This free beam calculator finds support reactions and draws the shear-force and bending-moment diagrams for idealized two-dimensional beams, with optional elastic deflection. It runs in your browser with no signup.
Enter a beam length, place supports, add loads or applied moments, select your units, and review the calculated reactions and diagrams. The calculator is useful for checking statics work and exploring idealized two-dimensional beam behavior.
Set the span, then add supports. A pin restrains horizontal and vertical translation, a roller restrains vertical translation, and a fixed support restrains translation and rotation. These let you model common simply supported and cantilever configurations.
Add multiple load types at the locations that match your idealized model:
The solver updates the following results as you configure the model:
Use a pin and roller for a simply supported beam, or a fixed support at one end for a cantilever. The current tool also supports overhanging geometry when supports are positioned inside the beam span. Add point loads, uniform or linearly varying distributed loads, and applied moments; combine load types to represent an idealized static load case.
Support reactions enforce equilibrium at the beam boundaries. Moving across a point load creates a jump in the shear-force diagram. A distributed load changes the slope of the shear diagram. Bending moment is the accumulated effect of shear, so its extrema commonly occur where shear is zero. Check the displayed sign convention before comparing results with another textbook or program.
For a 10 m simply supported beam with a 10 kN downward point load at midspan, symmetry gives an upward reaction of 5 kN at each support. The shear is +5 kN to the left of the load and −5 kN to the right. The maximum bending-moment magnitude occurs at midspan and is 25 kN·m. Load this case by entering a 10 m beam, pin and roller supports at its ends, and a 10 kN downward point load at 5 m.
PolyCalc models idealized, two-dimensional, static beam problems. Use results only when the support conditions, loading, material behavior, and geometry reasonably match the model. It does not replace a project-specific structural design, code check, connection design, or an engineer's review. See the assumptions and limitations and validation records for details.
Shear force is found by summing the vertical forces and reactions to one side of a section. The resulting shear force diagram shows how internal shear changes along the beam, and our calculator automates those calculations for the entire span.
A bending moment diagram is a graphical view of how internal bending moment varies from one end of the beam to the other. Engineers use it to locate maximum moments and size members appropriately for strength and serviceability.
Yes. The calculator is free to use with no signup required, so you can model beam supports, add loads, and generate shear and moment diagrams directly in the browser.
Yes. Add a fixed support at one end and no support at the free end, then apply loads or moments. The cantilever beam calculator guide includes a preset and a worked load case.
Yes. Add each concentrated load at its position along the beam. The resulting reactions, shear-force diagram, and bending-moment diagram reflect the combined static load case.
Yes. Enter elastic modulus and second moment of area in the Deflection Diagram card to calculate the elastic deflection curve and maximum deflection for the current beam model.