Beam Deflection Calculator
Where the Load Sits Changes Everything About How Much a Beam Bends
The same total load produces wildly different deflection depending on how it's applied and how the beam is supported. A cantilever carrying a point load at its free end deflects roughly 16 times more than a simply supported beam of the same span carrying the same point load at midspan — not because the material is different, but because the boundary conditions change the governing equation entirely. This calculator applies the correct linear-elastic formula for four common beam and loading configurations.
The Formulas
Simply supported, uniform load: δ = (5 × w × L⁴) / (384 × E × I)
Cantilever, point load at free end: δ = (P × L³) / (3 × E × I)
Cantilever, uniform load: δ = (w × L⁴) / (8 × E × I)
P is a point load, w is a distributed load per unit length, L is the span, E is the modulus of elasticity, and I is the moment of inertia of the cross-section.
Same Load, Four Very Different Outcomes
| Configuration | Deflection |
|---|---|
| Simply supported, point load at center | 0.0124 in |
| Simply supported, uniform load | 0.0078 in |
| Cantilever, point load at free end | 0.1986 in |
| Cantilever, uniform load | 0.0745 in |
The cantilever point-load case deflects roughly 16 times more than the simply supported point-load case for identical span, material, section, and total load — a direct result of the cantilever having only one support instead of two.
Where This Gets Used
- Checking serviceability limits — building codes typically cap allowable deflection as a fraction of span (e.g. L/360 for floors under live load), and this gives the raw deflection figure to compare against that limit.
- Comparing section options — since deflection is inversely proportional to I, doubling the moment of inertia halves the deflection, which helps evaluate whether a deeper or wider section solves a deflection problem.
- Early-stage sizing — a quick check before running a full structural analysis, useful for cantilevered balconies, shelving brackets, or simply supported joists.
How to Use This Calculator
- Choose Unit system — Imperial (in, psi, lb) or Metric (m, Pa, N).
- Choose Load Type — Simply Supported with a point load or uniform load, or Cantilever with a point load or uniform load.
- Enter Load, Span/Length, Modulus of Elasticity E, and Moment of Inertia I, using one consistent unit system throughout.
- Select Calculate to see the deflection.
Related Calculations
Check the load feeding into this beam with the Structural Load Calculator, or size a concrete pour with the Concrete Mix Calculator.