How we check the calculations

Glass U-value (U_g) EN 673

Open: U-value calculator for insulating glass

Method

Centre-of-pane U-value of double and triple glazing by the calculation of EN 673: radiation and gas conductance of each cavity, the gas part from the Nusselt number (Grashof and Prandtl, vertical glazing, A = 0.035, n = 0.38), standard conditions h_e = 23 and h_i = 8 W/(m²·K), mean temperature 283 K and ΔT = 15 K. Gas fills are 90 % gas and 10 % air, their properties mixed in proportion. The emissivity is chosen from five classes: 0.837 (uncoated), 0.16, 0.05, 0.03 and 0.013.

Published reference cases

Checked by internal consistency tests only; no published case checked against it yet.

Internal tests

The tests run the page's own script on 1 500 double and 1 500 triple make-ups and check that the copy of the engine in the glazing configurator gives the same U_g; every cell of the U_g table, in its six languages, is the calculator of its language run again on the make-up in its link. The rounded values the calculator page lists under «Values you can check us against» are typical figures we have not yet matched to a published source, so they are not counted here.

What it does not cover

• Centre of pane only: no spacer, glass edge or frame. That is the window calculator.
• Vertical glazing only: sloped and horizontal units convect differently.
• Emissivity by class, not by product. The exact coating decides the last decimal: for a declared value, use the manufacturer's figure.
• Heat loss only: no g-value or light transmission.

Known deviations

None known.

Window U-value (U_w) EN ISO 10077-1

Open: Window U-value calculator

Method

The simplified method of EN ISO 10077-1: U_w = (A_g·U_g + A_f·U_f + l_g·Ψ_g) / (A_g + A_f), with the areas and the length of the glazing edge worked out from the overall size, one frame face width all round and a regular grid of lights separated by mullions or transoms.

Published reference cases

Checked by internal consistency tests only; no published case checked against it yet.

Internal tests

The calculator page carries a worked example by hand (the 1230 × 1480 mm reference window of EN 14351-1, one light), and the tests run the U_w figures the window guides quote through this calculator again.

What it does not cover

• One frame face width all round: a wider bottom rail or a different mullion cannot be entered as such.
• Rectangular, regular grids only.
• No installation thermal bridge (Ψ_install), no solar gain, no air leakage.
• The typical U_f and Ψ_g are typical: a declared value comes from tested components or from EN ISO 10077-2.

Known deviations

None known.

U-value of walls, roofs and floors EN ISO 6946

Open: U-value calculator for walls, roofs and floors

Method

Homogeneous layers in series: R_total = R_si + Σ d/λ + R_air + R_se and U = 1/R_total, with the surface resistances of EN ISO 6946 for heat flowing horizontally, up and down, and a fixed 0.18 m²K/W for an unventilated air layer.

Published reference cases

Internal tests

The calculator page carries a worked example by hand, and the tests run the wall figures the guides quote through this calculator again. The published values above check the constants, not a whole wall: we have not yet found a public worked example made only of homogeneous layers.

What it does not cover

• No thermal bridges: studs, mortar joints, wall ties and fixings are not corrected for. EN ISO 6946 has a method for that; it is not here.
• No ground contact (that is EN ISO 13370) and no ventilated cavities.
• Typical conductivities: use the product's declared value for anything real.

Known deviations

• The air layer is always 0.18 m²K/W and its thickness cannot be entered. Table 2 of DA DB-HE/1 gives 0.18 for a 5 cm vertical cavity, but 0.17 for 2 cm, 0.15 for 1 cm and 0.16 for a horizontal one: on a thin cavity, or in a roof or a floor, the calculator over-reads that layer by 0.01 to 0.03 m²K/W.

Interstitial condensation (Glaser) EN ISO 13788

Open: Interstitial condensation calculator — Glaser method

Method

The Glaser method for one set of conditions: temperatures shared out by thermal resistance; saturation pressure from p_sat = 610.5·exp(17.269·θ/(237.3 + θ)) at or above 0 °C and with 21.875 and 265.5 below; vapour pressure shared out by s_d = µ·d; condensation wherever the vapour pressure exceeds saturation.

Published reference cases

Internal tests

The calculator page carries a worked example by hand, and a browser test reads back from the calculator the figures the page's answers quote (the wall it opens with, the interfaces that condense, the worst one, its excess pressure). The published values above check the saturation pressure, not a whole wall: we have not yet found a public worked Glaser example with all its inputs.

What it does not cover

• One set of conditions, not the twelve months of EN ISO 13788: no check that what condenses in winter dries out in summer.
• Steady state and diffusion only: no air leakage, rain, construction moisture or capillarity, and no moisture storage in the materials.
• No thermal bridges; plain build-ups only, no ventilated cavities.

Known deviations

None known.

Glass thickness under wind load plate theory, strength in the form of EN 16612

Open: Glass thickness calculator for wind load · Wind lab: watch a glass pane bend

Method

A rectangular pane simply supported on four edges, linear (small-deflection) plate theory with the classical coefficients α and β interpolated by aspect ratio: σ = β·q·b²/t² and w = α·q·b⁴/D, with E = 70 000 N/mm² and ν = 0.23. Design strength in the form of EN 16612 with k_mod = 0.663·t^−1/16 (a 10-minute wind, 0.74, by default; a 5-second gust, 1.00, on request), γ_M;A = 1.8 and γ_M;v = 1.2. Laminated glass by its effective thickness, with no shear transfer and with full transfer. The input is the factored design pressure. The wind lab is a view of this same engine.

Published reference cases

Internal tests

The page's worked example (1200 × 2200 mm, 10 mm toughened, 1.20 kN/m²) is run again by the tests figure by figure; every cell of the thickness chart printed on the page is recomputed; the same k_mod is checked in every copy of the formula on the site; and the whole coefficient table is recomputed by an independent series (Lévy) solution of the plate, within 0.0015 on β and 0.00004 on α.

What it does not cover

• Four supported edges only: no two- or three-edge support, point fixings or structural silicone.
• A single pane: load sharing between the panes of an insulating unit is not modelled.
• Linear theory: once the deflection passes about half the thickness, membrane action makes the real pane stiffer and less stressed (the page warns).
• It does not compute the wind pressure, and there are no post-breakage, thermal stress, barrier or impact checks.
• It is not ASTM E1300 and it applies no national annex.

Known deviations

• The β coefficients are the classical ones for ν = 0.3, while glass is nearer 0.23. Solving the plate with both shows the effect is on stress only — the deflection coefficient of a simply supported plate does not depend on ν — and that it overstates the stress by 5.7 % on a square pane, 2.5 % at 1.5 : 1, 1.2 % at 2 : 1 and nothing from 5 : 1. It errs on the safe side.
• Whether wind counts as a 10-minute load or as a gust for k_mod depends on EN 16612 and its national annex, which we have not been able to check. The page opens on 10 minutes (annealed glass 18.54 N/mm²) and offers the 5-second gust (25.00 N/mm²).

Glass balustrade EN 16612 strength; EN 1991-1-1 loads; US mode on the IBC

Open: Glass balustrade thickness calculator

Method

A free-standing cantilever clamped at the base, per metre of width: σ = 6·γ_Q·F·h/t² and δ = 4·F·h³/(E·t³), γ_Q = 1.5; laminated glass between its two bounds (no shear and full shear); EN 16612 design strength with k_mod by load duration; a check with one ply broken. The US mode applies the IBC loads (50 lb/ft along the top, 200 lb concentrated, one at a time) and the stress limits of section 2407.1.1 in the 2018, 2021 and 2024 editions.

Published reference cases

Checked by internal consistency tests only; no published case checked against it yet.

Internal tests

Ten US-mode cases worked by hand, step by step, and 2 000 generated cases compared with an independent calculation in SI units (the moment shared between plies instead of an effective thickness); the k_mod formula checked against the other glass pages; the thicknesses the page's answers quote read back from the calculator; and a worked example by hand on the page.

What it does not cover

• Free-standing cantilever only: a continuous handrail changes the model.
• The clamp is taken as rigid: the rotation of the base channel, often larger than the glass's own deflection, is not included.
• European mode: line load only, no infill load, point load, wind, crowd dynamics or impact test.
• No fixings, holes or local stresses.
• The interlayer bounds are bounds: a design that only works with full shear does not work.
• Barrier loads are national. The UK figures are the ones commonly published under BS 6180; we have not checked them against the text of BS 6180 or of the UK National Annex.

Known deviations

None known.

Wind pressure EN 1991-1-4, ASCE 7-16

Open: Wind pressure calculator for glazing

Method

EN 1991-1-4 with its recommended values: q_b = ½·ρ·v_b² with ρ = 1.25 kg/m³ and c_dir = c_season = 1; k_r = 0.19·(z₀/0.05)^0.07, c_r = k_r·ln(z/z₀) with z floored at z_min, c_o = 1, I_v = 1/ln(z/z₀) and q_p = (1 + 7·I_v)·½·ρ·v_m²; net pressure with the local coefficients c_pe,1 of the wall zones and c_pi +0.2/−0.3, and × 1.5 for the design value. ASCE 7-16, simplified, for components and cladding: K_z = 2.01·(z/z_g)^2/α with z floored at 15 ft, K_d = 0.85, K_zt = 1, GC_p interpolated on log(area) between 10 and 500 ft², GC_pi ±0.18.

Published reference cases

Internal tests

The page carries a worked example by hand (27 m/s, terrain II, 10 m, zone A). No published case has been run on the ASCE 7 side yet.

What it does not cover

• You supply the basic wind speed, from your national annex map or the ASCE hazard tool.
• Flat ground (c_o = 1): no hills, escarpments or cliff edges.
• Rectangular buildings and vertical walls only: no roofs, canopies, parapets or curved surfaces.
• No directional or seasonal reduction.
• ASCE side: enclosed buildings up to 60 ft and K_zt = 1.

Known deviations

• ρ is fixed at 1.25 kg/m³, the recommended value. Where a national annex or an example takes 1.225, its q_p is 2 % lower (second case above).
• The cases check q_p only. The published single-storey example goes on with c_pe,10 for whole walls, while the calculator uses c_pe,1 for a pane, so the net pressures are not comparable.

Aquarium glass thickness plate theory (Lévy), strength in the form of EN 16612

Open: Aquarium glass thickness calculator: rimless and braced

Method

Each pane as a plate under water pressure — rimless with a free top edge, or braced and held on four edges — with coefficients from a Lévy series solution; design strength in the form of EN 16612 for a permanent load (k_mod 0.29, γ_M;A 1.8) with a load factor of 1.35; the stock thickness is chosen on its minimum tolerance, with the deflection kept under half the thickness.

Published reference cases

Internal tests

Six design cases to the hundredth of a millimetre; the page's tables equal the Lévy solver digit for digit; the same solver reproduces the four-edge table of the wind-load calculator and the usual hobby chart within 1.5 %; and the scope limits, laminated and toughened glass, the top brace and the pond window each have their cases.

What it does not cover

• No silicone joints, holes or overflows; no curved, bow-front or acrylic tanks.
• No stand or floor check: you get the weight.
• A flat, level base and sound glass.
• No thickness over 19 mm, 80 cm of height, 1500 litres or 250 cm of length: that is an engineer's job.

Known deviations

• The three tanks are a coarse check: they confirm the stock thickness the method picks (6, 10 and 12 mm), not a stress or a deflection.

Weight: glass, metal and sheet materials geometry × density

Open: Glass weight calculator · Metal weight calculator · Sheet weight calculator

Method

Volume times density. Glass: 2500 kg/m³, that is 2.5 kg/m² per millimetre, PVB 1070 kg/m³, the gas in the cavities ignored. Metal: the cross-section by formula, with sharp corners and constant wall, times the density of the material (steel 7850 kg/m³). Sheet materials: density × thickness × area, each density taken from a manufacturer's data sheet named on the page.

Published reference cases

Internal tests

Glass: every cell of the weight chart is the calculator's figure, and several were checked by hand. Metal: eleven section shapes against the formula worked separately, impossible shapes refused, every figure of the nine metal charts recomputed. Sheets: worked examples by hand, and each density is the documented one, with its source.

What it does not cover

• Glass: spacers, sealant and coatings are left out, so a delivered unit weighs about 1 to 2 % more.
• Metal: no corner or root radii and no tapered flanges (UPN, IPN and IPE are not here).
• Sheets: one density per material, dry boards; not a structural self-weight.

Known deviations

• Metal sections are taken with sharp corners, so rolled hollow sections come out a few per cent lighter than the calculator says and hot-rolled angles a little heavier, as the calculator page states. We have not yet measured that against a published section table.

Sheet metal bend allowance DIN 6935 (K factor)

Open: Bend allowance and flat length calculator

Method

Bend allowance BA = A·(R + K·T), outside setback tan(A/2)·(R + T), bend deduction 2·OSSB − BA, and the flat length from the outside or the inside flanges. K from DIN 6935, (0.65 + 0.5·lg(R/T))/2 up to R/T = 5 and 0.5 above, or your own K.

Published reference cases

Checked by internal consistency tests only; no published case checked against it yet.

Internal tests

Cases worked on paper; on 5 000 random parts the flat length from the outside flanges equals the one from the inside flanges and the straight parts plus the bend zones; K is 0.325 at R = T, continuous at R/T = 5 and never above 0.5; invalid input is refused. The compensating values tabulated in supplement 2 of DIN 6935, a paid document, have not been compared.

What it does not cover

• K is an estimate until you bend a test piece: tooling, material and the press brake move it.
• One angle and one radius for every bend.
• No springback and no hems (the angle stays below 180°).

Known deviations

None known.

Cutting optimisers: glass, bars and panels heuristics, no standard

Open: Glass cutting optimiser: free software in your browser · Linear cutting optimizer · Cut list optimizer for sheets and panels

Method

Bars: the better of two plans (an exact search for the fullest bar, and best-fit decreasing), with kerf and end trim, next to a lower bound on the number of bars. Panels: guillotine bin packing tried with 108 combinations of ordering and splitting rules, next to the area lower bound. Glass: guillotine strips on one stock size, with an offcut rack.

Published reference cases

Checked by internal consistency tests only; no published case checked against it yet.

Internal tests

Bars: 3 002 random jobs check that every piece comes out once, kerfs and trims fit, the offcut is what is left and the count never beats the lower bound; on 784 small jobs compared with an exhaustive search, 783 plans are optimal and one uses one bar more. Panels: 401 jobs check every part inside the trimmed sheet, no overlap once the kerf is counted, the grain respected and a guillotine layout. Glass: only the chain from the optimiser to the cutting plan and the labels is tested; its layout geometry has no check of its own yet.

What it does not cover

• One stock size, one profile or one board at a time.
• No machine limits and no cutting sequence for a machine.
• Glass: strips without rotated sub-strips, so its yield is a floor; rectangles only; it does not know coating side, tong marks or the rack.
• The layouts are heuristics: the lower bound shown next to the answer is the honest measure.

Known deviations

None known.