Engineering Tools
Beam Deflection Calculator
Pick a support configuration, load, material, and cross-section and get the maximum deflection, bending stress, and moment — using classic Euler–Bernoulli beam formulas with the full breakdown shown.
Beam inputs
Metric units: mm, N, GPa. Distributed loads are entered in N/mm (1 N/mm = 1 kN/m).
Reference
The formulas behind the numbers
Maximum deflection and moment for the four classic load cases, with stress from the flexure formula σ = M·c / I.
Equations
| Cantilever, end load | δ = PL³/3EI · M = PL |
| Cantilever, uniform | δ = wL⁴/8EI · M = wL²/2 |
| Simply supported, center load | δ = PL³/48EI · M = PL/4 |
| Simply supported, uniform | δ = 5wL⁴/384EI · M = wL²/8 |
| Section properties | Rectangle I = bh³/12 · round I = πd⁴/64 · tube I = π(OD⁴−ID⁴)/64. c is the distance from the neutral axis to the extreme fiber. |
| Bending stress | σ = M·c/I at the extreme fiber, at the location of maximum moment. |
Watch-outs
- Valid for slender beams and small deflections. Deep beams (L/h < ~10) add shear deflection this tool ignores.
- Real supports are rarely perfectly fixed or perfectly pinned — a “fixed” end with compliance deflects more than the cantilever formula predicts.
- Loads are static. Impact, vibration, and fatigue need their own analysis.
- Plastics creep: for sustained loads on ABS, PC, or nylon, use a creep (apparent) modulus, not the short-term E.
- Check stress as well as deflection — a beam that deflects acceptably can still yield.
Structure flexing more than it should?
Beam formulas get you to a first answer. Real products add tolerances, joints, plastics that creep, and loads nobody wrote down. If stiffness or strength is on your critical path, bring the design to a consultation.
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