Beam Deflection Calculator
Calculate maximum beam deflection, check L/360 and L/240 limits, and determine bending stress for simply supported beams. See also our Beam Load Calculator, Floor Joist Calculator, and Lumber Calculator.
Beam Properties
How to Use the Beam Deflection Calculator
Enter the beam span length, select the load type (uniform distributed load in pounds per linear foot, or a point/concentrated load in pounds), choose the beam material, and specify the cross-section dimensions (width and height). The calculator computes maximum deflection at midspan, checks against standard L/360 (floor live load) and L/240 (total load) deflection limits per IBC, and calculates the maximum bending stress. Use this to verify that your beam selection meets code requirements before construction.
Formula
Uniform Load: Δmax = 5wL⁴ / (384EI)
Point Load at Center: Δmax = PL³ / (48EI)
Moment of Inertia (rectangular): I = bh³ / 12
Bending Stress: σ = Mc / I
L/360 Limit = Span (in) / 360
L/240 Limit = Span (in) / 240
Example Calculation
Beam: 4×10 Douglas Fir (3.5" × 9.25"), 12 ft span
Load: 200 PLF uniform
E = 1,700,000 psi, I = 3.5 × 9.25³ / 12 = 231.1 in⁴
L = 12 × 12 = 144 in, w = 200/12 = 16.67 lb/in
Δmax = 5 × 16.67 × 144⁴ / (384 × 1,700,000 × 231.1) = 0.237"
L/360 = 144/360 = 0.400" → PASS
L/240 = 144/240 = 0.600" → PASS
Reference Table — Modulus of Elasticity (E) Values
| Material | E (psi) | Allowable Fb (psi) | Deflection Limit |
|---|---|---|---|
| Douglas Fir #2 | 1,700,000 | 900 | L/360 |
| Southern Pine #2 | 1,800,000 | 1,000 | L/360 |
| Spruce-Pine-Fir #2 | 1,400,000 | 875 | L/360 |
| LVL (1.9E) | 1,900,000 | 2,600 | L/360 |
| Steel A36 | 29,000,000 | 22,000 | L/360 |
| Steel A992 | 29,000,000 | 33,000 | L/360 |
| Aluminum 6061-T6 | 10,000,000 | 19,000 | L/240 |
Frequently Asked Questions
What is the L/360 deflection limit?
L/360 means the maximum allowable deflection is the beam span divided by 360. For a 12-foot beam (144 inches), the limit is 0.4 inches. This standard applies to floor beams under live load per the International Building Code (IBC) to prevent noticeable bounce or cracking of finishes.
When should I use L/240 vs L/360?
L/360 applies to live load deflection for floors. L/240 applies to total load (dead + live) deflection. Roof beams without ceilings may use L/180. Beams supporting brittle finishes like plaster or tile should meet L/480 for live load.
What causes excessive beam deflection?
Excessive deflection results from undersized beams, spans that are too long, loads exceeding design capacity, or using materials with low stiffness (E value). Increasing beam depth is the most effective way to reduce deflection since moment of inertia increases with the cube of height.
How do I reduce beam deflection?
Increase beam depth (most effective), increase beam width, use a stiffer material (higher E value), reduce the span with intermediate supports, or reduce the applied load. Doubling the depth reduces deflection by 8x, while doubling width only reduces it by 2x.
Is deflection or bending stress more critical?
For wood beams, deflection often controls the design for longer spans, while bending stress controls for shorter, heavily loaded spans. For steel beams, deflection almost always controls. Always check both conditions to ensure the beam is adequate.
What is the moment of inertia?
Moment of inertia (I) measures a cross-section's resistance to bending. For a rectangular beam, I = bh³/12 where b is width and h is height. A larger I value means less deflection. This is why I-beams are efficient — they concentrate material far from the neutral axis.