Cat Shelf Sag Calculator: Span, Thickness, Wood and a Landing Cat

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Opens on the book's own cat and wall. Change any number to your own and press Calculate.

Start from fills the boxes below

Held

The board

Span between supports mm; for a floating shelf, how far it sticks out

Board width across the span mm; 1x12 = 285.75

Thickness mm; ¾ in = 19.05

Wood

Or its stiffness E MPa, optional

The load

Cat's weight kg

Landing check × the weight

Or a load N, optional

Enter the board and press Calculate.

The formula

I = width × thickness³ ÷ 12 (mm⁴): thickness counts three times
On two supports, load in the middle: sag = P × L³ ÷ (48 × E × I)
Held at one edge, load at the front: sag = P × L³ ÷ (3 × E × I); its limit is 2 × L ÷ 240
Limits: span ÷ 240 under a landing cat, span ÷ 600 for looks. Longest span inside ÷ 240: L = √(48 × E × I ÷ (240 × P))

The book's worked example, Chapter 6. A 1x12 step on brackets 406.4 mm apart, with the 353.16 N landing in the middle, sags 0.3529 mm, a fifth of the 1.6933 mm limit. On two brackets instead of three, the lookout would sag 2.8234 mm. As a plank across the 1,168.4 mm bridge gap it would sag 8.3868 mm, 1.72 times its 4.8683 mm limit: that is why the book's bridge hangs. The longest 1x12 plank that passes is 890.19 mm.

E values are clear-wood figures from the Forest Products Laboratory's Wood Handbook (MDF from its Table 12-1). Real boards have knots and vary; a shelf a cat sleeps on also creeps, roughly doubling its sag over time. Metric first, imperial beside it. Prices are illustrative US home-center prices from November 2026, shown without a currency sign; put in your own. Everything stays in your browser: no sign-up, nothing stored.