Trade toolkit · Carpentry
Find out how much a shelf will sag before you build it. Choose the material, thickness, depth and span and what goes on it, and the calculator gives the sag on day one and after months under load, and the longest span that will stay looking flat.
Sag by thickness and span
Long-term sag in millimetres for this material, depth and load. Green is fine, amber you will notice, red is too much.
Estimates from beam theory using typical stiffness values. Long-term sag includes creep: boards keep sagging under a constant load, chipboard and MDF far more than solid timber. We judge a shelf on two limits: sag on day one under span ÷ 600, and long-term sag under span ÷ 300. A housed or screwed shelf is treated as partly fixed, which gives it about two and a half times the stiffness of one sitting loose on pins.
How to use it
A shelf sitting on pins bends like a beam. The sag goes up with the span to the power of four, so a shelf 20% longer sags more than twice as much. It goes down with the thickness cubed, so going from 18 to 25 mm makes a shelf nearly three times stiffer. Depth only helps in proportion.
Chipboard and MDF also creep: under a constant load such as books, they keep sagging for months. That is why a shelf that looked fine when it went in has a dip a year later. The calculator includes this using the creep factors from Eurocode 5.
For a shelf on pins under an even load, sag = 5wL⁴ ÷ 384EI, where w is the load per millimetre, L the span, E the stiffness of the material and I = depth × thickness³ ÷ 12. Long-term sag is that multiplied by (1 + kdef).
Questions
For books on a 300 mm deep shelf sitting on pins, around 400 to 450 mm before it sags noticeably over time. With light items it can go to around 600 mm. A hardwood lipping under the front edge nearly doubles that.
MDF is a little stiffer than chipboard, but both creep a lot under constant load. For long or heavily loaded shelves, birch plywood or solid timber sags far less.
Most people will not notice a sag of less than about span ÷ 600 when the shelf goes in, or span ÷ 300 over the long term. That is under 1.5 mm and 3 mm on a 900 mm shelf.
More trade tools
Kitchens
Door and drawer front sizes from your cabinet list, for overlay or inset, ready to order.
Materials
Running metres, lengths to buy and a cutting plan for liner bar, skirting, plinth, cornice and battens.
Materials
Square metres for floors, walls and ceilings, packs needed, and cubic metres and tonnes for concrete or screed.
Building shelving or wardrobes?
We cut and edge shelves and panels in 18 and 25 mm board, in any of 300+ Egger decors, in 5 working days. Email info@dtjinteriors.co.uk, call 0115 784 8231 or WhatsApp 07956 032306.
DTJ Interiors Ltd
Unit 5 Atlas Mills, Birchwood Avenue
Long Eaton, NG10 3ND
Workshop and collection
Monday to Friday, 8am to 4:30pm
Delivery across the East Midlands for £99 + VAT, and further afield priced per job.
DTJ Interiors Limited · Company no. 15242186 · VAT GB460641310
Registered office: The Mills, Canal Street, Derby DE1 2RJ
Every DTJ cabinet comes with a 5-year guarantee. How it works · FAQs · Samples · Terms of sale
