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Beam Analysis Calculator

Free beam calculator: reactions, shear force & bending moment diagrams, and deflection for simply supported, cantilever & overhanging beams under any loads.

Analyse a statically determinate beam: add point loads, distributed loads and applied moments, and get the support reactions, the shear-force and bending-moment diagrams, the maximum values with their locations, and the deflection. Everything runs in your browser — no upload.
Beam configuration
Deflection (optional) — needs E and I

Tip: get I from the Cross-Section Properties calculator.

Loads (kN, m)

Point load: magnitude + position. Distributed load: intensity + start/end. Moment: value + position. Downward and counter-clockwise are positive.

What does this beam calculator do?

This tool analyses statically determinate beams — simply supported, cantilever and overhanging — under any combination of point loads, uniformly distributed loads and applied moments. It solves the support reactions from statics, then builds the shear-force diagram (SFD) and bending-moment diagram (BMD) and reports the maximum shear and moment with the exact locations. If you supply the elastic modulus E and second moment of area I, it also integrates the curvature to give the deflection. The diagrams are drawn in a clean blueprint style so you can sanity-check a design in seconds.

How to use it

  1. Choose the beam type and enter the span length.
  2. For a cantilever pick the fixed end; for an overhanging beam set the two support positions.
  3. Add your loads — point loads, distributed loads (with start and end) and applied moments.
  4. Optionally enter E and I to also get the deflection, then press Analyze.

Sign conventions

  • Downward loads are positive; upward reactions are positive.
  • Sagging bending moment (tension on the bottom fibre) is positive; hogging is negative.
  • Applied moments are positive counter-clockwise.
  • Positions are measured from the left end of the beam.

Method

Reactions from equilibrium: ΣFy = 0, ΣM = 0

V(x) = dM/dx    M(x) = ∫ V dx

EI · v″(x) = M(x)

Frequently Asked Questions

Statically determinate beams: simply supported, cantilever, and overhanging beams with two supports. These cover the large majority of quick checks and coursework. Fixed-fixed, propped and continuous (indeterminate) beams need the stiffness method and are not yet supported.

After solving the reactions from statics, the shear and moment are evaluated in closed form at every section by summing the forces and moments to the left of the cut, with extra sample points at each load and support so the steps and peaks are exact.

By numerically integrating the curvature M(x)/EI twice and applying the displacement boundary conditions at the supports (or zero slope and deflection at a fixed end). Results match the classic formulas, e.g. 5wL⁴/384EI for a uniformly loaded simply supported beam.

Pick a length unit (m or ft) and a force unit (kN, N, kip or lbf). Distributed loads are force per length and moments are force × length in those units. Deflection is reported in mm (or inches for ft).

Yes. All calculations run locally in your browser with JavaScript. Nothing is uploaded, so the tool also works offline.
Beam Analysis Calculator — Free beam calculator: reactions, shear force & bending moment diagrams, and deflection for simply supported, cantilever
Beam Analysis Calculator
See also
Engineering CalculatorsENGINEERING CALCULATORS42
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