What this calculator does
A timber beam span calculator gives a rough first estimate of how much a simply-supported timber beam will sag under a uniformly distributed load, using the standard engineering deflection formula for that loading case. Enter the span, the load per metre, the beam's width and depth, and a timber elastic modulus, and it works out the expected deflection at the centre of the span.
This is a simplified check, not a substitute for a proper span table or an engineer. Real span tables published in building codes account for species and stress grade, load duration and sharing between joists, bending strength as well as deflection, and safety factors that a single formula does not capture. Treat the result here as a starting estimate for early planning, and get span tables or a structural engineer to sign off anything load-bearing.
The formula
The calculator treats the beam as a simply-supported rectangular timber section carrying a uniformly distributed load, and applies the standard formula for that case: maximum deflection δ equals 5wL⁴ divided by 384EI, where w is the load per unit length, L is the span, E is the timber's elastic modulus and I is the second moment of area of the section (bd³/12 for a rectangle of width b and depth d). The result is then compared against an allowable deflection of span divided by a chosen ratio, such as span/360, a common limit for floors carrying finishes that could crack if the floor flexed too much.
| Term | Meaning |
|---|---|
| δ (deflection) | How far the centre of the beam sags under the load, in millimetres. |
| w | The uniformly distributed load along the beam, in force per unit length, such as kN/m. |
| L | The span, the distance between the two supports. |
| E | The elastic modulus of the timber, a measure of stiffness that varies by species and grade. |
| I | The second moment of area of the beam's cross-section, bd³/12 for a rectangle. |
The inputs explained
| Field | What to enter |
|---|---|
| Span length (L) (m) | The clear span between supports, not the total length of the timber if it overhangs. |
| Uniformly distributed load (w) (kN/m) | The total uniform load per metre of beam, combining dead load (the structure itself) and live load (occupants, furniture, snow) as appropriate. |
| Beam width (b) (mm) | The actual dressed width of the beam, not the nominal size it was sold as. |
| Beam depth (d) (mm) | The actual dressed depth of the beam, measured in the direction the load bends it. |
| Timber species / grade | A rough elastic modulus band by species and grade. For real work, use the graded modulus stamped on the timber or quoted by the supplier. |
| Custom elastic modulus (E), if selected above (GPa) | A number, measured in GPa. Starts at 12. |
| Deflection limit | How much sag is acceptable relative to the span. Span/360 is a common default for floors under brittle finishes; span/240 or span/180 are looser limits sometimes used for less sensitive structures. |
When to use it
Early-stage deck or floor planning
Before committing to a joist size, running a few widths and depths through the calculator shows roughly which sections are in the right ballpark for the span and load being considered, ahead of checking an actual span table.
Sanity-checking a span table result
If a span table gives a maximum span for a given section, plugging the same numbers in here should show a deflection close to the chosen limit, which is a useful check that the load and section have been read correctly.
Comparing timber species or grades
Because stiffness varies with species and grade, holding the span, load and section fixed while changing the elastic modulus shows how much extra safety margin a stiffer species buys, without changing the beam's dimensions.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How deflection changes as the span increases
The same beam section and load, carried over a range of spans.
| Span | Estimated maximum deflection | Allowable deflection (span / 360) | Result against that limit |
|---|---|---|---|
| 2.4 m | 0.7 mm | 6.7 mm | Within the chosen limit |
| 3.0 m | 1.7 mm | 8.3 mm | Within the chosen limit |
| 3.6 m | 3.5 mm | 10.0 mm | Within the chosen limit |
| 4.2 m | 6.5 mm | 11.7 mm | Within the chosen limit |
| 4.8 m | 11.1 mm | 13.3 mm | Within the chosen limit |
| 5.4 m | 17.8 mm | 15.0 mm | Exceeds the chosen limit |
How deflection changes with beam depth
The same span and load, with the beam's depth varied while width stays fixed.
| Beam depth | Estimated maximum deflection | Allowable deflection (span / 360) | Result against that limit |
|---|---|---|---|
| 140 mm | 17.7 mm | 10.0 mm | Exceeds the chosen limit |
| 190 mm | 7.1 mm | 10.0 mm | Within the chosen limit |
| 240 mm | 3.5 mm | 10.0 mm | Within the chosen limit |
| 290 mm | 2.0 mm | 10.0 mm | Within the chosen limit |
| 340 mm | 1.2 mm | 10.0 mm | Within the chosen limit |
Questions
Can I use this instead of a span table?
No. This checks deflection only, for one specific loading case (a simply-supported beam under a uniform load). Real span tables also check bending strength, shear, load sharing between multiple joists, load duration factors and safety margins set by the relevant building code. Use span tables, or an engineer, for anything structural.
What deflection limit should I use?
Span/360 is a common default for floors that carry brittle finishes such as tiles, since more sag than that risks cracking. Looser limits like span/240 are sometimes used for less sensitive applications such as garden decking, but the appropriate limit depends on what the beam supports and the applicable building code.
Why does the elastic modulus matter so much?
Deflection is inversely proportional to E, so a stiffer species or higher grade directly reduces sag for the same span, load and section size. The elastic modulus figures here are rough bands; an actual graded value from the timber supplier will be more accurate for a real project.
What if my beam has a point load instead of a uniform load?
This calculator only covers a uniformly distributed load. For a beam under a single point load, see the beam-deflection.html calculator, which covers a cantilever or simply-supported beam with a point load, and the bending-stress.html calculator for the stress that load produces.
For a beam carrying a point load rather than a uniform load, see the Beam Deflection calculator. To check the bending stress a load produces in a beam, use the Bending Stress calculator.