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Sag & Deflection — Calculator

Calculate beam deflection under UDL or point loads for any wood species. Covers IS 883:2016, NDS 2018, Eurocode 5 and AS 1720.

Units & Configuration

Unit System

Load Type

Deflection Limit

Wood Species & MOE

Species (auto-sets MOE)

Modulus of Elasticity (E)

MPa

Auto-filled from species. Override for custom grade.

Beam Dimensions & Load

Span Length (L)

Width (b)

Depth (h)

Applied Load (w)

N/mm

✓

Deflection Analysis Results

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Max Deflection δ

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L/δ

Actual Ratio

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Allowable

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×10⁶ mm⁴

Moment of Inertia

Step-by-Step Calculation

📐 Beam Sag / Deflection Calculator

Calculates how much a wood beam deflects (sags) under load. Excess deflection causes finish cracking, visible sag, and code violations. Critical for floor joists, rafters, deck beams, shelves and timber framing.

Where Used?

Floor JoistsRoof RaftersDeck BeamsPergola BeamsShelf DesignStair Stringers

Formulas

Simply Supported UDL: δ = (5 × w × L⁴) / (384 × E × I)Simply Supported Point: δ = (P × L³) / (48 × E × I)Cantilever Point: δ = (P × L³) / (3 × E × I)Moment of Inertia: I = (b × h³) / 12

FAQ

Acceptable sag limit for floors?

IS 883 and US IBC: L/360 under live load. Eurocode 5: L/300. For a 3000mm span L/360 = 8.3mm max. Doubling beam depth reduces sag by 8× (I = bh³/12).

Best way to reduce sag?

Increase depth (most effective — doubles depth = 8× less sag). Add mid-span support. Use stiffer species. Reduce span. Increasing width alone is least efficient per kg of timber.

Sag & Deflection Calculator