Beam Deflection Calculator
Estimate beam deflection for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Reviewed by Abdullah, Technical Content Specialist
Formula
Uniform: 5wL^4/(384EI) | Point: PL^3/(48EI) | Cantilever: PL^3/(3EI)
For a simply supported beam with uniform load, max deflection is 5wL^4/(384EI) at midspan. For a center point load, it is PL^3/(48EI). For a cantilever with tip load, PL^3/(3EI). E is elastic modulus, I is moment of inertia, L is span, w is load per unit length, and P is point load.
Worked Examples
Example 1: Uniformly Loaded Floor Beam
Problem:A W12x26 beam (I = 204 in^4) spans 20 ft with 500 plf uniform load. Check deflection against L/360.
Solution:w = 500/12 = 41.67 lb/in, L = 240 in\nEI = 29,000,000 x 204 = 5.916 x 10^9\nDeflection = 5 x 41.67 x 240^4 / (384 x 5.916 x 10^9)\n= 0.296 in\nL/360 = 240/360 = 0.667 in\n0.296 < 0.667 = PASS
Result:0.296 in deflection, L/810 ratio, passes L/360
Example 2: Center Point Load on Cantilever
Problem:A W8x18 cantilever (I = 61.9 in^4) extends 6 ft with 2,000 lb point load at the tip.
Solution:P = 2,000 lbs, L = 72 in, I = 61.9 in^4\nDeflection = PL^3/(3EI)\n= 2000 x 72^3 / (3 x 29,000,000 x 61.9)\n= 0.139 in\nL/240 = 72/240 = 0.300 in, PASS
Result:0.139 in deflection, passes L/240
Frequently Asked Questions
What is beam deflection and why does it matter?
Beam deflection is the vertical displacement of a beam under load, measured at the point of maximum sag. While a beam may be strong enough to carry the load without breaking, excessive deflection can cause problems such as cracking of finishes, visible sagging, doors and windows that do not operate properly, and a feeling of unsafeness for occupants. Building codes limit deflection to L/240 for total load and L/360 for live load, where L is the span length.
What is the difference between L/240 and L/360 deflection limits?
L/240 is the deflection limit for total load (dead plus live) and applies to most general applications. L/360 is a stricter limit used for live load deflection only, particularly important when the beam supports brittle finishes like plaster or ceramic tile. Some applications require even stricter limits such as L/480 for beams supporting glass panels. The number represents the span divided by the maximum allowable deflection. For a 20-foot span, L/360 means maximum deflection of 0.67 inches.
How does moment of inertia affect beam deflection?
Moment of inertia (I) measures a cross-section resistance to bending and directly affects deflection. Deflection is inversely proportional to I, meaning doubling the moment of inertia halves the deflection. Deeper beams have much higher moments of inertia because I depends on the cube of the depth. A W12x26 beam (I = 204 in^4) deflects about half as much as a W10x22 (I = 118 in^4) under the same load and span. Selecting a deeper beam section is the most effective way to reduce deflection.
What causes beam deflection to increase most significantly?
Span length has the greatest effect on deflection because it appears raised to the third or fourth power in deflection formulas. Doubling the span increases deflection by 8 times for a point load (L^3) or 16 times for a uniform load (L^4). Reducing the span by even 10-20 percent through adding intermediate supports can dramatically reduce deflection. After span, the next most effective factors to control are moment of inertia (beam depth) and load magnitude.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy