How beam deflection is calculated
For a simply supported beam with a single load at the center, the maximum deflection is δ = F × L³ ÷ (48 × E × I), where F is the load, L the span, E the material's elastic modulus, and I the moment of inertia of the cross-section. A 1,000 lb load on a 120-inch steel beam (E = 29,000,000 psi, I = 50 in⁴) deflects about 0.025 inch. Sizing the timber itself is easier once you price it with the board foot calculator.
How to use this calculator
Enter the point load, the span, the elastic modulus of the material (steel ≈ 29,000,000 psi, aluminum ≈ 10,000,000 psi), and the moment of inertia of the beam's cross-section. Keep all units consistent (pounds and inches here). For joist and stud layouts at standard spacing, use the stud calculator.
For reference only
This covers the textbook center-load case and ignores the beam's own weight, distributed loads, and connection details. Real structural design must account for those and meet code. Use this for a quick estimate, and have a licensed engineer verify any load-bearing member.
Deflection also grows with the cube of the span, so doubling a beam's length increases sag eightfold at the same load. Lengthening a span is far more demanding than adding load to it. Decking spans are covered by the deck boards calculator.
Frequently asked questions
- How do I calculate beam deflection?
- For a center point load on a simply supported beam, deflection = F × L³ ÷ (48 × E × I), with consistent units.
- What is the elastic modulus of steel?
- About 29,000,000 psi. Aluminum is roughly 10,000,000 psi and wood far lower and variable.
- What is moment of inertia?
- A property of the cross-section's shape that resists bending. Deeper beams have a much larger I and deflect less.
- Is this calculator code-compliant for design?
- No. It's a quick estimate for one load case. Structural design must include all loads, the beam's weight and code requirements — consult an engineer.
- What deflection is acceptable?
- Common limits are span divided by 360 for floors under live load and span divided by 240 for roofs. A 120-inch span at L/360 allows about 0.33 inch, so a 0.025-inch result is well inside it.