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Vriksai Timber Intelligence

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.

Why this calculation matters

Deflection decides whether a shelf looks like it is failing, long before it actually is. Clients report sag as a defect at a fraction of the load the timber can carry.

IS 883 IndiaNDS 2018 USAEurocode 5 EU60 Wood SpeciesPDF Report
📐

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
Wood Species & MOE
MPa
Auto-filled from species. Override for custom grade.
Beam Dimensions & Load
mm
mm
mm
Applied Load (w)
N/mm
✓
Deflection Analysis Results
—
mm
Max Deflection δ
—
L/δ
Actual Ratio
—
mm
Allowable
—
×10⁶ mm⁴
Moment of Inertia
Step-by-Step Calculation
Engineering note Deflection is estimated from the inputs and assumed modulus; long-term creep and point loads are not modelled. Final structural design must be verified by a qualified engineer against your local code.
📐 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
About the Sag & Deflection Calculator
Any shelf or beam bends a little under load — the question is how much, and whether it will look or feel like sagging over time. Wood also creeps, so a shelf that's fine on day one can dip noticeably after months under constant weight. This calculator estimates deflection from the span, load, timber stiffness and section size, so you can size a shelf or beam to stay visibly flat, using the same beam-theory relationships engineers rely on. It settles the old workshop argument — how thick should a shelf be — by computing real deflection for your bookshelf span, load and species.
Where Is This Used?
Shelving DesignFurniture MakersBookcasesWorkbench BuildingStructural Checks
Sources & verification
  • Euler–Bernoulli beam theory: 5wL⁴/384EI, PL³/48EI, PL³/3EI
Formula checked against the sources above by an automated regression test (tests/test-calculators.js) that derives each expected value independently of this page. Last reviewed .
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.
How is sag different from the deflection limit I see in span tables?
They're two sides of the same thing. Sag is the actual droop in millimetres that this calculator gives you; the deflection limit (like L/360) is the rule of thumb that says how much droop is acceptable for a given span. A shelf can be structurally safe and still look like it's sagging — wood creeps over time under constant load, so a shelf that's fine on day one can dip noticeably after a year of holding books. That's why people aim well inside the limit for anything that stays loaded.
ResourcesView the formulasFormula Library
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Wood species data
Density, hardness and movement for 60 timbers
Browse all species 
How the calculation works
Deflection rises with the fourth power of span and falls with the cube of thickness. That is why doubling a shelf’s span makes it sag sixteen times as much, and why a mid support or a stiffening front lip beats simply using a thicker board.
Show the formula
Second moment I = b h^3 / 12. Uniformly distributed load: deflection = 5 w L^4 / (384 E I). Centre point load: deflection = W L^3 / (48 E I). The result is reported as a span ratio L/deflection and compared with the limit selected.
Elastic deflection at constant modulus, simply supported. Long-term creep under sustained load can roughly double the figure in service, and is not included.
References and what each one provides
  • EN 338CEN (European Committee for Standardization)Structural timber strength classes — characteristic bending strength, mean modulus of elasticity and density for C and D classes.
  • USDA Wood Handbook (FPL GTR-190)USDA Forest Products LaboratoryModulus of elasticity by species and grade.
Unverified values are marked as such rather than presented as sourced.
Limitations of this calculation
Estimates elastic deflection under a uniformly distributed load at a constant modulus. It does not account for long-term creep, point loads, shear deflection in short spans, or the stiffening effect of a fixed back or front lip.
Do not use this for Structural design approval, or any shelf or beam carrying people, machinery or stored liquids.
Figures are engineering estimates from the inputs and assumptions shown. Verify against the actual material and, where the result affects structure or safety, against a qualified professional.
Hem-FirDensity · Janka · movementHinoki CypressDensity · Janka · movementIndian RosewoodDensity · Janka · movement
Full listing in the strength properties table.
How to use this tool
  1. Enter your stock sizes below, then press Calculate.
  2. Pick your load type and deflection limit from the dropdown.
  3. Fill in modulus of elasticity, span length, width, depth. 
  4. Press Calculate. 
Worked example
With the tool's starting values — modulus of elasticity = 12000, span length = 3000, width = 100, depth = 200 — pressing Calculate gives: 6.592 mm (max deflection δ); L/455 L/δ (actual ratio); 8.33 mm (allowable). 
Common mistakes to avoid