Guide · 4 examples
How to calculate beam deflection
Rule: match the support first — it moves the answer 4–16×. Then span, load, E, I. Deflection limits are span ratios (L/360), not fixed inches.
Example 1 — wooden bench, 400N, 1.5m, 300×40 pine
I = 300 × 40³ ÷ 12 = 1.6×10⁶ mm⁴. E = 9.65 GPa (SPF). δ = 400 × 1.5³ ÷ (48 × 9.65e9 × 1.6e-6) = 1.82 mm at center. L/360 = 4.2 mm — passes easily.Open this in the calculator →
Example 2 — steel beam, 20ft, 1000 plf, W12×26
I = 204 in⁴, E = 29,000 ksi. w = 1000 lb/ft, L = 20 ft. δ = 5wL⁴/384EI = 0.61 in. L/360 = 0.667 in — passes at 91%. Strength still needs M = wL²/8 = 50 kip·ft checked against the section.Open this in the calculator →
Example 3 — balcony cantilever, 2m, 3 kN/m
δ = wL⁴/8EI — the 8 in the denominator (vs 384 for fixed UDL) is why cantilevers feel bouncy. Check L/180 at the tip, and remember the wall moment wL²/2 needs a real fixed connection, not a toenail.
Example 4 — fixed vs simply supported, same beam
Same P, L, EI: fixed-fixed δ = PL³/192EI vs simply supported PL³/48EI — exactly one quarter. If your "fixed" connection is actually two bolts through a ledger, analyze it as simply supported: the honest (larger) number governs.
The 3 mistakes that sag ceilings
1) Modeling a ledger/joist-hanger end as fixed (under-reads up to 4×). 2) Mixing GPa with inches, or kips with millimetres — use one system per run. 3) Forgetting that deflection ≠ strength: a beam can hold the load and still crack the drywall.