📐 Beam Calculator

Reactions, shear force, bending moment and deflection of a simply supported beam or a cantilever with a uniform load and a point load – with diagrams. Everything is calculated in your browser.

Beam

Span L [m] Uniform load q [kN/m] Point load P [kN] Position of P, a [m] from the left support

Section and material (only for deflection)

Material E [GPa] Second moment of area I [cm⁴] …or rectangle b × h [cm]

8360 cm⁴ is an IPE 300 steel beam. For a rectangle, I = b·h³/12. Self-weight is not included – add it to q.

Results

How it is calculated

The beam is linear elastic and the loads are added together (superposition). The tool writes the shear force V(x) and bending moment M(x) along the beam from the equilibrium equations, and gets the deflection by integrating the curvature M / EI twice, with w = 0 at both supports of a simply supported beam, or w = 0 and zero rotation at the fixed end of a cantilever. Positive moment means tension at the bottom (sagging); a cantilever has negative (hogging) moments.

For the common cases the results match the textbook formulas:

Case	Max. moment	Max. deflection
Simply supported, uniform load q	q·L²/8	5·q·L⁴ / (384·EI)
Simply supported, P at mid-span	P·L/4	P·L³ / (48·EI)
Cantilever, uniform load q	q·L²/2	q·L⁴ / (8·EI)
Cantilever, P at the free end	P·L	P·L³ / (3·EI)

Typical deflection limits are around L/250 to L/300 for floors and L/150 for cantilevers – the exact values depend on the code and the use.

The theory behind it is in my note Structural Statics, and free programs for bigger models are in Structural Analysis resources.

For learning and quick checks only. No load factors, no stability or shear checks, no code verification. Real structures must be designed by a licensed engineer.