Cantilever Beam Calculator — Deflection, Moment & Shear

A cantilever is a beam rigidly fixed at one end (the support or wall) and completely free at the other (the tip). Balconies, canopies, diving boards, aircraft wings, traffic-sign brackets and the overhanging edge of a slab are all cantilevers. Because there is only one support, the whole load has to be carried back to that fixed end as a vertical reaction AND a large bending (fixing) moment — which is exactly why cantilevers deflect and rotate far more than a simply supported beam of the same span, and why the connection to the wall is the critical detail.

A cantilever beam calculator finds, for a given length, section and load: the bending moment diagram (BMD) — always peaking at the fixed end, the shear force diagram (SFD), the tip deflection δ, the tip rotation θ, and the fixed-end reactions (force R and moment M). Those are the numbers you size the beam and design the fixing for.

Most free tools evaluate the closed-form textbook formula for one specific case (a single tip point load, or a single uniform load). This calculator is different: it runs a real finite-element solver — the same direct-stiffness method used by commercial structural software. The cantilever is meshed into 60 Euler-Bernoulli elements, the fixed end is imposed by direct elimination, and K·u = F is solved with Gaussian elimination. That means you can stack any number of point loads and uniform, trapezoidal or partial distributed loads at once — combinations no single formula covers — and still get exact linear-elastic results. Pick any of the 974+ real catalog profiles (W/IPE/HEA/HEB, channels, hollow sections) and the calculator computes the flexural stiffness EI from the actual cross-section, the bending stress σ = M/Sx, and the utilization against your yield strength.

1. Set the cantilever length L. The support is always a fixed end at x = 0 and the tip is free at x = L — that is what makes it a cantilever. The fixed symbol in the sketch uses the standard hatched-wall convention.
2. Pick a quick load case (point load at the tip, point load at mid-length, full uniform load, or a triangular 0 → w load) to start from a classic pattern, then fine-tune or add loads. Point loads take a magnitude and a position measured from the wall; distributed loads take start/end intensity (trapezoids) and start/end position (partial coverage). Positive is downward; enter a negative value for uplift (wind suction). There is no limit on the number of loads.
3. Choose the section. Select a catalog profile (grouped by standard) or switch to Manual EI and type the flexural stiffness directly for timber, aluminium or composite. Set the yield strength fy and the deflection limit — L/180 is the usual cantilever default (measured on the cantilever length L).
4. Read the results — they update instantly, no “calculate” button. The KPI strip shows the fixed-end moment, the fixed-end shear, the tip deflection δ, the tip rotation θ and the utilization. The sketch draws the solved reaction R and the fixing moment M as a couple at the wall; the diagrams annotate every maximum directly on the curve.
5. Compare codes. NBR 8800 and AISC 360 are checked side by side on every solve — click either to make that code govern the ranking. Compact W sections also get a plastic-moment (Mp = Zx·fy) screening.
6. Check the lightest profiles that pass table: the whole flexural catalog is screened against bending and tip-deflection for your loads and the five lightest are ranked. Click Use to adopt one.
7. Export or continue for free — PNG/SVG of the sketch and diagrams, a CSV with every V/M/δ point and the ranking, and a one-click PDF report (no watermark). Press Open in 3D editor to convert this exact cantilever into a full CalcSteel model for the complete NBR 8800 / AISC 360 verification, including lateral-torsional buckling.

Tip: the SI ⇄ imperial toggle converts every input and output (kN ↔ kip, m ↔ ft, mm ↔ in, MPa ↔ ksi); the math always runs in SI internally.

The solver does not evaluate these formulas — it solves the stiffness system numerically — but for the classic cases its output matches them to machine precision. For a prismatic cantilever of length L, stiffness EI (E = 200 GPa for steel), with the origin at the fixed end:

After the analysis, the stress and the checks are:

• Elastic bending stress: σ = Mmax / Sx (Sx = elastic section modulus about the strong axis).
• Bending check, both codes side by side: NBR 8800 style σ ≤ fy / γa1 with γa1 = 1.10, and AISC 360 LRFD style σ ≤ φb · fy with φb = 0.90 (fy in MPa). For fy = 250 MPa that is 227.3 MPa vs 225.0 MPa.
• Deflection check: δtip ≤ L / n with n selectable — L/180 is the customary cantilever limit (some codes use 2L/360 on twice the cantilever length, which is the same number), L/120 for roof edges, L/240–L/360 where deflection is architecturally sensitive.
• Plastic-moment screening (compact I sections): when the selected W shape meets the compact limits (flange b/2tf ≤ 0.38√(E/fy), web hw/tw ≤ 3.76√(E/fy)), the calculator also shows Mp = Zx·fy with the two capacities Mp/γa1 (NBR) and φb·Mp (AISC F2.1), valid for continuous lateral restraint (Lb ≤ Lp).

Section properties are computed from the nominal plate dimensions (fillets neglected — slightly conservative; e.g. an IPE 200 gives Ix = 1,846 cm⁴ vs the 1,943 cm⁴ handbook value that includes root fillets).

The single most important thing to understand about a cantilever is how quickly its tip deflection grows. Compare the tip point-load case, δ = PL³/3EI, with a simply supported beam under a central point load, δ = PL³/48EI: for the same span, load and section, a cantilever deflects 16× more. Under a uniform load the ratio is even larger — wL⁴/8EI versus 5wL⁴/384EI, a factor of 9.6×.

That is why:

• Deflection, not stress, usually governs a steel cantilever. You will often find the section is only 40–50% utilised in bending but 100% utilised on tip deflection. Always check δ.
• The cube of the length dominates. Doubling a cantilever's length increases its tip deflection eightfold under a tip load (L³) and sixteenfold under a uniform load (L⁴), for the same section. Small increases in reach are expensive.
• Tip rotation matters too. The free end rotates by θ, so anything cantilevering further (a handrail, a facade panel, a secondary beam framing into the tip) picks up that rotation — this calculator reports θ so you can check it, something formula tools omit.
• The fixing moment is huge. All of the load's moment about the wall is resisted at that one connection. The calculator draws the fixing moment M as a couple at the support precisely because sizing that connection (the base plate, the moment end-plate, the anchor bolts) is the make-or-break detail of any cantilever.

Stiffening a cantilever means adding EI (a deeper section moves δ down fast, since δ ∝ 1/EI) or, better, shortening the reach or back-propping the tip — turning it into a propped cantilever and slashing the deflection.

• Loads: positive input = downward (gravity). Enter negative values for uplift (wind suction on a canopy).
• Shear V: for downward loads the shear is constant or increasing toward the fixed end and peaks there; it is plotted above the axis.
• Bending moment M: a downward-loaded cantilever hogs — it puts the top fibre in tension. Following the Brazilian/European drafting convention of drawing the moment on the tension side, the BMD is plotted above the axis, peaking at the fixed end. The magnitude Mmax = PL (tip load) or wL²/2 (UDL) is annotated on the curve. If you use the US convention the curve is simply mirrored; the values are identical.
• Deflection δ: plotted as the beam actually moves — the tip drops, so the deflected shape curves downward, largest at the free end. Reported as a magnitude.
• Tip rotation θ: the slope of the deflected beam at the free end, in radians (and degrees), reported as a magnitude.
• Reactions: at the fixed end the calculator reports the vertical reaction R (positive upward, equal to the total downward load) and the fixing moment M (the couple the wall applies back on the beam), both drawn on the sketch.
• Positions x: always measured from the fixed end (x = 0 at the wall, x = L at the tip).

The engine is a direct-stiffness (matrix) finite-element solver for Euler-Bernoulli bending — the same code that powers CalcSteel's profile pages, not a lookup table:

• 60 beam elements, cubic Hermitian shape functions, 2 DOFs per node (deflection v and rotation θ);
• the fixed end constrains both v and θ at x = 0, imposed by direct elimination;
• distributed loads converted to consistent nodal forces (exact for uniform AND linearly varying loads, including partial coverage);
• K·u = F solved by Gaussian elimination with partial pivoting;
• V(x) and M(x) recovered by equilibrium using the same snapped load positions the FEM uses, so the reactions, the fixing moment and the diagrams are always mutually consistent.

Against the closed-form cantilever solutions the results agree to better than 0.001%. Verified 2026-07-12 (npx tsx): IPE 200, L = 2 m, tip P = 10 kN → δ engine 7.2244 mm vs theory PL³/3EI = 7.2244 mm; θ engine 0.005418 rad vs theory PL²/2EI = 0.005418 rad; M = 20.000 kN·m; fixing moment 20.000 kN·m. A uniform case (w = 8 kN/m, L = 3 m) reproduces δ = wL⁴/8EI and M = wL²/2 identically.

Assumptions: linear elastic material, small deflections, shear deformation neglected (fine for span/depth > 10), prismatic member (constant EI), loads in the plane of bending, lateral-torsional buckling prevented. Self-weight is one click away — the Include self-weight toggle adds the selected profile's kg/m as an extra uniform load (1 kg/m ≈ 0.00981 kN/m). Local buckling, web crippling at the support, LTB and the fixed-connection design are not covered here — run the full NBR 8800 / AISC 360 check in the 3D editor.