Cantilever Beam Deflection Calculator
Cantilever beam deflection calculator. Returns tip deflection and slope from a point load at the free end plus a uniform distributed load. Educational only.
Cantilever Beam Deflection Calculator
Please tick the acknowledgement above before calculating.
How to use the cantilever deflection calculator
Enter the material and section
Young's modulus E sets the material stiffness (steel ≈ 200 GPa). The moment of inertia I describes the cross-section — use the Moment of Inertia calculator if you don't have it.
Enter the length and loads
L is the cantilever span from the fixed support to the free end. Add a point load P at the free end and/or a uniform load w spread along the span; the calculator superposes them.
Acknowledge the disclaimer
These are educational estimates for a simple, prismatic, linear-elastic beam. Tick the acknowledgement to reveal the result.
Read deflection, slope and moment
You get the tip deflection (the headline number), the slope at the tip, and the maximum bending moment at the fixed end. Compare deflection against your serviceability limit (often L/250 to L/360).
Cantilever deflection — how a beam bends under load
Stiffness, geometry and load
A cantilever is a beam fixed rigidly at one end and free at the other — a balcony, a diving board, an aircraft wing, a road sign on a single post. Under load it bends downward, and the question engineers ask is: how far does the free end move, and is that acceptable? The answer comes from Euler-Bernoulli beam theory, which for the common load cases gives clean closed-form formulas. For a single point load P at the free end, the tip deflection is P·L³/(3EI); for a uniform load w spread along the whole span, it is w·L⁴/(8EI). The three quantities in the denominator tell the whole story: E, the material's Young's modulus, captures how stiff the material is (steel is roughly three times stiffer than aluminium and far stiffer than timber); I, the second moment of area, captures how the cross-section is shaped (deep sections resist bending dramatically better than shallow ones); and L, the length, dominates everything because it is raised to the third or fourth power. Double the length of a cantilever and a tip point load deflects eight times as much.
Because deflection scales with the cube or fourth power of length, cantilevers are unusually sensitive to span, and small changes in section depth pay off enormously: doubling the depth of a rectangle multiplies I — and therefore stiffness — by eight. This is why engineers reach for deep, efficient sections (I-beams, hollow tubes) and why the moment of inertia is the lever that controls deflection. The same formulas, superposed, handle combinations of loads, which is what this calculator does when you enter both a point load and a uniform load.
"Length dominates a cantilever: deflection grows with L³ or L⁴. Double the span and a tip load sags eight times further — which is why depth, captured by the moment of inertia, is the engineer's most powerful lever."
What the simple formula assumes
These elegant formulas come with assumptions that matter in practice. They model a prismatic beam (constant cross-section), a linear-elastic material that obeys Hooke's law and isn't loaded near yield, small deflections relative to the span, and a truly rigid fixed support — no rotation or settlement at the wall. Real structures can violate these: a flexible support, a tapered or built-up section, large deflections, shear-dominated short beams, dynamic or impact loads, and material non-linearity all change the answer. Deflection is usually a serviceability check (will it feel bouncy, crack finishes, or pond water?) governed by limits like span/250 or span/360, while strength is a separate check against the bending moment and stress. This tool computes the classical elastic deflection, slope, and the maximum moment at the fixed end as an educational estimate and a sanity check — not as a substitute for a full structural design. Any real cantilever supporting people or property must be designed and verified by a licensed engineer to the applicable code, with appropriate load factors and safety margins.
10 Facts About Cantilever Deflection
Point load at the tip: δ = P·L³ / (3EI).
Uniform load over the span: δ = w·L⁴ / (8EI).
Deflection grows with length cubed (or to the fourth).
Double the span → a tip load deflects 8× as much.
E = stiffness; steel ≈ 200 GPa, aluminium ≈ 69, timber ≈ 11.
I = the section; doubling depth multiplies it by 8.
The maximum bending moment is at the fixed end.
Deflection limits are often span/250 to span/360.
The formulas assume small, linear-elastic deflections.
They need a truly rigid support — no rotation at the wall.
Frequently asked questions
For a point load P at the free end, the tip deflection is P·L³/(3EI). For a uniformly distributed load w over the span, it is w·L⁴/(8EI). E is Young's modulus, I the moment of inertia, and L the cantilever length. If both loads act together, the deflections add (superposition), which is what this calculator does. The slope at the tip is P·L²/(2EI) for the point load and w·L³/(6EI) for the uniform load.
Because deflection scales with the length cubed (point load) or to the fourth power (uniform load). Doubling the span increases a tip-load deflection by a factor of eight and a uniform-load deflection by sixteen. This extreme sensitivity is why cantilevers are kept as short as practical and why even a small increase in span can turn an acceptable design into an unacceptably bouncy one.
The moment of inertia (second moment of area), I, describes how a cross-section's material is distributed about the bending axis — deeper sections have much larger I and resist deflection far better. For standard steel sections it's listed in section tables; for simple shapes you can compute it from the dimensions. Our Moment of Inertia calculator handles rectangles, circles, tubes, box and I-sections. Enter the value in cm⁴ here.
Deflection is a serviceability issue, and acceptable limits depend on the application and the governing code. Common limits for cantilevers fall around span/180 for total load down to span/360 where brittle finishes must be protected, but the exact figure is set by the code and the use case. Meeting a deflection limit doesn't guarantee adequate strength — the bending stress must be checked separately against the material's capacity with proper safety factors.
Deflection is how much the beam moves under load (a serviceability check — comfort, appearance, cracking), while strength is whether the beam can carry the load without failing (an ultimate check against bending stress and yielding). A beam can be strong enough yet too flexible, or stiff yet overstressed. Both must be satisfied. This calculator gives deflection and the maximum bending moment; converting the moment to a stress and comparing it to the material's allowable value is the separate strength check.
Yes — the formulas assume a perfectly fixed support that neither rotates nor settles. In reality, a connection that allows even a little rotation adds extra tip movement that the simple equation ignores, sometimes substantially. A flexible or poorly detailed fixed end is a common reason a real cantilever deflects more than calculated. Designing the connection to genuinely behave as fixed is part of the engineer's job.
Not directly. The closed-form formulas assume a prismatic beam with a constant cross-section and a single homogeneous material. Tapered beams, built-up or composite sections, and members where shear deformation is significant (short, deep beams) need more general methods — numerical integration, the moment-area method, or finite-element analysis. Use this tool for uniform sections as an estimate, and a proper analysis for anything else.
Enter Young's modulus in gigapascals (GPa), the moment of inertia in cm⁴, the length in metres, the point load in kilonewtons (kN), and the uniform load in kN per metre. The calculator handles the unit conversions internally and returns the deflection in millimetres, the slope in degrees, and the bending moment in kN·m. Keeping consistent units is essential — mixing them is the most common source of wrong answers.
No. This is an educational tool for understanding and preliminary checking. A cantilever that supports people or property — a balcony, canopy, or sign — must be designed and verified by a licensed structural engineer to the governing code, with proper load combinations, factors of safety, connection design, and consideration of effects this calculator ignores. Treat the output as a sanity check, never as a substitute for stamped engineering.
No. The values you enter are processed entirely in your browser. Nothing is sent to a server, stored, or shared, and no account is required. The calculation runs on your device only.
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