computedeez
computedeez.com2026-10-08

Span and Sag Calculator

How much a shelf, bench top, joist or beam will sag under its load, whether that is within a limit you choose, whether it is strong enough, and the longest span or heaviest load that stays within it.

Sag
≈1/8"
L/263, at 18" along
Limit
1/16"
over it
Strength
44%
of the rating, fine
Longest span
27 11/32"
at this load, within the limit
The span
The wood
The load
The limit
Span
36", resting on both ends
Wood
3/4" plywood, 11 1/4" across, 3/4" through
Load
25 lb/ft; limit 1/16"

Wood under a load it carries for years sags about half again as much as it does at first. If the load is permanent, allow for that.

It sags 0.14" at the worst point, past the 0.06" limit. Shorten the span to 27", add a support, go thicker, or lighten the load to 11 lb/ft.

The span

sag drawn larger than life, and labeled with the real figure
Under its load
25 lb/ftsag ≈1/8", drawn ×24836"

Along the span

inches of sag at every point, against the limit
Sag
-0.16-0.12-0.09-0.05-0.010.020714222936inches along the spanincheslimit

The figures

WhatValue
Section11 1/4" × 3/4"across × through the load
Stiffness, EI332,813 lbf·in²from the panel capacity per foot of width
Largest moment338 lbf·inat midspan
Moment against capacity338 of 764 lbf·in44% of the rating
Longest span for the sag limit27 11/32"at this load
Longest span for strength≈54 5/32"at this load
Load at the sag limit11 lb/ftat this span
Load at the strength limit57 lb/ftat this span

How this is worked out

A piece of wood carrying a load between supports bends like any beam, and the amount is the standard beam formula for its case: how it is held, and whether the load is spread along it or sits at one point. What the formula needs is the span, the load, and the stiffness of the piece, which is the material's stiffness (its modulus of elasticity) times a number that depends only on the section's shape. For a rectangle that number is width × thickness³ / 12, which is why doubling the thickness makes a shelf eight times stiffer and doubling its depth does nothing. Sag grows with the fourth power of the span, which is why one more support helps far more than thicker stock.

The example on this page, a 0.75" plywood shelf 11.25" deep on a 36" span with 25 lb of books per foot, sags 0.14" in the middle: 0.06" is where the eye starts to see it, so this one shows. The same shelf stays within that limit out to 27".

Strength is checked separately, because a span can be stiff enough and still overstressed or, more often, the other way round. The largest bending moment is turned into a stress and set against what the material is rated for: the grading rules' design value for lumber from the yard, the panel makers' published capacities for plywood, and for clear wood by species a working stress derived from its breaking stress the way the grading rules do it.

How to use it

  1. Enter the clear span between supports, and how the ends are held.
  2. Pick what it is made of. Plywood and panels go by width; lumber by a nominal size or a measured width and thickness, laid flat like a shelf or on edge like a joist.
  3. Enter the load: pounds per foot spread along it, with the usual shelf loads a tap away, or pounds at one point and where.
  4. Choose the sag you will accept. For a shelf, what the eye notices is the useful limit; for a floor, the code's L/360.
  5. Read the sag, whether it is within the limit and the strength rating, and the two answers people usually want next: the longest span that stays within the limit at this load, and the load at which this span reaches it.

What it assumes

  • The standard beam formulas: a straight piece of one material with the same section all along, deflecting a small amount, with no shear deflection counted. Fine for shelves, furniture and understanding a span.
  • Clear-wood figures are averages for small, defect-free samples at 12% moisture. A working stress is derived from the breaking stress the way the grading rules do: the value 95% of pieces exceed, divided by 2.1. A board with a knot mid-span is weaker than that.
  • Graded lumber is No. 2, at the reference values for a normal ten-year load, dry, at room temperature, with the size and flat-use factors from the grading rules, and the repetitive-member factor when asked for. Wet-service, temperature and the other adjustments are not applied.
  • Plywood is sanded Group 1 with the face grain running along the span; particleboard and MDF are at the minimums their standards require.
  • This is not a substitute for a span table, the building code or an engineer where a structure carries people or a roof. It tells you what the wood will do; it does not tell you what is permitted.

Sources