Woodworking & Construction Calculators

Fine woodworking & cabinetry

Shelf Sag Calculator (Deflection L/360)

Uniform load on a simply supported rectangular shelf: δ = 5WL³ / (384EI) with I = bh³/12, where W is the total load. Compare deflection to span/360.

Inputs

Units
in
in
in
lb

Results

Deflection
0.058in
Span / deflection
625

Higher is stiffer. 360 is a common furniture target.

Meets L/360?
Yes

Recommended gear

Calculation method

A simply supported beam with uniform load sags most at mid-span. Thickness dominates because it is cubed in the moment of inertia. MDF looks thick but its E is low, so it often fails L/360 sooner than plywood of the same size.

Exact formula

E is a generic psi for pine, oak, maple, plywood, MDF or particleboard. Load is total pounds (or kilograms) spread along the span.

Metric loads

Kilograms convert to pounds for the engine, then deflection comes back in millimetres.

Frequently asked questions

What is L/360?

Deflection no more than the span divided by 360. On a 36 in shelf that is 0.10 in (2.5 mm).

Are books a uniform load?

Close enough for this sketch. Point loads from a statue sag more locally.

Do brackets change the formula?

Yes. Fixed or bracketed ends sag less. This model is conservative (simple supports).

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