Deflection Limit Calculator
Estimate deflection limit for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Formula
delta = 5wL4/(384EI) (uniform) | delta = PL3/(48EI) (point at midspan)
Maximum midspan deflection for a simply supported beam with uniform load w is 5wL4/(384EI). For a concentrated load P at midspan, it is PL3/(48EI). The calculated deflection is compared against the allowable deflection limit, which is the span L divided by a code-specified ratio such as 360 for floor live load or 240 for roof live load.
Worked Examples
Example 1: Steel Floor Beam
Problem: A 20-foot simply supported steel beam (E = 29,000 ksi, I = 500 in4) carries a uniform live load of 2 kips/ft. Check against L/360.
Solution: L = 20 * 12 = 240 in\nw = 2/12 = 0.1667 kip/in\ndelta = 5 * 0.1667 * 240^4 / (384 * 29000 * 500)\ndelta = 0.4643 in\nAllowable = 240/360 = 0.667 in\n0.4643 < 0.667 = PASS
Result: Actual = 0.4643 in, Allowable = 0.667 in, PASS
Example 2: Roof Beam with Point Load
Problem: A 16-foot roof beam (E = 29,000 ksi, I = 200 in4) has a 10-kip point load at midspan. Check L/240.
Solution: L = 192 in\ndelta = 10 * 192^3 / (48 * 29000 * 200)\ndelta = 0.2546 in\nAllowable = 192/240 = 0.800 in\nPASS
Result: Actual = 0.2546 in, Allowable = 0.800 in, PASS
Frequently Asked Questions
What are standard deflection limits for beams?
The International Building Code (IBC) and AISC specify deflection limits as a fraction of the span length L. For floor beams supporting live load only, the limit is L/360. For roof beams with live load, the limit is L/240. For total load deflection (dead plus live), L/240 is typical. Members supporting plaster ceilings use L/360 for the live load portion to prevent cracking. These limits ensure serviceability by controlling visible sag, preventing damage to finishes, and maintaining occupant comfort.
How is beam deflection calculated for a uniform load?
For a simply supported beam with a uniformly distributed load, the maximum deflection at midspan is delta = 5wL4 / (384EI), where w is the load per unit length, L is the span, E is the elastic modulus, and I is the moment of inertia about the bending axis. For a point load P at midspan, the formula is delta = PL3 / (48EI). Both formulas assume linear elastic behavior and prismatic (constant cross-section) members. For other load patterns and support conditions, different coefficients apply.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Is Deflection Limit Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.