Maximum deflection and L/360 code check for simply supported and cantilever beams.
Last reviewed: April 2026
A beam deflection calculator computes how much a structural beam bends under a given load based on its material, cross-section, length, and support conditions. Engineers use it to verify that deflection stays within acceptable limits for safety and building codes.
Beam deflection is how much a structural beam bends under load. Engineers use deflection calculations to ensure beams meet building code limits — typically L/360 for floor joists (the beam can't deflect more than 1/360th of its span) and L/240 for roof rafters. Exceeding these limits doesn't necessarily mean failure, but it causes cracked drywall, bouncy floors, and visible sag.
Deflection depends on four variables: the load (weight applied), span (distance between supports), moment of inertia (the beam's cross-section geometry — deeper beams deflect less), and modulus of elasticity (material stiffness — steel is ~20× stiffer than wood). Doubling the span increases deflection by 16× (it's a fourth-power relationship), which is why long spans require much deeper beams. For load analysis, see our Wind Load Calculator and Snow Load Calculator.
| Application | Live Load Limit | Total Load Limit | Example (20 ft span) |
|---|---|---|---|
| Floor (general) | L/360 | L/240 | 0.67 in / 1.0 in |
| Roof (no plaster) | L/240 | L/180 | 1.0 in / 1.33 in |
| Roof (with plaster) | L/360 | L/240 | 0.67 in / 1.0 in |
| Cantilever | L/180 | L/120 | 1.33 in / 2.0 in |
| Glass panels | L/175 | — | 1.37 in |
Beam deflection is the displacement of a structural beam from its original position when subjected to applied loads. Controlling deflection is critical in structural design — excessive deflection causes visible sagging, cracked finishes (plaster, drywall, tile), door and window misalignment, and in extreme cases structural failure. Building codes limit deflection to prevent these problems: the standard limit for floor beams is L/360 (span length divided by 360) for live loads and L/240 for total loads, meaning a 20-foot (240-inch) floor beam can deflect no more than 0.67 inches under live load. Roof beams allow slightly more deflection (L/240 for live load) since visible sagging is less critical. Understanding beam deflection formulas helps engineers and builders select appropriate member sizes, spacing, and materials. For related structural calculations, see our Retaining Wall Calculator and Snow Load Calculator.
| Loading Condition | Maximum Deflection Formula | Location of Max Deflection |
|---|---|---|
| Simply supported, center point load | δ = PL³/(48EI) | Center of span |
| Simply supported, uniform load | δ = 5wL⁴/(384EI) | Center of span |
| Cantilever, end point load | δ = PL³/(3EI) | Free end |
| Cantilever, uniform load | δ = wL⁴/(8EI) | Free end |
| Fixed-fixed, center point load | δ = PL³/(192EI) | Center of span |
| Fixed-fixed, uniform load | δ = wL⁴/(384EI) | Center of span |
Beam deflection depends on three primary factors: material stiffness (E, the modulus of elasticity), cross-section geometry (I, the moment of inertia), and span length (L). The modulus of elasticity represents how stiff a material is — steel has E = 29,000 ksi (200 GPa), making it approximately 14 times stiffer than wood (E = 1,200–2,000 ksi for common species). Concrete has E = 3,000–6,000 ksi depending on mix strength. A higher E means less deflection for the same load and geometry.
The moment of inertia (I) measures how efficiently a beam's cross-section resists bending. It depends on both the amount of material and how far that material is from the neutral axis (the center of the cross-section). This is why I-beams (W-shapes) are so efficient — they concentrate material in the flanges, far from the center, maximizing I while minimizing weight. A W12×26 steel beam (12 inches deep, 26 lbs per foot) has a moment of inertia of 204 in⁴, while a solid rectangular section of similar weight would have significantly less. Doubling the depth of a rectangular beam increases I by a factor of 8 (I = bh³/12), making depth the most effective way to reduce deflection. Span length has the most dramatic effect — deflection increases with L³ for point loads and L⁴ for distributed loads, meaning doubling the span increases deflection 8–16 times.
In residential wood-frame construction, beam deflection calculations guide lumber selection for floor joists, headers, ridges, and carrying beams. Common dimensional lumber (2×8, 2×10, 2×12) has standard section properties that determine maximum spans for given load conditions. A 2×10 Douglas Fir floor joist at 16 inches on center can span approximately 16 feet for 40 psf live load while meeting L/360 deflection limits. Engineered lumber products — laminated veneer lumber (LVL), glue-laminated beams (glulam), and I-joists — offer higher strength and stiffness per unit weight, enabling longer spans and shallower depths that increase usable headroom in basements and lower levels.
For headers over window and door openings, deflection limits are more stringent because the finish above (drywall, brick veneer) is brittle and cracks easily. Many builders specify headers one size larger than structurally required for strength to ensure deflection stays well within limits. Point loads from columns or concentrated roof loads create the highest deflection demand — a beam carrying a point load at midspan deflects significantly more than the same beam under a uniform load of equal total weight, because the load cannot spread along the length. When stacking loads (upper floor walls bearing on lower floor beams), the cumulative load must be tracked down to the foundation to ensure every member in the load path is adequately sized. Calculate material quantities for your project with our Concrete Calculator and Soil Calculator.
Steel beams are selected by checking both strength (bending stress) and serviceability (deflection). In many cases, deflection controls the design rather than strength — the beam has adequate strength to carry the load without failing, but it deflects more than the allowable limit. The AISC Steel Construction Manual provides section properties for all standard steel shapes, and beam selection tables organize this information by span and load capacity. For a simply supported steel beam with a uniform load, the required moment of inertia is I ≥ 5wL⁴/(384E × δ_allowed), where δ_allowed = L/360 for typical floor applications. Online beam calculators simplify this process, but understanding the underlying relationships helps engineers optimize designs and troubleshoot problems.
Composite steel-concrete construction, where a concrete slab is connected to the top flange of a steel beam with shear studs, significantly increases effective stiffness. The concrete slab acts as the compression flange (concrete is strong in compression), while the steel beam handles tension. This composite action can reduce deflection by 40–60% compared to the steel beam acting alone, often allowing smaller steel sections and reducing material costs. Pre-cambering — fabricating the beam with a slight upward curve — offsets dead load deflection so the beam appears flat under permanent loads, with only the live load deflection visible during use. For load calculations and structural planning, see our Stress Load Calculator.
See also: Deck Calculator · Post Hole Calculator · Gravel Calculator · Roof Pitch Calculator · Brick Calculator
→ L/360 is the most common deflection limit for floors. For a 12-foot span, L/360 = 0.4 inches maximum deflection under live load. Roof beams use L/240 or L/180. Plaster ceilings require stricter L/360 for total load to prevent cracking.
→ Doubling the span quadruples the deflection. Deflection scales with the cube or fourth power of span length (depending on load type). A beam that works at 10 feet may be grossly inadequate at 15 feet. Always recalculate for span changes.
→ Moment of inertia (I) is everything. A 2×10 has roughly twice the I of a 2×8, even though the depth difference is only 25%. Deeper beams are exponentially stiffer. When in doubt, go deeper rather than wider. See our Square Footage Calculator for area loads.
→ This calculator is for preliminary sizing only. Actual structural engineering requires checking shear, bending stress, bearing, lateral stability, and load combinations — not just deflection. Always have a licensed engineer review structural members for building permit applications.
See also: Concrete Calculator · Square Footage Calculator · Stair Calculator · Lumber Calculator