WoodTools

Shelf Sag Calculator

A sagging shelf is a shelf nobody trusts. Enter the span, the wood and the load, and get the deflection, the maximum safe span and the minimum thickness you need.

A wooden shelf with books bending slightly under load, with span, thickness and deflection callouts. δ span (L) h
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Workshop AI assistant

Describe the piece you want to build and get a complete plan: dimensions, cut list, materials, cost, steps, tools and time.

Workshop assistant

Describe the piece you want to build and get a complete plan: dimensions, cut list, materials, cost, steps, tools and time.

AI-generated results are indicative. Verify dimensions, loads and local codes before building.

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How it works

  1. 1

    Enter the shelf span (the clear distance between supports).

  2. 2

    Set the shelf depth and thickness, and choose the wood (each species has its own stiffness).

  3. 3

    Enter the total load in kg and whether it is spread out or concentrated.

  4. 4

    Calculate: the tool estimates the deflection and the deflection ratio.

  5. 5

    Read the recommended maximum span and minimum thickness for a standard L/240 limit.

Formula

Deflection δ = 5·W·L³ / (384·E·I) for a distributed load, or δ = W·L³ / (48·E·I) for a concentrated load. I = b·h³/12 (moment of inertia). E is the modulus of elasticity of the wood (N/mm²). Acceptable limits: L/180 (heavy), L/240 (standard), L/360 (brittle panels).

Practical tips

  • Books are heavy: a full bookshelf can easily exceed 50 kg per metre of shelf.

  • The thickness matters more than the width — doubling the thickness makes the shelf 8 times stiffer.

  • Solid oak and beech are stiffer than MDF of the same thickness.

  • Support long shelves in the middle to split the span and dramatically reduce sag.

  • Add a 5 mm apron or edge strip to turn a shelf into a stiffer channel.

Common mistakes

  • Using the external width of the carcase instead of the clear span between supports.

  • Ignoring the actual load — decoration weight is not book weight.

  • Assuming MDF is as stiff as solid wood at the same thickness.

  • Loading the centre of a long shelf and wondering why it dips.

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Disclaimer

These results are indicative only. Always verify against local building codes, standards and professional advice before building.

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Frequently asked questions

What does L/240 mean?
It means the deflection must stay below the span divided by 240. A 1200 mm shelf should bend less than 5 mm under the rated load.
Why is the stiffness proportional to thickness cubed?
The moment of inertia I = b·h³/12 grows with the cube of the thickness h, so doubling the thickness multiplies stiffness by 8.
Is this a structural calculation?
It is an indicative engineering estimate. For load-bearing or safety-critical structures, validate with a professional and local codes.
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