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Shelf Span Calculator

Enter the load, shelf dimensions and material to find the safe maximum span.

How it is calculated

The shelf is treated as a simply supported beam carrying the total load spread evenly along it. Its cross-section is a rectangle of depth b (mm) and thickness t (mm), so I = b × t³ ÷ 12 in mm⁴. The load W = kg × 9.80665 in newtons. Midspan sag is 5·W·L³ ÷ (384·E·I), and the tool sets this equal to the allowed sag L ÷ n, which gives L = √(384·E·I ÷ (5·W·n)). Here n is your deflection limit (200 means span/200) and E is a built-in stiffness in MPa for the chosen material (plywood 8,000; particleboard 3,000; MDF 3,700; pine 9,000; oak 11,000; glass 70,000; steel 200,000; aluminium 69,000). An unknown material falls back to plywood. This checks stiffness (sag) only, not strength or bracket capacity.

Worked example

A plywood shelf 250 mm deep and 18 mm thick carries 25 kg, with a sag limit of span/200. Inertia: 250 × 18³ ÷ 12 = 121,500 mm⁴. Load: 25 × 9.80665 = 245.2 N. Then L² = 384 × 8,000 × 121,500 ÷ (5 × 245.2 × 200), about 1,522,000 mm², so L is about 1,234 mm, or 1.234 m. The same shelf in particleboard (E = 3,000) comes out at only 756 mm, so supports need to be much closer together.

Try this example →

Common mistakes

  • Entering the weight per shelf bay as the weight of the whole cabinet; the load must be the weight resting on this one span.
  • Mixing units: depth and thickness are in millimetres and the load is in kilograms, so 1.8 (cm) in the thickness field would be read as 1.8 mm.
  • Choosing a loose deflection limit like 100 for a bookshelf; visible sag appears at stricter limits (larger n), and a bigger n gives a shorter span.
  • Treating the result as a strength check: the tool checks sag, not whether the board, screws or brackets can carry the load without breaking.
  • Ignoring that real boards vary in stiffness and that edge-supported or fixed shelves behave differently from the simply supported case.

About this calculator

An unsupported shelf behaves like a simply-supported beam under a uniform load, and its deflection (sag) at the center is given by δ = 5wL⁴ / (384EI), where w is the load per unit length, L is the span, E is the material's modulus of elasticity (stiffness), and I is the shelf's moment of inertia (a function of thickness and depth). Solving for the span that keeps δ under an acceptable limit gives the maximum safe shelf span before sag becomes visible.

Furniture and cabinet makers, along with DIYers building bookshelves or garage shelving, use this calculation to decide how far apart to space shelf supports or brackets for a given material and expected load, since shelves built from softer materials like particleboard sag over a far shorter span than solid hardwood or plywood of the same thickness.

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