Cantilever Beam Calculator
Find the fixed-end bending moment, reaction and tip deflection of a cantilever beam in seconds. Enter the length, load and section, and the result is checked live against the FERS finite-element solver — so you can see the closed-form answer and the FE answer agree.
Bending moment and reactions are free. Create a free account to unlock deflections and to save your model.
Formulas used
A cantilever is fixed (built in) at one end and free at the other. For the two most common load cases the maximum bending moment (at the fixed end), reaction and maximum deflection (at the free end) are:
| Load case | Max moment | Reaction | Max deflection |
|---|---|---|---|
| Point load P at the free end | M_max = P·L | R = P | δ_max = P·L³ / (3·E·I) |
| Uniformly distributed load w | M_max = w·L² / 2 | R = w·L | δ_max = w·L⁴ / (8·E·I) |
where L is the span, P a point load, w a distributed load, E Young's modulus and I the second moment of area. The calculator above runs the FERS finite-element solver on your inputs and shows the analytical and finite-element answers agreeing live.
Worked example
Worked example: a 2.5 m cantilever IPE 240 steel beam (I = 3.89×10⁻⁵ m⁴, E = 210 GPa) with a 5 kN point load at the free end.
- Fixed-end bending moment, P·L
- 12.5 kNm
- Reaction at the fixed end, P
- 5.0 kN
- Free-end deflection, P·L³/3EI
- 3.2 mm (≈ L/785)
Frequently asked questions
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