Beam Deflection Calculator

Estimate the deflection, bending moment and stress of simply supported and cantilever beams.

Beam and load	Simply supported, uniform load
Span	4 m
Load (point: kN; uniform: kN/m)	5
Material	Softwood (≈11 GPa)
Rectangular section width	45 mm
Section depth	220 mm

Beam and load

Span

Load (point: kN; uniform: kN/m)

Material

Rectangular section width

Section depth

Maximum deflection

37.95 mm

Span/deflection = L/105. Maximum bending moment 10 kN·m and bending stress 27.5 MPa. Second moment of area 3.993e+7 mm⁴.

Deflection: 37.95 mm
Bending moment: 10 kN·m
Bending stress: 27.5 MPa

Deflected shape along the span (mm)

Maximumat (2, -37.9452)Point at the chart, or Tab to it and use ← →

Maximum: (2, -37.95)

About the Beam Deflection Calculator

These are the standard Euler–Bernoulli beam formulas for a prismatic, linear-elastic beam. Stiffness depends on the material's modulus E and the section's second moment of area I = b h³ ÷ 12 for a rectangle, so doubling depth makes a beam 8× stiffer. Floors are commonly limited to span/360 under live load.

The formula

Simply supported UDL: δ = 5 w L⁴ ÷ (384 E I); point load at centre: δ = P L³ ÷ (48 E I)

Worked example

Example: Maximum deflection = 31.57 mm

Inputs: Beam and load: Simply supported, uniform load; Span: 4 m; Load (point: kN; uniform: kN/m): 6; Material: Softwood (≈11 GPa); Rectangular section width: 50 mm; Section depth: 240 mm.
Formula: Simply supported UDL: δ = 5 w L⁴ ÷ (384 E I); point load at centre: δ = P L³ ÷ (48 E I)
Result: Maximum deflection = 31.57 mm
Deflection: 31.57 mm
Bending moment: 12 kN·m
Bending stress: 25 MPa

Things to keep in mind

For learning and quick checks only; structural members must be designed by a qualified engineer to your building code.

Questions people ask

What deflection limit should I use?

Often L/360 for floors and L/240 for roofs, per local codes.

Does self-weight count?

Yes; include it in the uniform load.