Model preview
Click a support symbol in the diagram to cycle through support types.Enter span lengths and select Generate Beam.
Enter span lengths and select Generate Beam.
Enter span lengths and select Generate Beam.
Use this calculator to find reactions, shear force and bending moment diagrams, and deflections for statically determinate and indeterminate beams. Check homework and hand calculations, verify results from other software, or make a quick estimate before detailed design. Results update as you edit. This is not a substitute for code-based member design.
Quick start: choose a preset beam and adjust its spans and loads.
Enter span lengths in the Span(s) field, separated by spaces or commas. Use * or x for repeated spans: 3 4*5 3 creates a six-span beam with spans of 3, 5, 5, 5, 5 and 3 m. Press Generate Beam (▶ on mobile).
Supports start as pinned and roller. Click or tap a support node to cycle through pinned → roller → fixed → free. Use free supports to model cantilevers and overhangs.
The default is steel (E = 210,000 MPa) with I = 1,000,000 mm⁴. Change E and I in the stiffness controls.
Choose a hinge or load, then click the beam to place it. A hinge, point load or moment takes one click. A uniform distributed load takes two clicks—at its start and end. Loads can cross supports and span several spans.
Set exact hinge and load positions from the left end of each span, either relative (x/L = 0.2) or absolute (0.3 m), and edit magnitudes (defaults: 1 kN, 1 kN·m, 1 kN/m). Change span lengths in the spans controls.
Click anywhere on a diagram to see the shear, moment and deflection at that position.
The calculator handles both statically determinate and statically indeterminate beams with any number of spans, including beams with internal hinges (Gerber beams). Simple single-span cases have textbook formulas (see Quick check formulas below), and you can verify them here in seconds. Where the calculator saves the most time is where hand calculation is slow: continuous and indeterminate beams, and beams with hinges. All the types below are set up the same way, through span lengths and support node types.
| Beam type | How to model it | What to review |
|---|---|---|
| Simply supported | 1 span, pinned + roller supports (default) | Maximum span moment, midspan deflection under symmetric load |
| Cantilever | 1 span, one node fixed, the other free | Fixed-end moment and reaction, tip deflection |
| Fixed-fixed | 1 span, both nodes fixed | End moments, reduced deflection |
| Propped cantilever | 1 span, fixed + roller | Fixed-end moment, moment redistribution |
| Overhanging | End span with a free outer node | Negative moment over the support next to the overhang, overhang tip deflection |
| Continuous | 2 or more spans | Negative moments over interior supports, redistribution between spans |
| Beam with hinges (Gerber beam) | Continuous beam + hinges within spans | Zero moment at hinges, kink in the deflected shape at hinges |
You can apply any number of loads of three types and combine them on the same beam.
A concentrated force at a single point, such as a reaction from a supported beam or column, an equipment load, or a wheel load.
A concentrated moment at a point on the beam, applied in either direction. Use it to model, for example, eccentric bearing or moment transfer from a connected member.
Defined by its intensity and loaded length. It can cover part of a span, a full span, or extend across supports over several spans. Use it for floor, roof or wall loads, and for the beam's self-weight: q = γ·A.
Diagrams are generated automatically and update with every change to the beam or loads. Bending moment (M), shear force (V) and deflection are shown below the beam.
Values are labeled at supports and at key points. Key points away from supports are also marked with a circle. Zero values are marked with a vertical tick.
Click anywhere on any diagram or on the beam to fix a section and see M, V, deflection and the position along that span. The cursor snaps to key points and zero values for exact readings.
The M diagram is drawn on the tension side: positive (sagging) moments are plotted downward, negative (hogging) moments upward.
A point load causes a jump in the V diagram, and a concentrated moment causes a jump in the M diagram. Where V crosses zero, M reaches an extremum. The moment at a hinge is always zero.
Deflection depends on span lengths, support conditions, loads and flexural stiffness EI, the product of the material's modulus of elasticity and the section's moment of inertia.
Under a uniform load, doubling the span increases deflection 16 times, while doubling I halves it. Set the modulus of elasticity E and moment of inertia I in Stiffness.
| Material | E, MPa |
|---|---|
| Steel | 200,000–210,000 |
| Aluminum | 70,000 |
| Concrete | 25,000–35,000 (depends on grade) |
| Softwood timber (parallel to grain) | 9,000–12,000 |
The calculator gives elastic short-term deflection based on Euler–Bernoulli beam theory. Actual deflection is larger for reinforced concrete beams due to cracking and creep, and for timber beams due to creep, plus shear deformation in short, deep members.
Standard results for common cases. Use them to verify the calculator or to sanity-check your own hand calculations. L is span length, w is uniform load, P is point load.
| Case | Reactions | Max moment | Max deflection |
|---|---|---|---|
| Simply supported, uniform load | R = wL/2 | wL²/8 (midspan) | 5wL⁴/384EI (midspan) |
| Simply supported, central point load | R = P/2 | PL/4 (midspan) | PL³/48EI (midspan) |
| Cantilever, point load at tip | R = P | PL (fixed end) | PL³/3EI (tip) |
| Cantilever, uniform load | R = wL | wL²/2 (fixed end) | wL⁴/8EI (tip) |
| Fixed-fixed, uniform load | R = wL/2 | wL²/12 (supports), wL²/24 (midspan) | wL⁴/384EI (midspan) |
| Propped cantilever, uniform load | 5wL/8 (fixed), 3wL/8 (roller) | wL²/8 (fixed end), 9wL²/128 (span) | wL⁴/185EI (0.42L from roller) |
| Two equal spans, uniform load | 3wL/8 (ends), 5wL/4 (middle) | wL²/8 (middle support), 9wL²/128 (spans) | wL⁴/185EI (0.42L from end supports) |
Values are magnitudes; sign depends on the convention used.
Three-span continuous beam with a hinge. Three spans of 3 m, a hinge at the middle of the center span, and a point load P = 1 kN applied at the hinge. Default stiffness: E = 210,000 MPa, I = 1,000,000 mm⁴, so EI = 210 kN·m².
The beam is statically indeterminate to the first degree, but both the beam and the load are symmetric about the hinge. The load therefore splits equally: each half carries P/2 = 0.5 kN at the tip of an overhang of length a = 1.5 m. Each half becomes a single-span beam with an overhang (l = 3 m), and the deflection at the hinge equals the overhang tip deflection.
δ = (P/2)·a²·(l + a) / 3EI = 0.5 · 1.5² · 4.5 / (3 · 210) = 8.04 mm
The calculator uses the finite element method: the direct stiffness method with Euler–Bernoulli beam elements. It runs entirely in your browser, so results are instant and no data is sent anywhere.
drawing diagrams, checking hand calculations and homework, comparing beam layouts, and preliminary beam estimates.
final member sizing and code checks (strength, stability, long-term deflection).
Yes, it's completely free and no sign-up is required. All calculations run in your browser, and no data is sent anywhere.
Add a uniformly distributed load over the full length of the beam: q = γ·A, where γ is the material's unit weight (about 78.5 kN/m³ for steel) and A is the cross-sectional area. For example, a steel beam with A = 0.005 m² gives q ≈ 0.39 kN/m.
Not yet. Point loads and distributed loads act downward, and distributed loads are uniform only. Concentrated moments can be applied in either direction.
Yes. It works on phones and tablets, and you can edit the beam, loads and diagrams by touch.