At a glance
| Shelf (source of E) | E (N/mm²) | Span at 1.0 kN/m² | at 1.92 | at 2.39 |
|---|---|---|---|---|
| MDF.H 18 mm (a) | 2,400 | 560 | 450 | 420 |
| Chipboard P2 18 mm (b) | 1,600 | 490 | 400 | 370 |
| Chipboard P2 25 mm (b) | 1,500 | 660 | 540 | 500 |
| Birch ply 18 mm, face grain along span (c) | 10,048 | 900 | 740 | 690 |
| Birch ply 18 mm, face grain across span (c) | 7,452 | 810 | 670 | 620 |
| Birch ply 21 mm, face grain along span (c) | 9,858 | 1,040 | 850 | 790 |
| Solid white oak 20 mm (d) | 12,300 | 1,060 | 870 | 810 |
| Solid white oak 25 mm (d) | 12,300 | 1,320 | 1,090 | 1,010 |
| Solid white oak 30 mm (d) | 12,300 | 1,560 | 1,300 | 1,210 |
| Solid white ash 25 mm (d) | 12,000 | 1,310 | 1,080 | 1,010 |
Longest span in millimetres, rounded down to 10: sag held to span/300 over the long term (initial sag to two thirds of that), bending only, a pin at each end, even load plus the shelf's own weight. Sources of E: (a) MDF.H data sheets, (b) P2 chipboard data sheets, (c) birch plywood data sheet, (d) US white oak and ash, Wood Handbook. 1.92 and 2.39 kN/m² are the US standard’s 40 and 50 lb per sq ft; 1.0 is ours. A starting point for a partner to confirm.
How a shelf sags, and the one formula
A shelf is a short beam resting on a pin at each end. Under book load it bends, and what the eye and the books notice is the sag, not the strength: at the spans below, the bending stress is under a tenth of the bending strength of the boards (our check, using the strengths on the data sheets and the Wood Handbook). Sag, called deflection, is what limits the span.
The Wood Handbook gives the deflection of a beam under an even load, supported at both ends, as δ = 5 w L⁴ / (384 E I), plus a smaller shear term that we leave out. Here w is the load per millimetre of span, L the span, E the stiffness of the material and I the stiffness of the section, which for a rectangle b wide and t thick is b t³ / 12. For a shelf carrying a load of q per square metre, the shelf’s depth cancels and the formula becomes δ = 0.15625 q L⁴ / (E t³). Depth does not change the span for a given load per square metre; thickness does, by its cube.
Worked example. An 18 mm MDF.H shelf, E = 2,400 N/mm², spanning 600 mm under 1.92 kN/m² plus its own weight of 0.13 kN/m² (750 kg/m³) carries 2.048 kN/m², which is 0.002048 N/mm². The stiffness term E t³ is 2,400 × 18³ = 13,996,800. So δ = 0.15625 × 0.002048 × 600⁴ ÷ 13,996,800 = 2.96 mm, which is span/203. The textbook form gives the same figure for a 300 mm deep shelf (w = 0.6143 N/mm, I = 145,800 mm⁴). The sag that matters after a few years is larger, so the table below holds the initial sag to two thirds of the limit.
- Thickness: moving from 18 to 25 mm makes the section 2.7 times stiffer ((25 ÷ 18)³). It is the cheapest stiffness there is.
- Span: double the span and the sag is sixteen times as much. Put another way, for a fixed limit of span/n the longest span goes with the cube root of the stiffness: a board 22 per cent less stiff than average (the Wood Handbook’s coefficient of variation for the modulus of elasticity of clear wood is 22 per cent) shortens the span by only 8 per cent.
- Time: shelves keep sagging under a steady load. The Wood Handbook says that after several years the creep may roughly equal the first deflection, and that for dry timber it is customary to design for an initial deflection of about two thirds of the long-term limit. We use that factor of 1.5 for every board; it is not sourced for panel products.
- Which limit: the US Architectural Woodwork Standards (2009) call span/144 “the industry standard” for the most a shelf may sag, and say creep is not a defect. The birch plywood data sheet we read draws its charts to span/300. Forum and trade pages quote anything from span/180 to span/400. Choose one, write it in the specification and say whether it is initial or long-term.
Spans by material and thickness: starting points
The table in the at-a-glance box gives the longest span for ten constructions at three loads. The loads are 1.0 kN/m² for light display (ours), and 1.92 and 2.39 kN/m², the 40 and 50 pounds per square foot the US standard adopts for general shelving and for school, hospital, library or book shelving. The same standard caps any one shelf at 200 lb (90.7 kg). One kilonewton per square metre is about 102 kg of load on every square metre of shelf.
What each stiffness figure is. They are not the same kind of number, and the table does not hide that:
| Shelf | E used (N/mm²) | Density used (kg/m³) | Where the stiffness comes from |
|---|---|---|---|
| MDF.H 18 mm | 2,400 | 750 | Minimum requirement for MDF.H over 12 up to 18 mm thick, EN 310 test, from two manufacturers’ data sheets. Density is our assumption. |
| Chipboard P2 18 mm | 1,600 | 640 | P2 board, EN 310 test: 1,600 for over 13 up to 20 mm and 1,500 for over 20 up to 25 mm (a data sheet and a declaration of performance). Density from the data sheet. |
| Chipboard P2 25 mm | 1,500 | 620 | P2 board, EN 310 test: 1,600 for over 13 up to 20 mm and 1,500 for over 20 up to 25 mm (a data sheet and a declaration of performance). Density from the data sheet. |
| Birch ply 18 mm, face grain along span | 10,048 | 700 | Mean bending modulus of one film-faced birch plywood formwork product, 10 per cent moisture. Weight per square metre from the same sheet. |
| Birch ply 18 mm, face grain across span | 7,452 | 700 | Mean bending modulus of one film-faced birch plywood formwork product, 10 per cent moisture. Weight per square metre from the same sheet. |
| Birch ply 21 mm, face grain along span | 9,858 | 700 | Mean bending modulus of one film-faced birch plywood formwork product, 10 per cent moisture. Weight per square metre from the same sheet. |
| Solid white oak 20 mm | 12,300 | 762 | US species at 12 per cent moisture, Wood Handbook Table 5-3a. Density is specific gravity x 1.12 x 1,000. |
| Solid white oak 25 mm | 12,300 | 762 | US species at 12 per cent moisture, Wood Handbook Table 5-3a. Density is specific gravity x 1.12 x 1,000. |
| Solid white oak 30 mm | 12,300 | 762 | US species at 12 per cent moisture, Wood Handbook Table 5-3a. Density is specific gravity x 1.12 x 1,000. |
| Solid white ash 25 mm | 12,000 | 672 | US species at 12 per cent moisture, Wood Handbook Table 5-3a. Density is specific gravity x 1.12 x 1,000. |
Thicker MDF is left out because no stiffness for it was read, and veneered or lacquered faces are assumed not to change the board’s stiffness. The solid timber rows use US species because those are the figures we could read; European oak was not in the tables. The birch ply rows show why the face grain should run along the span: across it the span is shorter.
The limit changes the answer more than the load does. The same shelves at 1.92 kN/m² under four different limits:
| Shelf | L/144 | L/200 | L/300 | L/360 |
|---|---|---|---|---|
| MDF.H 18 mm | 580 | 520 | 450 | 430 |
| Chipboard P2 18 mm | 510 | 460 | 400 | 370 |
| Chipboard P2 25 mm | 690 | 620 | 540 | 510 |
| Birch ply 18 mm, face grain along span | 940 | 840 | 740 | 690 |
| Birch ply 18 mm, face grain across span | 850 | 760 | 670 | 630 |
| Birch ply 21 mm, face grain along span | 1,090 | 980 | 850 | 800 |
| Solid white oak 20 mm | 1,120 | 1,000 | 870 | 820 |
| Solid white oak 25 mm | 1,390 | 1,240 | 1,090 | 1,020 |
| Solid white oak 30 mm | 1,660 | 1,490 | 1,300 | 1,220 |
| Solid white ash 25 mm | 1,380 | 1,240 | 1,080 | 1,020 |
The first column is the US standard’s limit applied to the long-term sag (with our 1.5 factor); the others are tighter. For a visible display shelf, hold the limit tight: sag shows against a straight line of books.
Stiffening a shelf with its edge
A solid lip glued along the front and back edge is the usual way to stretch a board’s span, because it puts stiff material where bending needs it most, at the top and bottom of the section. We worked it out for an 18 mm MDF.H shelf 300 mm deep with oak lips (E = 12,300 N/mm², flush with the top face), treating the section as one piece and the glue line as perfect:
| Edge detail (18 mm MDF.H shelf, 300 deep, oak lips) | Stiffness against the plain board | Longest span at 1.92 kN/m², L/300 long-term (mm) |
|---|---|---|
| Edge-banded board only | x 1.00 | 450 |
| Flush solid lip, 20 x 18, front and back | x 1.55 | 530 |
| Deep solid lip, 20 x 40, front and back | x 10.8 | 1,010 |
| Deep solid lip, 30 x 40, front and back | x 14.7 | 1,120 |
A flush lip the same thickness as the board adds little. A deep lip, standing below the board like a nosing, multiplies the stiffness several times, because stiffness rises with the cube of depth. The arithmetic assumes the lips and board act together, so the glue line, the fixing and the difference in movement between oak and MDF matter, and a lip 40 mm deep changes how the shelf looks. A trade knowledge-base article we read puts the gain from a 1¼ in. strip on a plywood edge at about 20 per cent, in line with our 16 per cent for the flush lip. Rear rails and upstands do the same job as the back lip. The partner workshop confirms the lip size and how it is fixed.
On finishing, the US Architectural Woodwork Standards treat the visible front edges of shelves as exposed surfaces and the three non-visible edges of adjustable shelves as concealed ones: that is where a specification can say what must be edged and what may be left raw. It is a US definition.
Adjustable shelves and the 32 mm system
Most adjustable shelving in cabinets stands on small pins in drilled holes. The 32 mm system is the trade convention that sets the holes out: rows of 5 mm holes 32 mm apart, the front row 37 mm in from the front edge, and the rear row, if there is one, 37 mm in from the rear edge, so that one drilling setup serves hinges, runners and shelf pins. The holes are 12 to 14 mm deep, and the distance from the first hole to the bottom of the cabinet equals the distance from the last hole to the top. Rows are a multiple of 32 mm apart. We read this in one encyclopaedia article and in search summaries of drilling-jig pages; we did not read a hardware maker’s catalogue, so treat the figures as the convention and ask the partner which system it drills.
If both rows sit 37 mm from their edges and the rows are n steps of 32 apart, the side panel is 74 + 32n deep:
| Steps of 32 between the rows | Panel depth (mm) |
|---|---|
| 7 x 32 = 224 | 37 + 224 + 37 = 298 |
| 8 x 32 = 256 | 37 + 256 + 37 = 330 |
| 9 x 32 = 288 | 37 + 288 + 37 = 362 |
| 10 x 32 = 320 | 37 + 320 + 37 = 394 |
Each step is a possible shelf height, so a finer pitch is not needed: a shelf can sit at any multiple of 32 mm. Some points are for the workshop to state, because we found no source: how many pins per shelf (four is the usual), the pin type (steel or brass, plain or locking), the pin’s load capacity, whether the pin bears on a plate or in a recess so that it does not crush the edge of a board, and how much clearance the shelf has between the sides. The pin is another reason to ask for the shelf load: five millimetres of steel in a thin board is a small bearing area.
What this sheet does not cover, and what to ask
- Point loads and heavy objects such as stone, ceramics, equipment or a stack of art books: the table assumes an even load.
- Glass shelves: thickness and support come from the glazier’s data and the glass standard, not from this table. None was read.
- Wall-hung shelves and overturning: fixings and the wall are outside the span arithmetic. BS EN 16121 (non-domestic storage furniture) and BS EN 14749 (domestic storage) deal with safety, strength and stability of units; neither was read, and the BSI page for an earlier edition of BS EN 16121 says its requirements do not include the wall or its attachments.
- Shelves in public places and anywhere a falling shelf could injure someone: ask an engineer or ask for a test.
Ask the partner workshop for: the board and its stiffness value with the test it comes from; the load and sag limit the shelf was checked to; the span between supports as built; the lip or rail; the pin type and number; and whether the shelf has been tested. Our wardrobe and dressing-room dimensions sheet shows where shelves sit in a wardrobe, and the MDF sheet explains the board types.
Specification wording
Paste into your schedule or specification and replace anything in [square brackets] with your own figures. Wording is a starting point: your specification governs.
Shelves [25] mm [solid oak / MDF.H with veneer], [20 x 40] mm solid lip bonded the full length of the front and back edges, maximum span between supports [800] mm. Design load [1.9] kN/m2 uniformly distributed, no point loads. Sag not to exceed span/[300] over the long term. The maker is to confirm by calculation from the stiffness of the board supplied, or by test, before production.
Board: [MDF.H to BS EN 622-5], [18] mm, grain [along] the span. The maker is to state the modulus of elasticity in bending (BS EN 310) from the supplier's current data sheet and the calculation used.
Adjustable shelves on [5] mm holes at [32] mm pitch in two rows, [37] mm from the front and rear edges, line-bored. [Four] [steel locking] pins per shelf, shelf [2] mm short of the internal width. Hole positions to drawing [number]. Shelf load and pin capacity to be confirmed by the supplier of the pins.
Shelves carrying more than [2.4] kN/m2, point loads or [glass / stone] are to be designed by [engineer / specialist] and tested before installation. Wall-hung shelves to have fixings designed for the wall construction.
Terms used on this page
- 32 mm system
- A cabinet-making convention of drilling rows of small holes at 32 mm spacing so shelves, hinges and runners can be fixed at standard positions.
- Lipping
- A thin strip of solid timber glued to the edge of a board to protect it, hide the core or give a solid look.
- Deflection
- How far a shelf or beam bends under load, measured as the distance its middle falls from a straight line between its supports. Often limited to a fraction of the span, such as span/300.
- Modulus of elasticity (E)
- A measure of a material's stiffness: the bigger the number, the less it bends under the same load. In bending it is measured on boards by the EN 310 test.
- Creep
- Extra sag that develops slowly under a steady load, as with books left on a shelf for years. The Wood Handbook says it can roughly equal the first deflection after several years.
Standards and sources
- USDA Forest Products Laboratory, Wood Handbook FPL-GTR-282 (2021): Chapter 9, Table 9-1, p. 9-4; Chapter 5 Tables 5-3a, 5-6; Chapter 12 Table 12-1.
- Architectural Woodwork Standards, 1st edition (2009), Section 10 Casework: 1.2.21 shelf loading and deflection. US practice.
- Manufacturers' data sheets (two MDF.H, two P2 chipboard, one birch plywood), read 5 Nov 2026
- 32 mm cabinetmaking system (encyclopaedia article): a convention; catalogues not read.
- BS EN 16121, 16122, 14749, 310, 622-5: named only; not read.
Questions we are asked
How far can an 18 mm MDF shelf span?
On our arithmetic, about 450 mm under a general load of 1.92 kN/m2 with the sag held to span/300 over the long term, and about 560 mm under a light display load of 1.0 kN/m2. Under the US standard's looser span/144 the same shelf reaches about 580 mm. A solid lip along the front and back edges lengthens it. These are starting points for the workshop to confirm.
Why do shelves sag over time?
Wood and wood boards creep: under a steady load they keep bending slowly. The Wood Handbook says that after several years the extra sag may roughly equal the first deflection, which is why a shelf that looks straight when loaded can be sagging a year later. A stiffer board, a thicker shelf, a shorter span or a lip are the cures.
What sag is acceptable on a shelf?
There is no single limit. The US Architectural Woodwork Standards (2009) call span/144, a quarter of an inch in 36 inches, the industry standard; the birch plywood data sheet we read uses span/300; web sources quote span/180 to span/400. Pick one, say whether it applies to the first or the long-term sag, and write it in the specification.
Does a solid lip stiffen a shelf?
Yes, because it puts stiff timber at the top and bottom of the section. On our arithmetic a 20 x 18 mm oak lip flush with the face of an 18 mm MDF shelf makes it about 1.5 times stiffer, and a 20 x 40 mm lip below the board about ten times, though that assumes a perfect glue line and the partner workshop should confirm the detail.
What is the 32 mm system?
A cabinet-making convention in which rows of 5 mm holes are drilled 32 mm apart, the front row 37 mm from the front edge, so that shelf pins, hinges and runners all fit one drilling pattern. It is a trade convention, not a standard we could read; ask the workshop which system it drills.
Download the factsheet
A two-page A4 PDF with the span table, the formula and its worked arithmetic, the lip stiffness figures, the 32 mm set-out and paste-in wording, to keep with your project file.