Beam Deflection Calculator
Find how much a beam sags under a point or uniform load, with the bending moment, stress and deflection ratio.
- Deflection ratio
- Max moment
- Bending stress
- Max shear
- Stiffness EI
- Limits
- Metric
Saved Beams
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| Beam | Case | Span | Deflection | L/Δ | Stress (PSI) | Remove |
|---|
How to Calculate Beam Deflection
Deflection depends on the load, the span, the stiffness of the material (E) and the stiffness of the shape (I). Span has the biggest effect: double the span of a uniformly loaded beam and it sags 16 times as much.
| Case | Max Deflection | Max Moment |
|---|---|---|
| Simple span, center point load | P L³ ÷ 48 E I | P L ÷ 4 |
| Simple span, uniform load | 5 w L⁴ ÷ 384 E I | w L² ÷ 8 |
| Cantilever, point load at the end | P L³ ÷ 3 E I | P L |
| Cantilever, uniform load | w L⁴ ÷ 8 E I | w L² ÷ 2 |
| Both ends fixed, uniform load | w L⁴ ÷ 384 E I | w L² ÷ 12 |
Use consistent units: here L is converted to inches and w to pounds per inch. Bending stress is M × c ÷ I.
Worked Example
Deflection Limits
Building codes limit deflection as a fraction of the span. The IRC (Table R301.7) allows L/360 for floors and ceilings with plaster or drywall under live load, L/240 for other members, and L/180 for cantilevered and some roof members. E values for lumber above are from the NDS Supplement for No. 2 grade.
Tips
This page checks stiffness and bending stress for one simple load case. It does not check shear, bearing, buckling, or combined loads, and it leaves out the beam's own weight unless you add it to the uniform load. Size structural members with span tables or an engineer.