The two standards

One duct, two legitimate quantities

A quantity surveyor and a sheet metal shop measure the same fitting differently, and both are right. DuctForge keeps them apart and states which one produced every figure.

Commercial billing

Mean perimeter × centreline

Nominal measurement to BOQ / IS 655 / DW 144 practice: the perimeter of the duct multiplied by the length along its centreline. This is what MEP consultants, clients and quantity surveyors accept on an invoice claim.

Shop fabrication

The true unfolded blank

The flat sheet a fabricator actually cuts, including slant hypotenuses on transitions, heel arc expansion on bends and wrapper triangulation. It is a cutting quantity, not a billing one.

They do not always differ, and where they agree it is worth knowing why. A straight duct has no slant and no arc, so both give the same area. An elbow does too — its 2·cheek + heel + throat development simplifies exactly to mean perimeter × centreline arc, which is Pappus’s theorem rather than a coincidence. A dropper goes the other way: its shop blank is smaller than its billed area, because the side cheeks are parallelograms and shearing a parallelogram adds no area.

Formulas

Every fitting, both standards

W and H are the duct's width and height, L its length, R the inside (throat) radius, θ the included angle, O a dropper's offset and F a collar's flange lip.

Fitting	Commercial billing	Shop fabrication
Straight ductA plain rectangular run.	A = 2(W + H) × L	A = 2(W + H) × L
ReducerTransition between two rectangular sizes.	A = (W₁ + H₁ + W₂ + H₂) × L	A = (W₁ + W₂)·√(L² + ((H₁−H₂)/2)²) + (H₁ + H₂)·√(L² + ((W₁−W₂)/2)²)
ElbowRadiused bend through an angle.	A = 2(W + H) × [θπ/180 × (R + W/2)]	A = 2·A_cheek + A_heel + A_throat, A_cheek = θπ/360·[(R+W)² − R²], A_heel = θπ/180·(R+W)·H, A_throat = θπ/180·R·H
DropperOffset or swan neck.	A = 2(W + H) × √(L² + O²)	A = 2(L × H) + 2(W × √(L² + O²))
CollarBranch takeoff with a flange lip.	A = 2(W + H) × (L + F)	A = 2(W + H)·L + 2(W + H)·F + 4F²
Y-pieceTrouser splitting one duct into two.	A = A_B1 + A_B2, A_Bn = (W₁/2 + H + Wₙ + H) × θπ/180·(R + Wₙ/2)	A = Σ branches [ 2·A_cheek + A_heel + A_throat ], each branch taken on its own width Wₙ
Round ductA plain round or spiral run.	A = πD × L	A = πD × L
Round elbowGored bend in round duct.	A = πD × [θπ/180 × R]	A = πD × [θπ/180 × R]
Round reducerConcentric cone between two diameters.	A = π(D₁ + D₂)/2 × L	A = π(D₁ + D₂)/2 × √(L² + ((D₁−D₂)/2)²)

What each one assumes

Straight duct: A straight duct has no slant and no arc, so both standards give exactly the same area.
Reducer: Concentric transition — both openings on one centreline. An eccentric (flat-on-one-side) reducer has a larger slant on the offset face and is not modelled here.
Elbow: R is the inside (throat) radius, so the centreline radius the billing formula uses is R + W/2. Both standards give the same area here, and that is not a coincidence: 2·cheek + heel + throat simplifies to θπ/180·(2R + W)(W + H), which is the mean perimeter times the centreline arc. A swept constant section develops exactly to its mean perimeter (Pappus), so an elbow bills what it cuts.
Dropper: The only fitting where the shop blank comes out SMALLER than the billing area: the two side cheeks are parallelograms, and shearing a parallelogram does not add area. Both figures are correct — they answer different questions.
Collar: The shop blank is the billing area plus the four corner squares at the flange — the material the billing standard treats as scrap.
Y-piece: OUR STATED INTERPRETATION, not a published formula: the source specification gives the Y-piece shop area only as “sectors + heels + throats” with no sub-formulas, so each branch is developed as an elbow on its own width. The crotch (splitter) plate is NOT included — add it as a separate straight entry if your shop cuts one. Note also that the two standards cross over at Wₙ = W₁/2: a branch narrower than half the main duct bills for more than it cuts, because the billing perimeter averages in the main's half width.
Round duct: A cylinder unrolls flat with no distortion at all, so the blank is exactly πD wide by L long and both standards agree. Spiral-wound duct is made from a continuous strip rather than this blank — the AREA is the same, the cutting is not.
Round elbow: Both standards agree, by Pappus's theorem: a constant section swept about an axis develops to exactly its perimeter times the path of its centroid. The gore count changes the BLANKS — each gore is a cylinder cut at an angle, so its edges unroll as sine curves — and therefore the cutting waste, but never the surface area.
Round reducer: The blank is an annular sector — the classic cone development — so the shop area is the mean circumference times the SLANT height, not the length. Concentric only: an eccentric cone has a different development on each side and is not modelled here.

Gauge

Sheet gauge by largest dimension

The common size-only shortcut from the SMACNA duct construction standards. The metric and imperial bands are two published tables rather than conversions of each other — 12 inches is 304.8 mm — so a job is graded on the table matching its own units.

Gauge	Thickness	Largest dimension (metric)	Largest dimension (imperial)	kg/m²	lb/ft²
26 ga	0.55 mm	up to 300 mm	up to 12″	4.32	0.885
24 ga	0.70 mm	301 – 750 mm	13″ – 30″	5.50	1.126
22 ga	0.85 mm	751 – 1000 mm	31″ – 40″	6.67	1.366
20 ga	1.00 mm	1001 – 1500 mm	41″ – 60″	7.85	1.608
18 ga	1.20 mm	1501 – 2100 mm	61″ – 84″	9.42	1.929
16 ga	1.60 mm	over 2100 mm	over 84″	12.56	2.572

This is a simplification, and it matters. Real gauge selection also depends on the duct’s pressure class and on reinforcement spacing. Treat the table as a starting point, check it against the project specification, and override the gauge by hand on any line where the spec differs — the calculator carries the override through to the weight, the sheet count and the export.

Densities are not transcribed, they are derived: thickness × 7850 kg/m³, which reproduces the published table exactly. That is bare metal — it excludes any coating, stiffeners, flange steel, gaskets and fixings.

Round duct carries an extra caveat. Round duct is graded on the rectangular table here, because that is the table this app has. SMACNA publishes a separate and generally lighter one for round and spiral duct — a cylinder is stiffer than a flat panel — so this over-specifies. Override the gauge on any line where your specification differs.

Material

A gauge is a thickness, so the band table above survives a change of material untouched — only the density moves, and with it the weight.

Material	Density	Note
Galvanised steel	7850 kg/m³	Bare steel. The zinc coating adds roughly 1% and is not counted.
Stainless steel	8000 kg/m³	Austenitic (304 / 316). Ferritic grades run nearer 7700 kg/m³.
Aluminium	2700 kg/m³	The gauge table is a steel standard. The THICKNESS is what carries over — aluminium duct is normally specified a gauge or two heavier for the same duty, so check it against your specification.

Also counted

Insulation, flanges and hangers

Three quantities an estimator has to price alongside the sheet. Every one of them is DERIVED from the geometry you already typed — none is a new measurement, and each is off until you switch it on.

Insulation

The billing formula, on a fatter duct

The same billing formula re-run with every cross-section dimension grown by twice the thickness. Lagging a 600 × 400 duct with 25 mm measures it as 650 × 450.

The centreline never moves. A rectangular elbow’s R is its throatradius, so it shrinks by the thickness while the width grows by twice it — get that backwards and insulating a bend silently lengthens it. A round elbow’s R is already a centreline radius, so it is left alone.

Flanges

Two ends per piece

Every piece is counted with a flange at each end, and a straight run is as many pieces as the supplied length divides into — a 6 m run of 1.2 m duct is five pieces, so ten ends.

Two flanges meet at every joint and both are material you buy, which is why this counts ends rather than joints. Corner pieces are four per rectangular end; a round flange has none.

Hangers

One per piece, plus spacing

One support for every piece, plus one more for each further full spacing of centreline run.

A rule of thumb rather than a structural calculation. Real hanger spacing depends on duct size, weight and the building — check it against the specification.

Rates are the same idea in reverse: your figure per kg or per m², applied to the quantities above. This app has no prices of its own and never will.

Sheets

Why the sheet count is only an estimate

Gross area divided by one commercial sheet — 2.88 m² (1200 × 2400 mm) or 32 ft² (4 × 8 ft) — rounded up, and counted separately for each gauge.

Per gauge, never in total. 22 ga cannot be cut out of a 24 ga sheet, so a single combined sheet count would be a number you could not take to a merchant.
It ignores nesting. A real shop reuses offcuts across fittings, and some blanks — cheeks and trapezoids especially — do not tile. The true figure moves in both directions.
Seam laps are in the allowance, not the drawing. The flat patterns show the developed blank only. Pittsburgh seam and flange lip material is covered numerically by the waste percentage, so drawing it as well would count it twice.

Allowance	Where it applies
0% — net BOQ	Pure theoretical area, for direct subcontractor invoicing.
8% — slip & drive	Factory-run straight duct in light gauge, minimal seam scrap.
12% — industry standard	SMACNA / TDF / TDC transverse flange roll-forming: a 35 mm flange lip per side plus the longitudinal Pittsburgh seam.
15% — heavy fittings	Complex multi-branch fittings and angle-iron companion flanges.
20% — high wastage	Heavy gauge sheet, awkward nesting, high offcut loss.

Standards, formulas and constants