Simply supported beam deflection calculator (uniform load)
Deflection, not strength, is what usually decides a beam size in a building. A section can be comfortably strong and still bounce enough to crack a plastered ceiling. This calculator uses the closed-form elastic solution for a simply supported beam under a uniform load, and reports the result against the two serviceability limits specified on most projects: span/360 for members supporting brittle finishes and span/250 for general cases.
Beam deflection calculator
- Mid-span deflection
- 11.34mm
- Deflection as span /
- L/529
- Span/360 limit
- 16.7 mm — PASS
- Span/250 limit
- 24 mm — PASS
- Maximum moment
- 54kNm
- End reaction / shear
- 36kN
Formula
δ = 5wL⁴ / (384EI), M = wL²/8, V = wL/2Elastic small-deflection theory for a single-span beam on simple supports carrying a uniformly distributed load. Use unfactored (serviceability) loads for deflection and factored loads for moment and shear checks.
Worked examples
| Input | Result |
|---|---|
| 12 kN/m over 6 m, 305x102 UB (I ≈ 8500 cm⁴) | 14.9 mm ≈ L/402 — passes L/360 |
| 20 kN/m over 8 m, I = 21,400 cm⁴ | 23.7 mm ≈ L/337 — fails L/360 |
| 6 kN/m over 4 m timber, E = 11 GPa, I = 5300 cm⁴ | 6.9 mm ≈ L/580 |
Questions
Which deflection limit should I use?
Span/360 where the beam supports plaster, tiling or glazing, and span/250 for general floors and roofs. Project specifications override both, and long-span members often carry an absolute cap as well.
Does this include the beam's self-weight?
Only if you add it to the uniform load. Add the section's mass per metre (kg/m x 0.00981 kN) to w.
Where do I find I for a steel section?
From the section tables — I is quoted in cm⁴ for the major axis, which is the unit this calculator takes. For timber and concrete, calculate bd³/12 for the effective section.
Is this good enough for design?
It is the correct closed-form check for this load case, but a design must be signed off by a qualified engineer against the governing code, including creep, long-term load factors and continuity.
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