Beam Deflection Calculator

Your details

Choose metric (Newtons, mm) or imperial (lbf, inches). All inputs and outputs use the chosen system.
Simply supported: pinned at both ends. Cantilever: fixed at one end, free at the other.
Select the loading configuration. The list is filtered by beam type.
Total length of the beam from support to support (simply supported) or from fixed end to free end (cantilever).
mm
Magnitude of the concentrated point load. Leave at 0 for distributed-load-only cases.
N
Distance from the left (or fixed) support to where the point load is applied. Only used for "load at any position" cases.
mm
Intensity of the distributed load per unit length. For triangular/varying loads, this is the maximum ordinate.
N/mm
Concentrated moment applied at the specified location. Only used for moment-load cases.
N·mm
Young's modulus of the beam material. Steel: 200,000 MPa / 29,000,000 psi. Concrete: 25,000-30,000 MPa. Timber: 9,000-12,000 MPa.
N/mm² (MPa)
Area moment of inertia of the cross-section about the bending axis. For a W200x52 steel section: ~52.9×10⁶ mm⁴. For a 100x200 rectangle: b*h³/12 = 100*200³/12 = 66.7×10⁶ mm⁴.
mm⁴
Maximum deflectionDeflection OK (>= L/360)
3.376

The largest vertical displacement, positive downward

Deflection unitmm
Span/deflection ratio (L/delta)889
Maximum bending moment7,500,000
Maximum shear force5,000
Maximum slope0.00338rad
Flexural rigidity (EI)1,666,000,000,000
Deflection checkPass: L/delta >= L/360 - meets typical floor beam serviceability limit
889 L/delta
Excessive<240Marginal240-360Adequate360+

Your simply-supported beam under a midspan point load deflects 3.376 mm (L/889).

  • Maximum deflection is 3.376 mm - that is 1/889 of the span.
  • The beam passes the L/360 serviceability check, which is the typical code limit for floor beams supporting plaster or brittle finishes.
  • Flexural rigidity EI = 1.666e+12 N·mm². To halve the deflection, double EI (for example, increase beam depth so that I doubles, or use a material with twice the modulus).

Next stepThe beam meets typical serviceability targets. Check the bending moment and shear force values against the section's capacity to confirm structural adequacy.

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