model below.

Span

12 ft

Pitch

3/12 (14.0°)

High wall

10 ft

Low wall

7 ft

Rise

3 ft

Member length table — one 12 ft mono truss

Member	Runs between	Length	Board to order
Top chord ×4 segments	heel → low eave (the slope)	3 ft 1 1/8 in each	one 14 ft board covers all four
End post (high vertical)	high heel to high wall plate	3 ft 0 in	offcut from the 14 footer
Bottom chord ×2	high wall to low wall (through mid)	6 ft 0 in each	one 12 ft board
Central vertical	top-chord mid to bottom mid	1 ft 6 in	offcut
Steep diagonal ×2	bottom mid up to top chord	3 ft 9 in	one 8 ft board
Shallow diagonal	high heel up to first top joint	3 ft 9 in	same 8 ft board

1Geometry: rise = (3 ÷ 12) × 12 = 3.00 ft exactly; low wall = 10 − 3 = 7.00 ft; rafter = √(12² + 3²) = 12.369 ft = 12 ft 4 7/16 in.
2Truss count: a 16 ft building at 24 in o.c. takes floor(192 ÷ 24) + 1 = 9 trusses — nine positions, fencepost rule.
3Roof load: at 25 psf combined (dead + snow screening value), each interior truss carries 2 ft of spacing × 12 ft of horizontal tributary = 24 ft² × 25 psf = 600 lb spread across the top chord.
4Joint loads: the three loaded top-chord joints take 1 kip each in the model (the two eave joints carry half of an interior bay's tributary). Total model load: 3 kip down, split between the pin and roller reactions.
5Solver check: the model reports 11 members + 3 reactions = 2 × 7 joints — statically determinate, and the low-end roller reaction confirms the low wall carries its share of gravity while taking almost no horizontal thrust.

Open the 12 ft Mono-Pitch Model

Seven joints, eleven members, 3/12 pitch, 1 kip on each interior top-chord joint — rebuilt instantly in the Structural Analysis tab with every axial force, reaction, and the determinacy check.

▶ Load the 12 ft lean-to model

Shed Roof Truss Calculator FAQ

What is a mono pitch roof truss?▼

A mono pitch (single-slope) truss is half of a gable truss: one sloping top chord, one horizontal bottom chord, and webs triangulating between them. The high end bears on the tall wall, the low end on the short wall, and the whole profile is defined by three numbers — span, high-wall height, and pitch. The low-wall height falls out as high wall minus (pitch ÷ 12) × span, which is exactly the arithmetic the calculator above runs.

How do you calculate a 12 foot shed roof truss?▼

Work the triangle: at a 3/12 pitch, a 12 ft span rises 3 ft, so a 10 ft high wall lands on a 7 ft low wall. The rafter (top chord) length is √(12² + 3²) = 12.369 ft ≈ 12 ft 4 7/16 in. For a 16 ft building at 24 in o.c., floor(192 ÷ 24) + 1 = 9 trusses. The full member-by-member table in the worked example below extends this to every web, and the preloaded model reproduces all of it in the solver.

What is the minimum pitch for a lean-to shed roof?▼

It depends on the membrane. Asphalt shingles require at least 2/12 with double underlayment below 4/12; exposed-fastener metal generally wants 1/12 or more; standing-seam metal with sealed seams works down to 1/2/12. For lean-tos that dump water against or near a house wall, practical experience favors staying at 2/12 or steeper — flat mono roofs concentrate the splash and drift zone exactly where the two structures meet.

How do you attach a lean-to truss to an existing wall?▼

The standard detail is a ledger ledger-bolted to the house rim or studs — commonly 1/2 in lag screws at 16 in staggered spacing into doubled rim material, flashed top and bottom — with the trusses hung in fabricated hangers off that ledger rather than notched into it. Never rely on toenails into sheathing. Two checks dominate: the ledger fastener schedule for the vertical load, and the snow drift load that accumulates in the wedge against the wall, which can exceed the open-roof snow load substantially.

How tall should the walls be for a lean-to truss?▼

Fix the high wall at what the existing structure allows (often just under the house eave), then check that the low wall keeps at least 6–7 ft of clear height where you will stand and a 4 ft absolute minimum everywhere. With a 3/12 pitch every foot of span costs 3 inches of height, so a 12 ft lean-to off a 10 ft wall lands at 7 ft on the low side — the worked example on this page walks the exact arithmetic and the headroom check.

Can you use mono trusses for a metal building or metal trusses?▼

Yes — 'lean to metal trusses' is one of the most common steel applications: the same single-slope geometry solved here works with steel C-purlins and welded or bolted steel trusses, typically at wider spacings (4–8 ft) because steel spans further between members. The connection detail changes from hurricane ties to welded clips or bolted gussets, and the high wall usually becomes a steel column. The geometry, drainage minimums, and drift caution on this page apply unchanged.