Free Online Beam Calculator
Welcome to the Beam Calculator. A free, online tool to generate shear force diagrams, bending moment diagrams, deflection curves and slope curves for simply supported and cantilevered beams. Select a beam and enter dimensions, then scroll down to see results.
Displacement ()
Moment ()
Slope (degrees)
Shear ()
| Max Displacement | @ | ||
|---|---|---|---|
| Max Shear | @ | ||
| Max Moment | @ |
What This Beam Calculator Does
This free beam calculator analyzes a single-span beam for any of 17 standard load cases: nine for simply supported beams and eight for cantilevers, including uniform, partial, triangular and point loads and applied moments. For the case you pick it plots the deflection, slope, bending moment and shear along the beam, gives the maximum of each and where it occurs, and lists the values at regular points in a table. The shear at each end is the support reaction. The closed-form equations for the selected case are shown under the inputs, so you can check the numbers by hand.
It works for any material. You enter the modulus of elasticity, E, and the moment of inertia, I, in English (inches, kips, ksi) or metric (meters, kN, kPa) units.
How to Use It
- Pick a beam and load case from the pictures at the top.
- Choose English or metric units.
- Enter E and I for your beam. The table below lists typical E values. For I, use a steel shape table or the cross-section calculator.
- Enter the load and the dimensions shown in the picture, and a point of interest, x.
- Click Calculate and scroll down to the diagrams and the results table.
| Material | Typical E (ksi) | Typical E (GPa) |
|---|---|---|
| Structural steel | 29,000 | 200 |
| Aluminum | 10,000 | 69 |
| Concrete, 4,000 psi | 3,600 | 25 |
| Douglas fir-larch No. 2 lumber | 1,600 | 11 |
In metric units the calculator takes E in kPa, so 200 GPa is entered as 200,000,000.
Common Beam Formulas
The four cases engineers use most, for a span L, uniform load w or point load P, and stiffness EI:
| Beam and load | Reactions | Maximum moment | Maximum deflection |
|---|---|---|---|
| Simply supported, uniform load | wL/2 each end | wL²/8 at midspan | 5wL⁴/(384EI) at midspan |
| Simply supported, point load at midspan | P/2 each end | PL/4 at midspan | PL³/(48EI) at midspan |
| Cantilever, uniform load | wL at the support | wL²/2 at the support | wL⁴/(8EI) at the free end |
| Cantilever, point load at the free end | P at the support | PL at the support | PL³/(3EI) at the free end |
Beam Calculator or Beam Designer?
This calculator tells you how a beam you have already chosen behaves: its moments, shears and deflections. It doesn't pick a beam size or check the beam against a design code.
To size a steel or wood beam, use the WebStructural Beam Designer. It has AISC steel shapes and sawn and engineered lumber, multiple spans and cantilevers, load cases and LRFD or ASD load combinations, and checks bending, lateral-torsional buckling, shear and deflection, then tells you whether the beam passes. The steel beam design guide walks through those checks by hand.
Frequently Asked Questions
Is the beam calculator free?
Yes. It's free to use with no account or sign-up.
Can it analyze continuous or multi-span beams?
No. It covers single simply supported spans and cantilevers. The beam designer handles continuous beams, overhangs and combinations of loads.
Does it include the beam's own weight?
Not automatically. Add the self weight to the uniform load, for example 26 lb/ft for a W16X26 steel beam.
Can I draw a shear and moment diagram for my own loads?
For other combinations of loads, use the shear and moment diagram calculator.