Floors and substrates
Timber joist deflection check for a tiled floor
- where
- second moment of area of the joist (mm⁴)
- joist breadth (mm)
- joist depth (mm)
- load carried by one joist (N/mm)
- total floor load, dead + imposed (kN/m²)
- joist centres (mm)
- mid-span deflection (mm)
- clear span (m)
- mean modulus of elasticity (N/mm²)
- allowable deflection (mm)
- limit ratio: 360 for ceramic, 720 for most natural stone
Explain this equation
Checks whether timber joists are stiff enough to take a tiled floor. Run it before tiling any suspended timber floor, especially with large-format tiles or natural stone, which crack if the floor bends too much.
I measures how stiff the joist section is: it rises with the cube of the depth d, so depth matters far more than breadth b. w is the share of the floor load q each joist carries, set by the joist centres s. E is the stiffness of the wood (about 11,000 N/mm² for C24) and n the limit ratio.
The 5/384 shape is the standard result for a simply supported beam under a uniform load. Deflection grows with the fourth power of span, which is why long spans fail first. The 1000 turns metres into millimetres, and q in kN/m² times s in mm divided by 1000 gives N/mm.
Sense check: a 47 × 195 C24 joist at 400 centres over 3.6 m sags about 5.5 mm at 2 kN/m², against 10 mm allowed. Add 10% to the span and deflection rises by almost half.
Watch out: this covers bending of the joists only. Flexing of thin boards between joists, notches cut for pipes and point loads such as a full bath are not included.
Checks whether a simply supported timber joist under a uniform floor load will stay within the deflection limit commonly applied to tiled floors: span/360 for ceramic and porcelain, span/720 for most natural stone.
Enter your values to see the result.
Good to know
Use the actual joist size and span, measured between bearings. E is the mean modulus for the strength class: about 11,000 N/mm² for C24 and 8,000 N/mm² for C16 (BS EN 338). The Tile Association uses 2 kN/m² for residential floors; timber floors should also be designed for up to about 0.8 kN/m² extra dead load from a tiled finish. Set n to 720 for most natural stone. Overboarding (minimum 12 mm plywood screwed at about 300 mm centres, then a backer board or uncoupling membrane) controls movement between joists but does not cure an under-sized joist; that detail is information only and is not modelled here.
Common mistake
Checking only the joist span and ignoring the boards between joists. A floor can pass span/360 on the joists yet still flex between them if the deck is thin or poorly fixed.
Limits
Bending deflection of a single simply supported beam under uniform load only. It ignores shear deflection, load sharing between joists, notches, creep and point loads (baths, kitchen islands). For anything marginal, or for natural stone, have the floor checked by a structural engineer to the timber design code.
Sources
- BS 5385-3:2024 Wall and floor tiling – Design and installation of ceramic, mosaic, natural stone, agglomerated stone and terrazzo flooring – Code of practice (BSI)
- Tile & Stone Journal: Subfloor preparation – guarding against deflection (L/360 ceramic, L/720 most natural stone; 12 mm minimum plywood overlay)
- BS EN 338:2016 Structural timber – Strength classes (C16 E0,mean 8 kN/mm², C24 E0,mean 11 kN/mm²)
- The Tile Association: Tiling to heated floors (2013/2014) – bay sizes, movement joints, thermal expansion coefficients, screed drying, floor loads
Results are calculations from the published methods and manufacturer figures shown, and depend on the data you enter. Always follow the tile, adhesive and grout manufacturers’ instructions, BS 5385 and the Tile Association guidance. Coverage rates vary by product and substrate. Check prices and VAT rules with your own records and HMRC.