Beam Deflection Calculator — Simply Supported & Cantilever
Calculate the maximum mid-span or tip deflection of a structural beam. Choose simply supported or cantilever, select your load type and material, enter the cross-section dimensions, and get δ_max in millimetres plus the deflection profile chart.
Beam configuration
kN
m
Material
mm
mm
Largest downward displacement under the applied load
- 1
Second moment of area I (cm⁴)
100 × 200³ ÷ 12 ÷ 10,000 = 6,666.67I = bh³/12 for a rectangular section; doubling the depth h reduces deflection by 8×. - 2
Flexural rigidity EI (kN·m²)
200 × 6,666.67 ÷ 100 = 13,333 - 3
Maximum deflection δ_max (mm)
5 × 3³ ÷ (48 × 13,333) × 1000 = 0.211
How does this calculator work?
Maximum deflection = PL³/(48EI) for a simply supported beam with central point load, where I = bh³/12. A steel beam (E = 200 GPa) 3 m long with a 100 mm × 200 mm section under a 5 kN load deflects about 1.7 mm. Check L/δ ≥ 250 for typical serviceability. These formulas assume linear-elastic behaviour; consult an engineer for structural design.
Formula
How this is calculated
Beam deflection depends on four things: the applied load (P in newtons or w in N/m), the span (L in metres), the material stiffness (Young's modulus E in pascals), and the cross-section's resistance to bending (second moment of area I in m⁴). The product EI is called "flexural rigidity" — larger EI means less deflection. For a rectangular section, I = bh³/12, so doubling the depth h reduces deflection by a factor of eight.
This calculator covers four standard cases derived from Euler–Bernoulli beam theory: (1) a simply supported span with a single central point load (the most common textbook case), (2) a simply supported span under a uniform distributed load (UDL, e.g. self-weight), (3) a cantilever fixed at one end with a point load at the free tip, and (4) a cantilever under a UDL. The deflection profile curve shows how the beam bends along its length.
The L/δ ratio is a serviceability check: structural codes typically require L/δ ≥ 250–500 for floors and L/δ ≥ 150 for rafters. These are linear-elastic formulas and assume small deflections, prismatic sections, and no lateral buckling — consult a structural engineer for safety-critical designs. Material E values used are approximate (steel 200 GPa, aluminum 70 GPa, timber 12 GPa, concrete 30 GPa).
Frequently asked questions
For a simply supported beam with a central point load P and span L: δ_max = PL³/(48EI). For a UDL of intensity w: δ_max = 5wL⁴/(384EI). For a cantilever with point load at the free end: δ_max = PL³/(3EI). All require EI, the flexural rigidity, and I = bh³/12 for rectangular sections.
Most structural codes require L/δ ≥ 250 for floors under live load, L/δ ≥ 350 for finishes sensitive to cracking, and L/δ ≥ 150 for roof members. A higher ratio (larger number) means less deflection relative to span.
The second moment of area I = bh³/12 grows with the cube of depth. Doubling h multiplies I by 8, which divides deflection by 8. This is why deepening a beam is far more effective than widening it when stiffness is the goal.
TG we-Calculate Editorial Team. (2026). Beam Deflection Calculator — Simply Supported & Cantilever [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/beam-deflection-calculator
TG we-Calculate Editorial Team. "Beam Deflection Calculator — Simply Supported & Cantilever." TG we-Calculate. 2026. https://we-calculate.com/calculator/beam-deflection-calculator.
TG we-Calculate Editorial Team, "Beam Deflection Calculator — Simply Supported & Cantilever," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/beam-deflection-calculator
@misc{wecalculate_beam_deflection_calculator, title = {Beam Deflection Calculator — Simply Supported & Cantilever}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/beam-deflection-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?