Beam Deflection Calculator
Estimate how much a simply supported beam sags under load, and check it against the L/360 limit.
Reviewed by the ToolNestr Editorial Team — July 2026
How the beam deflection calculator works
Deflection is how far a loaded beam sags at its worst point. For a beam resting on two supports with a load spread evenly along it, the maximum deflection at midspan is 5·w·L⁴ ÷ (384·E·I). Here w is the load per unit length, L is the span, E is the material's modulus of elasticity (its stiffness), and I is the moment of inertia of the cross-section. A single load at the center uses P·L³ ÷ (48·E·I) instead.
Two things dominate the result. Span enters to the fourth power for a uniform load, so doubling the length makes the beam sag sixteen times as much — length is the single biggest factor. The section's depth matters far more than its width, because the moment of inertia of a rectangle is b·d³ ÷ 12: depth is cubed. This is why joists are installed on edge, tall and thin, rather than laid flat.
The calculator compares the result to the common L/360 serviceability limit — the span divided by 360 — which keeps finishes from cracking and floors from feeling bouncy. Passing that check does not mean the beam is adequately sized: bending stress, shear, bearing, connections, and code load combinations all have to be checked separately. Treat this as an educational estimate for one simple load case, not a design.
Deflection limits and design methodology follow the AISC Steel Construction Manual and the NDS (National Design Specification for Wood Construction) serviceability provisions.
Describe the load
Uniform or center point load, in pounds, and the span.
Enter the section
Rectangular width and depth, plus the material.
Check the limit
Compare the deflection to L/360.
The formula explained
Moment of inertia
I = b·d³ ÷ 12. A 1.5 × 7.25 in section: 1.5 × 7.25³ ÷ 12 = 47.6 in⁴.
Uniform-load deflection
= 5wL⁴ ÷ (384 E I) with L in inches and w = total load ÷ span.
Serviceability check
Compare deflection to L ÷ 360; report the actual ratio as L/n.
Worked example
A 2×8 softwood joist (1.5 × 7.25 in), 12 ft span, 1,000 lb uniform load, E = 1.6M psi.
Real-world context
Floor joists are the most common use of this calculator. A 2×10 joist (actual 1.5 × 9.25 in) spanning 14 ft with an 800 lb uniform load has I = 1.5 × 9.25³ ÷ 12 = 98.9 in⁴. Deflection works out to 5 × (800/168) × 168⁴ ÷ (384 × 1,600,000 × 98.9) ≈ 0.312 in, comfortably under the L/360 limit of 0.467 in — roughly L/538 — which is why 2×10s at 14 ft are a common span table entry for residential floor framing.
Steel framing behaves very differently under the same math. A steel member with an 4 × 8 in rectangular section (a rough stand-in for a small wide-flange shape), spanning 20 ft with a 4,000 lb center point load, has I = 4 × 8³ ÷ 12 = 170.7 in⁴. Because steel's modulus of elasticity (E ≈ 29,000,000 psi) is about eighteen times that of softwood lumber, deflection comes out to only about 0.233 in against a 0.667 in limit — around L/1,031 — illustrating why steel beams can span much farther than wood joists of similar depth.
Engineered lumber sits between the two. An LVL beam 3.5 × 11.875 in, spanning 18 ft with a 2,000 lb uniform load and E ≈ 1,900,000 psi, has I = 3.5 × 11.875³ ÷ 12 = 488.4 in⁴, giving a deflection of about 0.283 in against a 0.600 in limit (L/764). LVL's higher, more consistent modulus of elasticity compared to sawn lumber is exactly why it is favored for longer garage door headers and multi-story floor beams.
Deflection limits also vary by application, which is worth noting when you interpret the calculator's pass/fail check. Floors with plaster or drywall ceilings below them commonly use L/360 for live load, but many designers tighten that to L/480 to reduce cracking risk, and roof members carrying only occasional snow load are sometimes allowed L/240. The calculator here uses L/360 as a general-purpose benchmark — always confirm the governing limit in your local building code before finalizing any real design.
Common misconceptions
"If the beam passes the L/360 deflection check, it's safe to build." Deflection is only one of several checks. A beam also has to pass bending stress, shear, and bearing checks, and its connections and load combinations must meet code. This calculator only evaluates one simple deflection load case — it does not replace a full structural design by a licensed engineer.
"Making a joist wider is as effective as making it deeper." Not even close. Because the moment of inertia is width × depth³ ÷ 12, depth is cubed while width is linear. Doubling the depth increases stiffness eightfold, while doubling the width only doubles it — which is exactly why joists are always installed standing on edge rather than laid flat.
Related calculators
Frequently asked questions
How is beam deflection calculated?
For a simply supported beam with a uniform load, maximum deflection = 5·w·L⁴ ÷ (384·E·I), where w is load per unit length, L is span, E is the material modulus, and I is the moment of inertia. A center point load uses P·L³ ÷ (48·E·I) instead.
What is the L/360 deflection limit?
Building codes commonly limit live-load deflection to the span divided by 360 — about 0.4 inch over a 12-foot span. Plastered ceilings use L/360, floors often L/480, and less critical members L/240. Staying under the limit prevents cracked finishes and a bouncy feel.
What is the moment of inertia?
The moment of inertia measures how a cross-section resists bending. For a solid rectangle it is width × depth³ ÷ 12, so depth matters far more than width — doubling the depth increases stiffness eightfold, while doubling the width only doubles it.
Is this calculator enough to size a real beam?
No. It estimates deflection for one simple load case and does not check bending stress, shear, bearing, connections, or code load combinations. Use it for learning and rough comparison only; a licensed engineer must size any load-bearing beam.
Sources & references
This tool uses standard formulas and reference values from:
- • American Concrete Institute — ACI 318, Building Code Requirements for Structural Concrete. concrete.org
- • ICC — International Residential Code (IRC), span, footing and framing tables. codes.iccsafe.org
- • APA – The Engineered Wood Association, allowable span and load guidance.
Estimates for planning only. Span, load and code values vary by jurisdiction — verify against your local adopted code and a licensed engineer before building.