About this calculator
This calculator takes off the rainwater goods for a pitched roof: gutter length with a cut allowance and the stock lengths that really packs into, gutter brackets, corners, stop ends and unions, the downpipes — how many, how long, how many stock lengths — with their brackets, outlets, shoes or drain connectors.
One figure here is genuinely governed by a standard: how many downpipes a gutter run needs. EN 12056-3 (Gravity drainage systems inside buildings — Part 3: Roof drainage, layout and calculation) gives a method that relates the roof's effective catchment, the design rainfall intensity, the gutter's own flow capacity and the rainwater pipe's capacity. The calculator applies that method, and says plainly which part of it needs data you must supply.
What you must supply: the design rainfall intensity. EN 12056-3 leaves r
to each country's national annex or rainfall data. The default here, 75 mm/h,
is the fixed figure the superseded UK code BS 6367 used for eaves gutters —
a placeholder so the page works, not a design value for your site. Replace it
with your national annex's intensity; every result is flagged with the figure
used.
Everything else — bracket spacings, cut allowance, one shoe per pipe — is trade practice and labelled as such.
Formula
Design flow (EN 12056-3 Cl. 4.1), per gutter run:
r = rainfall intensity [mm/h] / 3600 [l/(s·m²)]
A_eff = A_plan × (1 + tan(pitch) / 2) Table 3: plan area plus half the exposed elevation
= A_plan Table 3: plan area only (no wind allowance)
Q = r × A_eff × C, C = 1 for an impermeable roof
Which effective-area rule applies is a national choice (the standard offers
both), so it is an input. For a planar slope the exposed elevation area is
plan × tan(pitch).
Gutter capacity (Cl. 5.1.2, half-round or similar eaves gutter, level, free discharge):
A_E = π D² / 8 water cross-section of a true half-round of brim diameter D [mm²]
Q_N = 2.78 × 10⁻⁵ × A_E^1.25 nominal capacity [l/s]
Q_L = 0.9 × F_L × Q_N design capacity of one drainage length
F_L = 1 for L / W ≤ 50 (W = gutter depth = D / 2)
= 1 − 0.2 (L/W − 50) / 150 for 50 < L/W ≤ 200 Table 6, nominally level gutter (≤ 3 mm/m)
= 0.8 − 0.2 (L/W − 200) / 300 for 200 < L/W ≤ 500
Drainage lengths (Annex ND, Fig. ND.1): n outlets at the quarter points of
a run of length R divide it into 2n drainage lengths of R / 2n, each
carrying Q / 2n; an outlet with a stop end on one side drains one length of
R / n carrying Q / n. Each outlet and its downpipe takes Q / n.
Rainwater pipe capacity (Cl. 6.1.1 / Table 8, the Wyly–Eaton equation):
Q_RWP = 2.5 × 10⁻⁴ × k_B^−0.167 × d_i^2.667 × f^1.667 k_B = 0.25 mm, d_i internal diameter [mm]
f = filling factor, a national choice (UK National Annex: 0.33)
Outlets per run = the smallest n for which every drainage length's flow is
within Q_L (at its own L / W) and every outlet's flow is within
Q_RWP. A run whose L / W exceeds 500 — the end of Table 6 — is given more
outlets rather than an extrapolated capacity.
Components (trade practice, not the standard):
gutter length = Σ runs; cut allowance = %, added as further pieces before packing
stock lengths = first-fit-decreasing packing of every run split at the stock length
unions = Σ (ceil(run / stock) − 1)
brackets = Σ (ceil(run / spacing) + 1)
corners / stop ends = from the roof type (gable 0 / 4, mono 0 / 2, hip 4 / 0) or as entered
downpipes = Σ outlets; length = count × eaves height; stock packed the same way
downpipe brackets = count × max(2, floor(height / spacing) + 1)
shoes = one per downpipe discharging to ground; drain connectors likewise to a drain
Worked example
Defaults: 10 × 8 m gable roof, 35°, eaves overhang 500 mm, gable overhang 300 mm, 75 mm/h, wind allowance on, 125 mm half-round, intermediate outlets, brackets at 800 mm, 3 m stock, 5 % allowance, 80 mm downpipes, f = 0.33, eaves 6 m high, 3 m pipe stock, pipe brackets at 2 m.
roof plan = 10.6 × 9.0 = 95.4 m²; each eave drains 47.7 m²
A_eff = 47.7 × (1 + tan 35° / 2) = 47.7 × 1.350 = 64.4 m²
r = 75 / 3600 = 0.0208 l/(s·m²)
Q per run = 0.0208 × 64.4 = 1.34 l/s
125 half-round A_E = π × 125² / 8 = 6136 mm²; Q_N = 2.78e-5 × 6136^1.25 = 1.51 l/s; 0.9 Q_N = 1.36 l/s
one outlet drainage length 5.3 m, L/W = 5300 / 62.5 = 85 → F_L = 0.954 → Q_L = 1.30 l/s
flow per drainage length = 1.34 / 2 = 0.67 l/s ≤ 1.30 ✓
80 mm pipe Q_RWP = 2.5e-4 × 0.25^−0.167 × 80^2.667 × 0.33^1.667 = 5.9 l/s; 1.34 ≤ 5.9 ✓
→ 1 downpipe per run, 2 in all
gutter 2 × 10.6 = 21.2 m → each run 3 + 3 + 3 + 1.6 m → 8 stock lengths (the two 1.6 m pieces
cannot share one 3 m length); allowance 1.06 m fits an offcut → 8 to buy = 24 m
unions 6, brackets 2 × 15 = 30, stop ends 4, corners 0, outlets 2
downpipes 2 × 6 m = 12 m → 4 × 3 m, 2 couplers, 2 × 4 = 8 brackets, 2 drain connectors
With the outlets at the ends of the runs instead, one outlet would have to
drain the full 10.6 m: L / W = 170, F_L = 0.84, Q_L = 1.14 l/s — less
than the 1.34 l/s arriving — so the calculator places two per run, four in all.
FAQ
Does EN 12056-3 give the downpipe count directly? No — it gives the method: design flow from effective area and rainfall, gutter capacity from its cross-section and drainage length, pipe capacity from its diameter and filling factor. The count falls out of the check. The calculator runs that check with the standard's own equations; what it cannot supply is the rainfall intensity, which is a national figure.
Where do I get the rainfall intensity? From your country's national annex to EN 12056-3 or its rainfall statistics (the UK annex, for instance, maps a 2-minute intensity by location and return period; values there range from about 0.010 to 0.022 l/(s·m²), i.e. 36–79 mm/h, for a 1-year return period). Without a verified figure for your site the 75 mm/h default is only a placeholder.
Is the gutter capacity my product's capacity? Not necessarily. It is the standard's formula for a true half-round of the chosen width filled to the brim. Many "half-round" gutters are shallower or a different profile, and manufacturers publish tested capacities (per the standard's Annex A) that replace the formula. Use those if you have them.
Why does "outlets at the ends" need more downpipes?
Because the drainage length doubles. A gutter run drained from its middle
splits into two lengths flowing toward the outlet; drained from one end it is
one length twice as long, and a longer gutter carries less (Table 6's F_L)
while receiving the same rain.
Are the outlets themselves checked? No. EN 12056-3 has no capacity formula for outlets in gutters without a flat sole (Cl. 5.3.1), and notes that a sharp-edged outlet in a round gutter does not normally ensure free discharge. The calculator assumes free discharge; oversized or tapered outlets per the standard's Figure 8 are how that is achieved in practice.
What are the bracket spacings based on? Trade practice and typical manufacturer instructions — not the standard. Your gutter maker's spacing (which depends on material and snow load) overrides the default; the input is there to be changed.
What is not counted? Swan necks and offset bends where the eaves project past the wall, running outlets versus stop-end outlets, angles other than 90°, hopper heads, leaf guards, and any pipework below ground. Add them by hand.
Assumptions and limits
Standard cited: LST EN 12056-3. What of it this calculator applies, each verified against the HR Wallingford design manual for the standard (SR 620), which quotes the clauses and whose worked example the calculator reproduces: Cl. 4.1 (design flow, C = 1), Cl. 4.3 / Table 3 (effective catchment, both the wind-allowance and plan-only options), Cl. 5.1.2 (half-round eaves gutter capacity, 0.9 design factor), Table 6 (length factor for a level gutter), Annex ND Fig. ND.1 (drainage lengths by outlet position), Cl. 6.1.1 / Table 8 (rainwater pipe capacity, Wyly–Eaton, k_B = 0.25 mm).
Not applied, and stated: the design rainfall intensity (national; default is a placeholder), outlet capacity (Cl. 5.3, no formula for round gutters), sloping gutters (fall > 3 mm/m increases capacity; assumed level), non-half-round profiles (rectangular/trapezoidal gutters use a different coefficient and depth factors), valley and parapet gutters, siphonic systems, and any part of EN 12056-3 concerning pipework inside the building.
Idealised gutter profile. Capacity assumes a true semicircle of the chosen width; a manufacturer's tested capacity replaces it.
Hip roof faces are split along 45° hip lines (equal pitches), the gable overhang is ignored, and each face drains to its own eave. Manual mode splits the total length and plan area equally between runs.
Trade practice, not the standard: bracket spacings, cut allowance, stock lengths, one shoe or drain connector per downpipe, at least two brackets per downpipe, one union per stock-length joint.
Downpipe length is the eaves height; offsets, bends and below-ground connections are not included.