Beam Deflection Calculator
Enter your span, load, modulus, and moment of inertia to estimate beam sag against the L/360 limit. This is an estimate, not a structural design.
What your result means
Deflection is how far the beam sags under a uniform load; the L/360 limit is the usual maximum for floor framing (roofs are often L/240). The check just compares the two. This is the textbook simply-supported formula and ignores load combinations and connection details, so treat it as a sanity check and have a licensed structural engineer confirm any real beam.
How to use this calculator
- Enter span in inches.
- Convert distributed load to lbs/inch.
- E value: 1,500,000 psi for Doug Fir-Larch #2.
- I value from lumber tables (2x8: 47.6 in^4; 2x10: 98.9 in^4).
- Compare deflection to max allowable (L/360 for typical floor).
- CONSULT ENGINEER for actual design.
The formula
For a simply-supported beam under a uniform load, the sag is 5 times the load per inch times the span to the fourth power, divided by 384 times the modulus times the moment of inertia. The L/360 limit is just the span divided by 360.
Worked example
Say you've got a 144 inch span carrying 4 lbs an inch, using Doug Fir (E = 1.5 million) and a 2x10 (I = 98.9). The sag works out to about 0.151 inches against an L/360 limit of 0.40 inches, so it passes, with room to spare.
Moment of inertia (I) for common lumber
| Lumber (single) | Moment of inertia I (in&sup4;) |
|---|---|
| 2x6 | 20.8 |
| 2x8 | 47.6 |
| 2x10 | 98.9 |
| 2x12 | 178.0 |
Double the I value for a doubled (two-ply) beam. E values: Doug Fir-Larch 1.5M, Southern Yellow Pine 1.6M, Hem-Fir 1.2M psi.
Tips & gotchas
- The formula is delta = 5wL^4 / (384EI), for a simple beam under a uniform load.
- E varies by species: Doug Fir 1.5 million, Southern Yellow Pine 1.6 million, Hem-Fir 1.2 million.
- Pull I values from the National Design Specification span tables.
- Max deflection is L/360 for floors, L/240 for roofs.
- This is a rough estimate. Real design uses load combinations.
Frequently asked questions
What is beam deflection?
How much a beam sags under load. Code limits it to keep floors from feeling bouncy.
What is L/360?
The maximum deflection equals the span divided by 360. It's the standard for typical floor framing.
How do I find the I value?
From the NDS span tables or the lumber manufacturer's specs. Common values are in the table above.
Is this calculator engineering-grade?
No. It's for estimates only. Always have a licensed structural engineer review the design.
What if my beam deflects too much?
Go with deeper lumber, double it up, or step up to an engineered LVL.
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Estimates only — see our full disclaimer.